Everyday Math Grade 5 Answers Unit 2 Whole Number Place Value and Operations

Everyday Mathematics 5th Grade Answer Key Unit 2 Whole Number Place Value and Operations

Solving Place-Value Riddles
Solve the number riddles.
Question 1.
I have 5 digits. My 5 is worth 50,000. My 8 is worth 8,000. One of my 6s is worth 60. The other is worth 10 times as much. My other digit is a 0.
What number am I?
The number is 58,660
Explanation:
Here I have 5 digits number.
My 5 is worth 50,000 ; Ten thousand place.
My 8 is worth 8,000 ; Thousands place.
One of my 6s worth is 60. The number is written as 66; Tens place.
My other digit is 0. 0 is in ones place.
By adding the above numbers we got the 5 digit number. The number is 58,660.

Question 2.
I have 5 digits. My 9 is worth 9 ∗ 10,000. My 2 is worth 2 thousand. One of my 7s is worth 70. The other is worth 10 times as much. My other digit is a 6.
What number am I?
The number is 92,776
Explanation:
Here I have 5 digits number.
My 9 is worth 9 ∗ 10,000 = 90,000; Ten thousand place.
My 2 is worth 2,000; Thousands place.
One of my 7s worth is 70. The number is written as 77; Tens place.
My other digit is 6. 6 is in ones place.
By adding the above numbers we got the 5 digit number. The number is 92,776.

Question 3.
I have 4 digits. My 7 is worth 7 ∗ 1,000. My 2 is worth 200. One of my 4s is worth 40. The other is worth $$\frac{1}{10}$$ as much.
What number am I?
The number is 7,244
Explanation:
I have 4 digits number.
My 7 is worth 7 ∗ 1,000 = 7,000; Thousands place.
My 2 is worth 200. Hundreds place.
One of my 4s is worth 40. The number is written as 44; tens place.
By adding the above numbers we got the 4 digit number. The number is 7,244.

Question 4.
I have 6 digits. One of my 3s is worth 300,000. The other is worth $$\frac{1}{10}$$ as much. My 6 is worth 600. The rest of my digits are zeros.
What number am I?
The number is 330,600
Explanation:
I have 6 digits number.
My 3s is worth 300,000; The number is written as 330,000.
My 6 is worth 600; Hundreds place.
The rest of my digits are zeroes.
By adding the above numbers we got the 6 digit number. The number is 330,600.

Question 5.
I have 5 digits. My 4s are worth 4 [10,000s] and 4 ∗ 10. One of my 3s is worth 3,000. The other is worth $$\frac{1}{10}$$ as much. My other digit is a 2.
What number am I?
The number is 43,342
Explanation:
I have 5 digits number.
My 4s is worth 4[10,000s]=40,000; and 4 ∗ 10= 40.
My 3s is worth 3,000. The number is written as 3,300.
The other digit is 2. keep 2 in ones place.
By adding the above numbers we got the 5 digit number. The number is 43,342.

Question 6.
I am the largest 7-digit number you can write with the digits 3, 6, 9, 4, 0, 8, and 2.
What number am I?
The largest 7-digit number with the above digits is 9,864,320
Explanation:
We can write the largest seven digits number with the above digits. Write the above numbers in descending order. The largest seven digit number is 9,864,320.

Practice
Solve.
Question 7.
4 ∗ (3 + 2) = _______
4 ∗(3 + 2) = 20
4 ∗ (5) = 20
Explanation:
In the above expression we can observe two arithmetic operations. One is multiplication and other one is addition. First we have to perform addition operation and then multiplication operation.
An addition sentence is a mathematical expression that shows two or more values added together. First add three and two then we got five.
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Then multiply four and five then we got 20.

Question 8.
100 – [($$\frac{25}{5}$$) ∗ 10] = ________
100 – [(25/5) ∗ 10] = 50
100 – [(5) ∗ 10] = 50
100 -[50] = 50
Explanation:
In the above expression we can observe three arithmetic operations. One is subtraction, division, and multiplication. First we have to perform division operation and then we have to perform multiplication operation and then subtraction operation.
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. First divide 25/5 which is equal to the five.
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Second multiply 5 with 10 then we got 50.
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. Third Subtract the result 50 from 100 then we got 50.

Question 9.
{($$\frac{24}{6}$$) + ($$\frac{36}{6}$$)} + 2 = ________
{(24/6) + (36/6)} + 2 = 12
{(4) + (6)} + 2 = 12
{10} + 2 = 12
Explanation:
In the above expression we can observe two arithmetic operations. One is division, and other is addition. First we have to perform division operation and then addition operation.
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. First divide 24/6 then we got four; and also divide 36/6 which is equal to the six.
An addition sentence is a mathematical expression that shows two or more values added together. After completion of division operation perform addition operation. First add four and six then we got ten. Then add ten with two which results twelve.

Question 10.
(3 ∗ 5) – (2 ∗ 5) = _________
(3 ∗ 5) – (2 ∗ 5)= 5
(15) – (10) = 5
Explanation:
In the above expression we can observe two arithmetic operations. One is Multiplication, and other is Subtraction. First we have to perform multiplication operation and then subtraction operation.
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. First multiply these two numbers 3 and 5 then we got 15. Second multiply these two numbers 2 and 5 then we got 10.
Subtraction is an arithmetic operation that represents the operation of removing objects from a collection. The result of a subtraction is called a difference. Subtract 10 from 15 then we got 5.

Question 11.
(3 ∗ 7) + (2 ∗ 5) = _______
(3 ∗ 7) + (2 ∗ 5) =31
(21) + (10) = 31
Explanation:
In the above expression we can observe two arithmetic operations. One is Multiplication, and other is addition. First we have to perform multiplication operation and then addition operation.
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. First multiply these two numbers 3 and 7 then we got 21. Second multiply these two numbers 2 and 5 then we got 10.
An addition sentence is a mathematical expression that shows two or more values added together. ADD the two numbers 21 and 10 then we got 31.

Question 12.
($$\frac{56}{7}$$) ∗ ($$\frac{42}{7}$$) = _________
([56/7] ∗ ([42/7]) = 48
([8] ∗ ([6]) = 48
Explanation:
In the above expression we can observe two arithmetic operations. One is division, and other is multiplication. First we have to perform division operation and then we have to perform multiplication operation.
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic, which gives a fair result of sharing. The division is an operation inverse of multiplication. First divide 56/7 which is equal to the 8. Second divide 42/7 then we got 6.
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 8 and 6 then we got 48.

Evaluating Expressions with Exponential Notation
Write each number in standard notation.
Question 1.
106 _________
101 =10
102 = 100
103 = 1,000
104 = 10,000
105= 1,00,000
106 = 1,000,000
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000,000 is written as 106.

Question 2.
3 ∗ 106 __________
3 ∗ 106= 3,000,000
3 ∗ 1,000,000 = 3,000,000
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000,000 is written as 106. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 3 with 1,000,000 then we got 3,000,000.

Question 3.
103 __________
103= 1,000
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000 is written as 103.

Question 4.
24 ∗ 103 __________
24 ∗ 103= 24,000
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000 is written as 103. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 24 with 1,000 then we got 24,000.

Explain to someone at home how you solved Problems 1–4.
Write each number in standard notation. Then compare them by writing >, <, or = in the box.

Explanation:
In the above image we can observe some standard notations with numbers.
In the sample 5 we can observe 3 ∗ 102 and 3 ∗ 103. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 3 with 100 then we got 300. Multiply 2 with 1000 then we got 2,000. By comparing these two numbers 300 and 2,000; 2,000 is greater number than 300.
In the sample 6 we can observe 15 ∗ 107 and 2 ∗ 108. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 15 with 107 then we got 150,000,000. Multiply 2 with 108 then we got 200,000,000. By comparing these two numbers 150,000,000 and 200,000,000; 200,000,000 is greater number than 150,000,000.
In the sample 7 we can observe  27 ∗ 108 and 9 ∗ 107. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply 27 with 108 then we got 2,700,000,000. Multiply 9 with 107 then we got 90,000,000. By comparing these two numbers 2,700,000,000 and 90,000,000; 2,700,000,000 is greater number than 90,000,000.
Practice
Jackie wants to ship a box of hockey sticks to a sports camp. She is using the box shown below.

Question 8.
What is the volume of the box? About ________ cubic feet
Volume of the box is = 16 cubic feet
Explanation:
Volume of the shipping box can be calculated by dividing the shipping box in to 2 parts.
First part having dimensions = 1 feet x 2 feet x 6 feet.
And second part having dimensions = 1 feet x 2 feet x 2 feet.
Volume of the first part = 1 x 2 x 6 = 12 feet3.
Volume of the second part = 1 x 2 x 2 = 4 feet3.
Now total volume = 12 + 4 = 16 cubic feet.

Question 9.
How much will Jackie pay for shipping? $__________ Answer: Charges to ship the box of hockey is$26.
Explanation:
Charges to ship a box having volume = $20 up to 10 cubic feet. Since this box has the volume = 16 Cubic feet. So charges to 10 cubic feet will be$20.
Remaining volume of the box = 16 – 10 = 6 cubic feet.
Now charges for rest volume = $1 x 6 =$6.
Total charges= $20 +$6 = $26. Therefore charges to ship the box of hockey is$26.

Solving Problems Using Powers of 10

Use estimation to solve.
Renee is in charge of the school carnival for 380 students. She has 47 boxes of prizes. Each box has 22 prizes. She wants to make sure she has enough prizes for each student to win 2 prizes.
Question 1.
Does Renee have enough prizes?
Explain how you solved the problem.
Yes Renee have enough prizes for each student to win 2 prizes.
Explanation:
To estimate the number of prizes Renee has, I rounded 47 boxes of prizes to 50 and 22 prizes to 20. I multiplied 50 and 20 to get 1,000. If each student wins 2 prizes, that is 380 x 2. I can round 380 students to 400 students. Multiply 400 x 2 = 800. Here Renee needs only 800 prizes. So she has enough prizes for each student to win 2 prizes.

Question 2.
Does Renee have enough prizes for each student to win 3 prizes? Explain.
No, Renee doesn’t have enough prizes for each student to win 3 prizes.
Explanation:
If each student wins 3 prizes, Renee needs 380 x 3 prizes. If i rounded 380 to 400, then 400 x 3 = 1,200 prizes. Renee only has about 1,000 prizes. So she doesn’t have enough prizes for each student to win 3 prizes.

Practice
Write each number in standard notation.
Question 3.
42 ∗ 106 _________
42 ∗ 106
42 ∗ 1,000,000
42,000,000
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 1,000,000 is written as 103. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 42 ∗ 1,000,000 then we got 42,000,000.

Question 4.
8 ∗ 101 ___________
8 ∗ 101
8 ∗ 10
80
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 10 is written as 101. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 8 ∗ 10 then we got 80.

Write each number in exponential notation.
Question 5.
30,000 _________
30,000 = 3 ∗ 104
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 10,000 is written as 104. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 3 ∗ 10,000 then we got 30,000.

Question 6.
70,000,000 ________
70,000,000 = 7 ∗ 107
Explanation:
Standard notation is also known as scientific notation where a large number is written in the form of power of 10. The number 10,000,000 is written as 107. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiply these two numbers 7 ∗ 10,000,000 then we got 70,000,000.

Family Note Today your child began learning a multiplication strategy called U.S. traditional multiplication. This strategy may be familiar to you, as it is the multiplication strategy that many adults learned when they were in school. Your child will be learning to use U.S. traditional multiplication with larger and larger numbers over the next week or two.
U.S. traditional multiplication is often challenging for students to learn. Do not expect your child to use it easily right away. There will be plenty of opportunities for practice throughout the school year.
As your child uses U.S. traditional multiplication to solve the problems below, encourage him or her to check the answers by solving the problems in another way or using an estimate.

Example:

Multiply the ones: 8 ∗ 3 ones = 24. Write 4 below the line and 2 above the 10s column.
Then multiply the tens: 8 ∗ 7 tens = 56 tens.
Add the 2 tens from the first step: 56 tens + 2 tens = 58 tens, or 5 hundreds and 8 tens.
Write 8 below the line in the 10s column and 5 below the line in the 100s column.

Question 1.

Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 6 ∗ 6 ones = 36. Write 6 below the line and 3 above the 10s column.
Then multiply the tens 6 ∗ 5 tens = 30 tens.
Add the 3 tens from the first step 30 tens + 3 tens = 33 tens, or 3 hundreds and 3 tens.
Write 3 below the line in the 10s column and 3 below the line in the 100s column.

Question 2.

Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 4 ∗ 6 ones = 24. Write 4 below the line and 2 above the 10s column.
Then multiply the tens 4 ∗ 9 tens = 36 tens.
Add the 2 tens from the first step 36 tens + 2 tens = 38 tens, or 3 hundreds and 8 tens.
Write 8 below the line in the 10s column and 3 below the line in the 100s column.

Practice
Write each number in expanded form.
Question 3.
397 _____________
The expanded form of 397 = 300 + 90 + 7
Explanation:
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 397 = 300 + 90 + 7.

Question 4.
1,268 ____________
The expanded form of 1,268 = 1 ∗ 1000 + 2 ∗ 100 + 6 ∗ 10 + 8 ∗ 1
Explanation:
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 1,268 = 1 ∗ 1000 + 2 ∗ 100 + 6 ∗ 10 + 8 ∗ 1.

Question 5.
4,082 ____________
The expanded form of 4,082 = 4000 + 80 + 2
Explanation:
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 4,082 = 4000 + 80 + 2.

Question 6.
29,141 __________
The expanded form of 29,141 = (2 ∗104 ) + (9 ∗ 103) +(1 ∗ 102) + (4 ∗ 101) + (1 ∗ 100)
Explanation:
The expanded form of the numbers helps to determine the place value of each digit in the given number. It means that the expansion of numbers is based on the place value. The expanded form splits the number, and it represents the number in units, tens, hundreds and thousands form. The Expanded form of 29,141 = (2 ∗104 ) + (9 ∗ 103) +(1 ∗ 102) + (4 ∗ 101) + (1 ∗ 100).

Multiplication Top-It: Larger Numbers
Make a set of number cards by writing the numbers 0–9on slips of paper or index cards. Make four of each number card. You can also use the 2–9 cards and the aces from a deck of regular playing cards.
Explain the rules of Multiplication Top-It: Larger Numbers to someone at home.

Multiplication Top-It: Larger Numbers
1. Each player draws 4 cards. Use 3 of the cards to make a 3-digit number. Use the other card to make a 1-digit number.
2. Multiply the numbers. Compare your product to the other player’s product. The player with the larger product takes all the cards.
3. Keep playing until you run out of cards. The player with more cards wins the game.
To play by yourself: Keep the cards if your product is more than 1,000. Discard the cards if your product is less than 1,000. If you have more than 20 cards at the end of the game, you win.

Use your number cards to play the game with a partner or by yourself. Record two rounds of the game below. Show how you multiplied. Use U.S. traditional multiplication to multiply in at least one round.
Question 1.
Player 1: 586 ∗ 3 = 1,758

Explanation:
First player draws 4 cards. We have to use 3 of the cards to make a 3-digit number. Then use the other card to make a 1-digit number. In the above image we can observe a three digits number is 586 and one digit number is 3. Multiply three digit number with one digit number.
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number.
Multiply the ones 3 ∗ 6 ones = 18 ones. Write 8 below the line and 1 above the 10s column.
Then multiply the tens 3 ∗ 8 tens = 24 tens.
Add the 1 tens from the first step 24 tens + 1 tens = 25 tens, Write 5 below the line and 2 above the 100s column.
Then multiply the hundreds 3 ∗ 5 hundreds= 15 hundreds.
Add the 2 hundreds from the second step 15 hundreds + 2 hundreds = 17 hundreds, or 1 thousand and 7 hundreds.
Write 7 below the line in the 100s column and 1 below the line in the 1000s column.
By multiplying 586 with 3 results 1,758.
Question 2.
Player 2: 377 ∗ 4 = 1,508

Explanation:
1. Second player draws 4 cards. We have to use 3 of the cards to make a 3-digit number. Then use the other card to make a 1-digit number. In the above image we can observe a three digits number is 377 and one digit number is 4. Multiply three digit number with one digit number.
2. The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 4 ∗ 7 ones = 28. Write 8 below the line and 2 above the 10s column.
Then multiply the tens 4 ∗ 7 tens = 28 tens.
Add the 2 tens from the first step 28 tens + 2 tens = 30 tens, Write 0 below the line and 3 above the 100s column.
Then multiply the hundreds 4 ∗ 3 hundreds= 12 hundreds.
Add the 3 hundreds from the second step 12 hundreds + 3 hundreds = 15 hundreds, or 1 thousands and 5 hundreds.
Write 5 below the line in the 100s column and 1 below the line in the 1000s column.
By multiplying 377 with 4 results 1,508. Compare first player product to the second player product. The player with the larger product takes all the cards. First player product is larger than second player product. So first player takes all the cards from second player. First player won the game.

Practice
Write each power of 10 using exponential notation.
Question 3.
100 = __________
100 = 102
Explanation:
It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 100 can be written as power of 10. The exponential notation of 100 is 102.

Question 4.
10,000 = __________
10,000 = 104
Explanation:
It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 10,000 can be written as power of 10. The exponential notation of 10,000 is 104.

Question 5.
100,000,000 = __________
100,000,000 = 108
Explanation:
It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 100,000,000 can be written as power of 10. The exponential notation of 100,000,000 = 108.

Question 6.
1,000 = __________
1,000 = 103
Explanation:
It is the shortest way of expressing a large number. It is also known as the Scientific Notation. The number 1,000 can be written as power of 10. The exponential notation of 1,000 = 103.

Converting Units

• a 1-cup measuring cup or a coffee mug
• a large bowl
• a stopwatch or clock
• a 12-inch ruler or tape measure
• a food package with a weight given in pounds

Question 1.
a. Pour cups of water into the large bowl. (A coffee mug holds about 1 cup of water.) How many cups of water does it take to fill the bowl?
________ cups
It takes 3 cups of water to fill the bowl.
Explanation:
First take one large bowl and take some water. Take one coffee mug. Coffee mug holds about 1 cup of water. The large bowl is filled with 3 cups of water.

b. Convert your measurement to fluid ounces. _________ fluid ounces
1 cup = 8 fluid ounces.
3 cups = 24 fluid ounces.
Explanation:
In the above image we can observe 1 cup = 8 fluid ounces. The larger bowl takes 3 cups of water to fill the bowl. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 3 = 3 cups; which is equal to 24 fluid ounces.

Question 2.
a. Time or estimate how long it takes you to walk around your block in minutes.
_________ minutes
It takes 15 minutes to walk around my block.
Explanation:
To walk around my block it takes 15 minutes to complete one round.

b. Convert your measurement to seconds. _________ seconds
1 minute = 60 seconds
15 minutes = 900 seconds
Explanation:
It takes 15 minutes to walk around our block. we have to convert minutes into seconds. 1 minute = 60 seconds. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 15 = 15 minutes; which is equal to 900 seconds.

Question 3.
a. Measure the length of your bed to the nearest foot. _________ feet
The length of my bed is 3 feet.
Explanation:
Measuring the length of my bed is 3 feet long.

b. Convert your measurement to inches. _________ inches
1 foot = 12 inches.
3 foot = 36 inches.
Explanation:
Measuring the length of my bed is 3 feet long. Convert the measurement into inches. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 3 = 3 foot; which is equal to 36 inches.

Question 4.
a. Record the weight on the food package in pounds. _________ pounds
The weight on the food package is 5 pounds.
Explanation:
Measuring the weight on the food package is 5 pounds.

b. Convert the weight to ounces. _________ ounces
1 pound = 16 ounces.
5 pounds = 80 ounces.
Explanation:
The weight on the food package is 5 pounds. The process of adding a number to itself a certain number of times is called as multiplication. Multiply 1 x 5 = 5 pounds; which is equal to 80 ounces.

Practice
Question 5.
358 ∗ 8 = ?
Estimate: ___________

Estimate: 360 ∗ 8 = 2,880

Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 8 ∗ 8 ones = 64. Write 4 below the line and 6 above the 10s column.
Then multiply the tens 8 ∗ 5 tens = 40 tens.
Add the 6 tens from the first step 40 tens + 6 tens = 46 tens, Write 6 below the line and 4 above the 100s column.
Then multiply the hundreds 8 ∗ 3 hundreds= 24 hundreds.
Add the 4 hundreds from the second step 24 hundreds + 4 hundreds = 28 hundreds, or 2 thousands and 8 hundreds.
Write 8 below the line in the 100s column and 2 below the line in the 1000s column.

Question 6.
377 ∗ 4 = ?
Estimate: __________

Estimate: 380 ∗ 4  = 1520

Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 4 ∗ 7 ones = 28. Write 8 below the line and 2 above the 10s column.
Then multiply the tens 4 ∗ 7 tens = 28 tens.
Add the 2 tens from the first step 28 tens + 2 tens = 30 tens, Write 0 below the line and 3 above the 100s column.
Then multiply the hundreds 4 ∗ 3 hundreds= 12 hundreds.
Add the 3 hundreds from the second step 12 hundreds + 3 hundreds = 15 hundreds, or 1 thousands and 5 hundreds.
Write 5 below the line in the 100s column and 1 below the line in the 1000s column.

Estimating and Multiplying
Make an estimate for each multiplication problem. Write a number sentence to show how you estimated.
Then solve ONLY the problems that have answers that are more than 1,000. Use your estimates to help you decide which problems to solve.

Use U.S. traditional multiplication to solve at least one of the problems. Show your work.
Question 1.
23 ∗ 41 = ?

Estimate: 20 ∗ 40 = 800
Explanation:
In the above multiplication problem the estimated answer is not more than 1,000. Then no need to solve the problem.

Question 2.
72 ∗ 56 = ?

72 ∗ 56 = 4032
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 6 ∗ 2 ones = 12. Write 2 below the line and 1 above the 10s column.
Then multiply the tens 6 ∗ 7 tens = 42 tens.
Add the 1 ten from the first step 42 tens + 1 ten = 43 tens, or 4 hundreds and 3 tens.
Multiply the ones 5 ∗ 2 ones = 10 ones. Write 0 in tens place below the 3 and 1 above the 10s column.
Then multiply the tens 5 ∗ 7 = 35 tens.
ADD the 1 ten from second step 35 tens + 1 ten = 36 tens, or 3 thousands and 6 hundreds. Keep the 6 below the four in hundreds place and 3 in thousands place.
By Multiplying the above numbers we got 4032.
Question 3.
32 ∗ 15 = ?

Explanation:
Estimate: 30 ∗ 15 = 450
In the above multiplication problem the estimated answer is not more than 1,000. Then no need to solve the problem.

Question 4.
82 ∗ 11 = ?

Explanation:
Estimate: 80 ∗ 10 = 800
In the above multiplication problem the estimated answer is not more than 1,000. Then no need to solve the problem.

Question 5.
63 ∗ 39 = ?

63 ∗ 39 = 2457
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 9 ∗ 3 ones = 27. Write 7 below the line and 2 above the 10s column.
Then multiply the tens 9 ∗ 6 tens = 54 tens.
Add the 2 ten from the first step 54 tens + 2 tens = 56 tens, or 5 hundreds and 6 tens.
Multiply the ones 3 ∗ 3 ones = 9 ones. Write 9 in tens place below the 6.
Then multiply the tens 3 ∗ 6 = 18 tens or 1 thousand and 8 hundreds. Keep the 8 below the 5 in hundreds place and 1 in thousands place.
By Multiplying the above numbers we got 2457.

Question 6.
91 ∗ 46 = ?

91 ∗ 45 = 4186
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 6 ∗ 1 ones = 6. Write 6 below the line.
Then multiply the tens 6 ∗ 9 tens = 54 tens, or 5 hundreds and 4 tens.
Multiply the ones 4 ∗ 1 ones = 4 ones. Write 4 in tens place below the 4.
Then multiply the tens 4 ∗ 9 = 36 tens or 3 thousand and 6 hundreds. Keep the 6 below the 5 in hundreds place and 3 in thousands place.
By Multiplying the above numbers we got 4186.

Practice
Solve.
Question 7.
a. 7 ∗ 10,000 = ________
b. 7 ∗ 104 = ________
a. 7 ∗ 10,000 = 70,000
b. 7 ∗ 104 = 70,000
Explanation:
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations.
a.  By multiplying these two numbers we got 7 ∗ 10,000 = 70,000.
b. By multiplying these two numbers we got 7 ∗ 104 = 70,000.

Question 8.
a. 2 ∗ 400 = ________
b. 2 ∗ 4 ∗ 102 = ________
a. 2 ∗ 400 = 800
b. 2 ∗ 4 ∗ 102 = 8 ∗ 102 = 800
Explanation:
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations.
a. By multiplying these two numbers we got 2 ∗ 400 = 800.
b. By multiplying these three numbers we got 2 ∗ 4 ∗ 102 = 8 ∗ 102 = 800.

Question 9.
a. 6,000 ∗ 300 = ________
b. 6 ∗ 103 ∗ 3 ∗ 102 = ________
a. 6,000 ∗ 300 =1,800,000
b. 6 ∗ 103 ∗ 3 ∗ 102 = 18 ∗ 105 = 1,800,000
Explanation:
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations.
a. By multiplying these two numbers we got 6,000 ∗ 300 =1,800,000.
b. By multiplying these four numbers we got 6 ∗ 103 ∗ 3 ∗ 102 = 18 ∗ 105 = 1,800,000.

Choosing Multiplication Strategies

Choose one problem to solve using U.S. traditional multiplication. Solve the other problems using any strategy. Try to choose strategies that are accurate and efficient. Show your work.
Question 1.
198 ∗ 25 = ?

198 ∗ 25 = _________

198 ∗ 25 = 4950
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 5 ∗ 8 ones = 40 ones. Write 0 below the line and 4 above the 10s column.
Then multiply the tens 5 ∗ 9 tens = 45 tens. Add the 4 tens from the first step 45 tens + 4 tens = 49 tens, Write 9 below the line and 4 above the 100s column.
Multiply the hundreds 5 ∗ 1 hundred = 5 hundreds.
Add the 4 hundreds from the second step 5 hundreds + 4 hundreds = 9 hundreds.
2. Multiply the ones 2 ∗ 8 ones = 16 ones. Write 6 in tens place below the 9 and 1 above the 10s column.
Then multiply the tens 2 ∗ 9 = 18 tens. ADD the 1 ten from first step 18 tens + 1 ten = 19 tens. Keep the 9 below the 9 in hundreds place and 1 in 100s column.
Multiply the hundreds 2 ∗ 1hundred = 2 hundreds.
Add the 1 hundred from the second step 2 hundreds + 1 hundred = 3 hundreds. Keep the 3 in thousands place.
By Multiplying the above numbers we got 4950.

Question 2.
642 ∗ 207 = ?

642 ∗ 207 = _______

642 ∗ 207 = 132,894
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 7 ∗ 2 ones = 14 ones. Write 4 below the line and 1 above the 10s column.
Then multiply the tens 7 ∗ 4 tens = 28 tens. Add the 1 ten from the first step 28 tens + 1 ten = 29 tens, Write 9 below the line and   two above the 100s column.
Multiply the hundreds 7 ∗ 6 hundred = 42 hundreds. Add the 2 hundreds from the second step 42 hundreds + 2 hundreds = 44   hundreds, or 4 thousands and 4 hundreds.
2. Multiply the ones 0 ∗ 2 ones = 0 ones. Write 0 in tens place below the 9.
Then multiply the tens 0 ∗ 4 = 0 tens. Write 0 in hundreds place below the 4.
Multiply the hundreds 0 ∗ 6 hundreds = 0 hundreds. Write 0 in thousands place below the 4.
3. Multiply the ones 2 ∗ 2 ones = 4 ones. Write 4 in hundreds place below the 0.
Then multiply the tens 2 ∗ 4 = 8 tens. Write 8 in thousands place below the 0.
Multiply the hundreds 2 ∗ 6 hundreds = 12 hundreds, or 1 lakh and 2 ten thousands.
By Multiplying the above numbers we got 132,894.

Question 3.
420 ∗ 41 = ?

420 ∗ 41 = _________

420 ∗ 41 = 17,220.
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 1 ∗ 0 ones = 0 ones. Write 0 below the line.
Then multiply the tens 1 ∗ 2 tens = 2 tens. Write 2 below the line
Multiply the hundreds 1 ∗ 4 hundred = 4 hundreds. Write the 4 below the line.
2. Multiply the ones 4 ∗ 0 ones = 0 ones. Write 0 in tens place below the 2.
Then multiply the tens 4 ∗ 2 = 8 tens. Write 8 in hundreds place below the 4.
Multiply the hundreds 4 ∗ 4 hundred = 16 hundreds. 1 ten thousand and 6 thousands.
By Multiplying the above numbers we got 17,220.

Question 4.
The distance from Chicago, Illinois, to Boston , Massachusetts, by plane is 851 miles. A pilot flew from Chicago to Boston 37 times in one year. How many miles was that?
Estimate: ___________
Estimate : 850 ∗ 40 = 34,000
The distance for Chicago to Boston = 851 miles.
A pilot flew from Chicago to Boston 37 times in one year.
So, 851 ∗ 37 = 31,487 miles
Explanation:
The distance from Chicago, Illinois, to Boston , Massachusetts, by plane is 851 miles. A pilot flew from Chicago to Boston 37 times in one year. So we have to multiply 851 miles with 37 times in one year. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. So, 851 ∗ 37 = 31,487 miles.

Question 5.
It takes 246 floor tiles to cover the floor of a classroom. There are 31 same-size classrooms in the school. How many floor tiles does it take to cover all the classroom floors?
Estimate: ___________
Estimate : 250 ∗ 30 = 7,500
The floor of a classroom covers 246 floor tiles.
There are 31 same-size classrooms in the school.
So, 246 ∗ 31 = 7,626
Explanation:
The floor of a classroom covers 246 floor tiles. There are 31 same-size classrooms in the school. So we have to multiply 246 floor tiles with 31 same size classroom in the school. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. So, 246 ∗ 31 = 7,626.
Question 6.
Explain to someone at home which strategy you used to solve each problem and why.
Here I used U.S traditional multiplication Strategy to solve the problems.

Practice
Solve.
Question 7.
a. 5 ∗ 300,000 = ________
b. 5 ∗ 3 ∗ 105 =____________
a. 5 ∗ 300,000 = 1,500,000
b. 5 ∗ 3 ∗ 105 = 15 ∗ 105 = 1,500,000
Explanation:
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations.
a. By multiplying these two numbers we got 5 ∗ 300,000 = 1,500,000.
b. By multiplying these three numbers we got 5 ∗ 3 ∗ 105 = 15 ∗ 105 = 1,500,000.

Question 8.
a. 40 ∗ 6,000 = _________
b. 4 ∗ 10 ∗ 6 ∗ 103 = _________
a. 40 ∗ 6,000 = 240,000
b. 4 ∗ 10 ∗ 6 ∗ 103 = 24 ∗ 104 = 240,000
Explanation:
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations.
a. By multiplying these two numbers we got 40 ∗ 6,000 = 240,000.
b. By multiplying these four numbers we got 4 ∗ 10 ∗ 6 ∗ 103 = 24 ∗ 104 = 240,000.

Question 9.
a. 20,000 ∗ 700 = _________
b. 2 ∗104  ∗ 7 ∗ 102 = __________
a. 20,000 ∗ 700 = 14,000,000
b. 2 ∗ 104 ∗ 7 ∗ 102 = 14 ∗ 106 = 14,000,000
Explanation:
Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations.
a. By multiplying these two numbers we got 20,000 ∗ 700 = 14,000,000.
b. By multiplying these four numbers we got 2 ∗ 104 ∗ 7 ∗ 102 = 14 ∗ 106 = 14,000,000.

Using Multiples of 10 to Estimate
Question 1.
He swims about 200 meters per day. There are 30 days in June. So 200 ∗ 30 = 6,000 meters.
Explanation:
Martin swims about 200 meters per day. There are 30 days in June. So multiply 200 meters and 30 days. Multiplication of two numbers is the repeated addition of one number to the number of times equal to the other number. Multiplication is one of the basic arithmetic operations. So 200 ∗ 30 = 6,000 meters.

Question 2.
Estimate how many days it would take Martin to swim 60,000 meters. Show how you made your estimate.
Martin swim 60,000 meters. We have to calculate the days. If he swim 200 meters per day. Then 200 ∗ 300 = 60,000 meters.
Explanation:
Martin swim 60,000 meters. We have to calculate the days. If he swim 200 meters per day. Then 200 ∗ 300 = 60,000 meters. Martin takes about 300 days to swim 60,000 meters.

Practice
Make an estimate and solve.
Question 3.
107 ∗ 19 = ? 4
Estimate: ________

Estimate : 110 ∗ 20 = 2,200

107 ∗ 19 = 2,033
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 9 ∗ 7 ones = 63 ones. Write 3 below the line and 6 above the 10s column.
Then multiply the tens 9 ∗ 0 tens = 0 tens. Add the 6 tens from the first step 0 tens + 6 tens = 6 tens, Write 6 below the line.
Multiply the hundreds 9 ∗ 1 hundred = 9 hundreds.
2. Multiply the ones 1 ∗ 7 ones = 7 ones. Write 7 in tens place below the 6.
Then multiply the tens 1 ∗ 0 = 0 tens. Write the 0 in hundreds place below the 9.
Multiply the hundreds 1 ∗ 1 hundred = 1 hundred. Keep the 1 in thousands place.
By multiplying the above numbers we got 2,033.
Question 4.
86 ∗ 975 = ?
Estimate: ________

Estimate : 975 ∗ 85 = 82,875

975 ∗ 86 = 83,850
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 6 ∗ 5 ones = 30 ones. Write 0 below the line and 3 above the 10s column.
Then multiply the tens 6 ∗ 7 tens = 42 tens. Add the 3 tens from the first step 42 tens + 3 tens = 45 tens, Write 5 below the line and 4 above the 100s column.
Multiply the hundreds 6 ∗ 9 hundred = 54 hundreds.
Add the 4 hundreds from the second step 54 hundreds + 4 hundreds = 58 hundreds, or 5 thousand and 8 hundreds.
2. Multiply the ones 8 ∗ 5 ones = 40 ones. Write 0 in tens place below the 5 and 4 above the 10s column.
Then multiply the tens 8 ∗ 7 = 56 tens. ADD the 4 tens from first step 56 tens + 4 tens = 60 tens. Keep the 0 below the 8 in hundreds place and 6 in 100s column.
Multiply the hundreds 8 ∗ 9 hundreds = 72 hundreds.
Add the 6 hundreds from the second step 72 hundreds + 6 hundreds = 78 hundreds. Keep the 8 in thousands place below the 5 and 7 in ten thousands place.
By Multiplying the above numbers we got 83,850.

Mental Division Practice
Use multiplication and division facts to solve the following problems mentally. Remember: Write an equivalent name for the dividend by breaking it into smaller parts that are easier to divide.
Example: 72 divided by 4

• Write some multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
• Write an equivalent name by breaking 72 into smaller numbers that are multiples of 4.
Equivalent name for 72: 40 + 32
• Use the equivalent name to divide mentally.
Ask yourself: How many 4s are in 40? (10) How many 4s are in 32? (8)
Think: How many total 4s are in 72? (10 [4s] + 8 [4s] = 18 [4s], so 72 ÷ 4 = 18)

Question 1.
57 ÷ 3 → ?
Multiples of 3: __________
Equivalent name for 57: __________
57 ÷ 3 → __________
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Equivalent name for 57: 30 + 27
57 ÷ 3 → 19
Explanation:
1. First write some multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
2. Then write an equivalent name by breaking 57 into smaller numbers that are multiples of 3.
3. Equivalent name for 57: 30 + 27
4. Use the equivalent name to divide mentally. First we have to check how many 3s are in 30 and how many 3s are in 27. There are (10) 3s in 30 and (9) 3s in 27.
5. Then check how many total 3s are in 57. There are 10[3s] +9[3s] = 19[3s]. So 57 ÷ 3 = 19.

Question 2.
96 ÷ 8 → ?
Multiples of 8: __________
Equivalent name for 96: __________
96 ÷ 8 → __________
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
Equivalent name for 96: 80 + 16
96 ÷ 8 → 12
Explanation:
1. First write some multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80
2. Then write an equivalent name by breaking 96 into smaller numbers that are multiples of 8.
3. Equivalent name for 96: 80 + 16
4. Use the equivalent name to divide mentally. First we have to check how many 8s are in 80 and how many 8s are in 16. There are (10) 8s in 80 and (2) 8s in 16.
5. Then check how many total 8s are in 96. There are 10[8s] +2[8s] = 12[3s]. So 96 ÷ 8 = 12.

Practice
Make an estimate and solve.
Question 3.
68 ∗ 23
Estimate: __________

Estimate: 70 ∗ 20 = 1,400

68 ∗ 23 = 1,564
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 3 ∗ 8 ones = 24 ones. Write 4 below the line and 2 above the 10s column.
Then multiply the tens 3 ∗ 6 tens = 18 tens. Add the 2 tens from the first step 18 tens + 2 tens = 20 tens, or 2 hundreds and 0 tens.
2. Multiply the ones 2 ∗ 8 ones = 16 ones. Write 6 in tens place below the 0 and 1 above the 10s column.
Then multiply the tens 2 ∗ 6 = 12 tens. ADD the 1 ten from first step 12 tens + 1 ten = 13 tens. Keep the 3 below the 2 in hundreds place and 1 in thousands place.
By Multiplying the above numbers we got 68 ∗ 23 = 1,564.

Question 4.
278 ∗ 15
Estimate: __________

Estimate: 280 ∗ 15 = 4200

278 ∗ 15 = 4,170
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
1. Multiply the ones 5 ∗ 8 ones = 40 ones. Write 0 below the line and 4 above the 10s column.
Then multiply the tens 5 ∗ 7 tens = 35 tens. Add the 4 tens from the first step 35 tens + 4 tens = 39 tens, Write 9 below the line and 3 above the 100s column.
Multiply the hundreds 5 ∗ 2 hundreds = 10 hundreds.
Add the 3 hundreds from the second step 10 hundreds + 3 hundreds = 13 hundreds, or 1 thousand and 3 hundreds.
2. Multiply the ones1 ∗ 8 ones = 8 ones. Write 8 in tens place below the 9.
Then multiply the tens 1 ∗ 7 = 7 tens. Keep the 7 below the 3 in hundreds place.
Multiply the hundreds 1 ∗ 2 hundreds = 2 hundreds. Keep the 2 below the 1 in thousands place.
By Multiplying the above numbers we got 278 ∗ 15= 4,170.

Division
Read the example of how to use partial-quotients division with multiples of the divisor.

Think: How many 11s are in 237? You know 20 ∗ 11 is 220, so there are at least 20 [11s]. Write 20 as your first partial quotient and 220 below 237.
Subtract. 17 is left to divide.
Think: How many 11s are in 17? 1, so 1 is the next partial quotient. Write 11 below 17.
Subtract. 6 is left to divide. 6 is less than 11, so we are done dividing.
Add the partial quotients. 20 + 1 = 21

Question 1.
You could have started solving the example problem by taking away 110 from 237. If this was your first step, what would have been the first partial quotient, and why?
10 is the first partial quotient, because there are 10 [11s] in 110.
Explanation:
The division is a method of distributing a group of things into equal parts. It is one of the four basic operations of arithmetic. In the example problem, if we are taking away 110 from 237 then 10 is the first partial quotient, because there are 10 [11s] in 110.

In Problems 2 and 3, make an estimate. Then divide using partial-quotients division.
Question 2.
Estimate: _________

Estimate: 485/15 = 32

32 R5
Explanation:
1. First we have to check how many 15s are in 485. We know that 32 ∗ 15 = 480. So there are at least 32[15s]. Write 32 as our first quotient and write 480 below 485.
2. Perform subtraction operation. Subtract 480 from 485 then we got 5. 5 is left to divide. 5 is less than 15, so we are done dividing.
3. Partial quotient is 32 and Remainder is 5. It can be written as 32 R5.

Question 3.
Estimate: _________

Estimate: 410/ 17 = 24

24 R0
Explanation:
1. First we have to check how many 17s are in 408. We know that 24 ∗ 17 = 408. So there are at least 24[17s]. Write 24 as our first quotient and write 408 below 408.
2. Perform subtraction operation. Subtract 408 from 408 then we got 0. 0 is left to divide. 0 is less than 17, so we are done dividing.
3. Partial quotient is 24 and Remainder is 0. It can be written as 24 R0.

Practice
Question 4.
751 ∗ 3 = ?
Estimate: _________
Estimate: 750 ∗ 3 = 2,250
Answer: 751 ∗ 3 = 2,253

751 ∗ 3 = 2,253
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 3 ∗ 1 ones = 3 ones. Write 3 below the line.
Then multiply the tens 3 ∗ 5 tens = 15 tens. Write 5 below the line and 1 above the 100s column.
Then multiply the hundreds 3 ∗ 7 hundreds= 21 hundreds.
Add the 1 hundred from the second step 21 hundreds + 1 hundred = 22 hundreds, or 2 thousands and 2 hundreds.
Write 2 below the line in the 100s column and 2 below the line in the 1000s column.

Question 5.
86 ∗ 94 = ?
Estimate: _________
Estimate: 85 ∗ 95 = 8,075
Answer: 86 ∗ 94 = 8,084

86 ∗ 94 = 8,084
Explanation:
The process of adding a number to itself a certain number of times is called as multiplication.
Multiply the ones 4 ∗ 6 ones = 24 ones. Write 4 below the line and 2 above the 10s column.
Then multiply the tens 4 ∗ 8 tens = 32 tens.
Add the 2 ten from the first step 32 tens + 2 tens = 34 tens, or 3 hundreds and 4 tens.
Multiply the ones 9 ∗ 6 ones = 54 ones. Write 4 in tens place below the 4 and 5 above the 10s column.
Then multiply the tens 9 ∗ 8 = 72 tens.
Add the 5 tens from the first step  72 tens + 5 tens = 77 tens, or 7 thousand and 7 hundreds. Keep the 7 below the 3 in hundreds place and 7 in thousands place.
By Multiplying the above numbers we got 86 ∗ 94 = 8,084.

Division with Multiples
Here is how to use partial-quotients division with a list of multiples to solve $$\frac{2106}{19}$$.
First, list some multiples of 19:
100 ∗ 19 = 1,900
50 ∗ 19 = 950
20 ∗ 19 = 380
10 ∗ 19 = 190
5 ∗ 19 = 95

Think: Are there at least 100 [19s] in 2,106? Yes, 100 ∗ 19 = 1,900. Use 100 as your first partial quotient.
Subtract. 206 is left to divide.
Think: Are there at least 10 [19s] in 206?
Yes, 10 ∗ 19 = 190. Are there at least 20 [19s] in 206? No, 20 ∗ 19 = 380. So use 10 as the next partial quotient.
Subtract. 16 is left. 16 is less than 19, so you are done dividing. Add the partial quotients: 100 + 10 = 110

Complete the list of multiples below. Then use it to help you solve $$\frac{1954}{18}$$.
Question 1.
100 ∗ __________ = ___________
50 ∗ __________ = __________
20 ∗ __________ = __________
10 ∗ __________ = __________
5 ∗ __________ = __________
2 ∗ __________ = __________
100 ∗ 18 = 1,800
50 ∗ 18 = 900
20 ∗ 18 = 360
10 ∗ 18 = 180
5 ∗ 18 = 90
2 ∗ 18 = 36
Explanation:
A multiple of a number is a number that is the product of a given number and some other natural number. Multiples can be observed in a multiplication table. Multiples of 18 are 100 ∗ 18 = 1,800, 50 ∗ 18 = 900, 20 ∗ 18 = 360, 10 ∗ 18 = 180,5 ∗ 18 = 90,
2 ∗ 18 = 36

Question 2.
$$\frac{1954}{18}$$ → ?
Estimate: ___________

Estimate: 1800/18 = 100

108 R10
Explanation:
1. First we have to think about there are at least 100 [18s] in 1,954. Yes, 100 ∗ 18 = 1,800. Then use 100 as your first partial quotient.
2. Perform subtraction operation. Subtract 1,800 from 1,954 then we got 154. Here 154 is left to divide.
3. Next we have to think are there at least 10 [18s] in 154. No ,10 ∗ 18 = 180, which is larger than 154.
4. We have to think about there are at least 5 [18s] in 154. Yes, 5 ∗ 18 = 90. So use 5 as the next quotient.
5. Perform subtraction operation. Subtract 90 from 154 then we got 64. Here 64 is left to divide.
6. Next We have to think about there are at least 2 [18s] in 64. Yes, 2 ∗ 18 = 36. So use 2 as the next quotient.
7. Perform subtraction operation. Subtract 36 from 64 then we got 28. Here 28 is left to divide.
8. We have to think about there are at least 1 [18s] in 28. Yes, 1 ∗ 18 = 18. So use 1 as the next quotient.
9. Subtract 18 from 28 then we got 10. Here 10 is left to divide. 10 is less than 18, So we are done dividing.
10. Add the partial quotients: 100 + 5 + 2 + 1 = 108. Remainder is 10. It can be written as 108 R10.

Practice
Divide using partial-quotients division. Show your work
Question 3.
$$\frac{931}{12}$$ → ?
Estimate: ___________
The list of multiple are
100 ∗ 12 = 1200
50 ∗ 12 = 600
20 ∗ 12 = 240
10 ∗ 12 = 120
5 ∗ 12 = 60
2 ∗ 12 = 24
Estimate: 600/12 = 50

77 R7
Explanation:
1. First we have to think about there are at least 50 [12s] in 931. Yes, 50 ∗ 12 = 600. Then use 50 as your first partial quotient.
2. Perform subtraction operation. Subtract 600 from 931 then we got 331. Here 331 is left to divide.
3. Next we have to think about there are at least 20 [12s] in 331. Yes, 20 ∗ 12 = 240. So use 20 as the next quotient.
4. Perform subtraction operation. Subtract 240 from 331 then we got 91. Here 91 is left to divide.
5. Next We have to think about there are at least 5 [12s] in 91. Yes, 5 ∗ 12 = 60. So use 5 as the next quotient.
6. Perform subtraction operation. Subtract 60 from 91 then we got 31. Here 31 is left to divide.
7. We have to think about there are at least 2 [12s] in 31. Yes, 2 ∗ 12 = 24. So use 2 as the next quotient.
8. Subtract 24 from 31 then we got 7. Here 7 is left to divide. 7 is less than 12, So we are done dividing.
9. Add the partial quotients: 50 + 20 + 5 + 2 = 77. Remainder is 7. It can be written as 77 R7.

Question 4.
$$\frac{716}{21}$$ → ?
Estimate: ___________
100 ∗ 21 = 2100
50 ∗  21 = 1050
20 ∗  21 = 420
10 ∗  21 = 210
5 ∗  21 = 105
2 ∗  21 = 42
Estimate: 420/21 = 20

34 R2
Explanation:
1. First we have to think about there are at least 20 [21s] in 716. Yes, 20 ∗ 21 = 420. Then use 20 as your first partial quotient.
2. Perform subtraction operation. Subtract 420 from 716 then we got 296. Here 296 is left to divide.
3. Next we have to think about there are at least 10 [21s] in 296. Yes, 10 ∗ 21 = 210. So use 10 as the next quotient.
4. Perform subtraction operation. Subtract 210 from 296 then we got 86. Here 86 is left to divide.
5. Next We have to think about there are at least 2 [21s] in 86. Yes, 2 ∗ 21 = 42. So use 2 as the next quotient.
6. Perform subtraction operation. Subtract 42 from 86 then we got 44. Here 44 is left to divide.
7. We have to think about there are at least 2 [21s] in 44. Yes, 2 ∗ 21 = 42. So use 2 as the next quotient.
8. Subtract 42 from 44 then we got 2. Here 2 is left to divide. 2 is less than 21, So we are done dividing.
9. Add the partial quotients: 20 + 10 + 2 + 2 = 34. Remainder is 2. It can be written as 34 R2.

Division Number Stories with Remainders
Create a mathematical model for each problem. Solve the problem and show your work. Explain what you did with the remainder.
Question 1.
Pizzas cost $14 dollars each. How many pizzas can you buy with$60?
Quotient: ___________ Remainder: ___________
Circle what you did with the remainder.
Ignored it Rounded the quotient up Why?
Mathematical model:

4 R4
I can buy 4 pizzas. Ignored it; The $4 left over won’t buy another pizza. Explanation: The division is a method of distributing a group of things into equal parts. Pizza costs$14 dollars each. I have $60. With this money I can buy 4 pizzas. In the above image we can observe division operation. In that remainder is 4 and Quotient is 4. I have$4 left with me. The \$4 left over won’t buy another pizza. Here I ignored the quotient.

Question 2.
Your classroom received 150 books. You are placing them in bins. Each bin holds 20 books. How many bins do you need?
Quotient: ___________ Remainder: ___________
Circle what you did with the remainder.
Ignored it Rounded the quotient up Why?
Mathematical model:

7 R10
I need 8 bins. Rounded the quotient up.
7 bins will hold 140 books. So one more bin is needed for the 10 books left over.
Explanation:
The division is a method of distributing a group of things into equal parts. Our classroom received 150 books. We are placing them in bins. Each bin holds 20 books. I need 8 bins to hold the books. Here I rounded the quotient up, because only 7 bins will hold 140 books. So one more bin is needed for the 10 books left over.

Practice
Question 3.
190 ÷ 15 →
Estimate: _________
The list of multiples are
100 ∗ 15 = 1,500
50 ∗ 15 = 750
20 ∗ 15 = 300
10 ∗15 = 150
5 ∗ 15 = 75
2 ∗ 15 = 30
Estimate: 150/15 = 10

12 R10
Explanation:
1. First we have to think about there are at least 10 [15s] in 190. Yes, 10 ∗ 15 = 150. Then use 10 as your first partial quotient.
2. Perform subtraction operation. Subtract 150 from 190 then we got 40. Here 40 is left to divide.
3. Next we have to think about there are at least 2 [15s] in 40. Yes, 2 ∗ 15 = 30. So use 2 as the next quotient.
4. Perform subtraction operation. Subtract 30 from 40 then we got 10. Here 10 is left to divide. 10 is less than 15, So we are done dividing.
5. Add the partial quotients: 10 + 2 = 12. Remainder is 10. It can be written as 12 R10.

Question 4.
427 ÷ 30 →
Estimate: _________
100 ∗ 30 = 3,000
50 ∗ 30 = 1,500
20 ∗ 30 = 600
10 ∗ 30 = 300
5 ∗ 30 = 150
2 ∗ 30 = 60
Estimate: 300/30 = 10

14 R7
Explanation:
1. First we have to think about there are at least 10 [30s] in 427. Yes, 10 ∗ 30 = 300. Then use 10 as your first partial quotient.
2. Perform subtraction operation. Subtract 300 from 427 then we got 127. Here 127 is left to divide.
3. Next we have to think about there are at least 2 [30s] in 127. Yes, 2 ∗ 30 = 60. So use 2 as the next quotient.
4. Perform subtraction operation. Subtract 60 from 127 then we got 67. Here 67 is left to divide.
5. Next We have to think about there are at least 2 [30s] in 67. Yes, 2 ∗ 30 = 60. So use 2 as the next quotient.
6. Perform subtraction operation. Subtract 60 from 67 then we got 7. Here 7 is left to divide. 7 is less than 30, So we are done dividing.
7. Add the partial quotients: 10 + 2 + 2 = 14. Remainder is 7. It can be written as 14 R7.

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