All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 4 Lesson 3 Divide by a Two-Digit Divisor will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 4 Lesson 3 Divide by a Two-Digit Divisor
Math in My World
Example 1
The yearbook committee took 836 photos with a digital camera over 76 days. If they took an equal amount of photos each day, how many photos did they take each day? Check your answer for reasonableness.
Let p represent the number of photos taken each day. Write an equation to find the value of p.
_____________ ÷ ______________ = p
Estimate 800 ÷ 80 = _____________ So, the first digit is in the tens place.
1. Divide the tens.
83 ÷ 76 ≈ 1
Write 1 in the quotient over the tens place.
2. Multiply. 76 × 1 = 76
Subtract. 83 – 76 = 7
Compare. 7 < 76
3. Bring down 6 ones. There are 76 ones in all.
4. Write 1 in the quotient over the ones place.
76 × 1 = 76
76 – 76 = 0
So, 836 ÷ 76 = ___________. Since p = ____________, the yearbook committee will take _____________ photos each day.
Check for Reasonableness _______________ ≈ _____________
Answer: Since p = 11, the yearbook committee will take 11 photos each day.
Check for reasonableness is 10 ≈ 11.
Explanation: Given that,
The yearbook committee took 836 photos with a digital camera over 76 days.
If they took an equal amount of photos each day. Then how many photos did they take.
Now, we will find out the value of how many photos did they take each day.
Using the estimation method, we can divide the given value to get the quotient value.
We know that, estimation means round off the given value to nearest ten and hundreds.
The given value is 836 and 76.
Now, 76 nearest ten is 80 and 836 is nearest hundreds is 800.
So, 800/10 = 10.
Next, the division process below,
The 83/76 to get quotient is 1. (i.e.,) 76 x 1 = 76 and 83-76 = 7.
Compare the values, 7 is less than 76 (7<76).
Now, bring down 6, the value is 76.
Again 76 x 1 = 76. The quotient is again 1.
Therefore, the final quotient is 11.
So,the yearbook committee will take 11 photos each day.
Example 2
Find 751 ÷ 30.
Estimate 750 ÷ 30 = _____________
1. Divide the tens.
75 ÷ 30 ≈ 2
Write 2 in the quotient over the tens place.
2. Multiply. 30 × 2 = 60
Subtract. 75 – 60 = 15
Compare. 15 < 30
3. Bring down 1 one. There are 151 ones in all.
4. Divide the ones.
151 ÷ 30 ≈ 5
Write 5 in the quotient over the ones place.
30 × 5 = 150
151 – 150 = 1
So, 751 ÷ 30 is ___________ R ____________
Check for Reasonableness ____________ ≈ ____________ R ____________
Answer: 751 ÷ 30 is 25 R 1
Check Reasonableness is 25 ≈ 25 R 1.
Explanation: Given that, the value is 751 ÷ 30.
Now, we will find the estimate value and quotient value.
The estimation value is 750 and 30, because the values are rounded to nearest tens.
i.e., 751 to 750 and 36 to 30.
So, the value is 750/30 = 25.
Now, perform the division of 751 and 30.
Therefore, the quotient is 25 R 1, which is approximately to 25.
Talk Math
Explain how estimation is used to help you place the first digit in the quotient.
Answer: When estimating a quotient, you can round the divisor and dividend to a more simple division problem. But choose numbers that are close to each. If the first digit is less than the divisor, then the first digit of the quotient will be in the hundreds place. If the first digit is greater than or equal to the divisor, then the first digit of the quotient will be in the thousands place.
Guided Practice
Question 1.
Find 176 ÷ 16.
Estimate 180 ÷ 20 = ____________
So, 176 ÷ 16 = _____________.
Check for Reasonableness ____________ ≈ ____________
Answer: The quotient for 176 ÷ 16 is 11.
Check for Reasonableness 16 ≈ 16
Explanation: Given that, the value is 176 ÷ 16.
Now, we will find the estimate value and quotient value.
The estimation value is 180 and 20, because the values are rounded to nearest tens.
i.e., 176 to 180 and 16 to 20.
So, the value is 180/20 = 16.
Now, the division of 176 and 16 is,
So, the quotient is 11.
Independent Practice
Divide. Check for reasonableness.
Question 2.
809 ÷ 62 = ______________
Answer: The quotient is 13 R 3.
Check Reasonable, the estimate value is 13.5 which is approximately to 13 R 3.
Explanation: Given that, the value is 809 and 62.
The estimation of given values nearest to tens is 810/60 = 13.5
The divison process is,
Therefore, the quotient is 13 R 3.
Now, Check Reasonable the estimate value is 13.5 which is approximately to 13 R 3.
Question 3.
925 ÷ 42 = _____________
Answer: The quotient is 22 R 1.
Check Reasonable, the estimate value is 23 which is approximately to 22 R 1.
Explanation: Given that, the value is 925 and 42.
The estimation of given values nearest to tens is 920/40 = 23
The divison process is,
So, the quotient of given values is 22 R 1.
Now, check Reasonable. The estimate value is 23 which is approximately to 22 R 1.
Question 4.
210 ÷ 15 = _______________
Answer: The quotient is 14.
Check Reasonable, the estimate value is 10 which is approximately to 14.
Explanation: Given that, the value is 210 and 15.
The estimation of given values nearest to tens is 200/20 = 10.
The divison process is,
Hence, the quotient of given values is 14
Now, check Reasonable. The estimate value is 10 which is approximately to 14.
Question 5.
Answer: The quotient is 31.
Check Reasonable, the estimate value is 28 which is approximately to 31.
Explanation: Given that, the value is 837 and 27.
The estimation of given values nearest to tens is 840/30 = 28
The divison process is,
So, the quotient of given values is 31.
Now, check Reasonable. The estimate quotient value is 28 which is approximately to 31.
Question 6.
Answer: The quotient is 17 R 16.
Check Reasonable, the estimate value is 15 which is approximately to 17 R 16.
Explanation: Given that, the value is 594 and 34.
The estimation of given values nearest to tens is 600/40 = 15
The divison of the given values is,
Therefore, the quotient of given values is 17 R 16.
Next, check Reasonable. The estimate quotient value is 15 which is approximately to 17 R 16.
Question 7.
Answer: The quotient of given value is 12 R 11.
Check Reasonable, the estimate value is 15 which is approximately to 12 R 11.
Explanation: As given that, the value is 155 and 12.
The estimation of given values nearest to tens is 150/10 = 15
Next, the given values divison process is,
Then, the quotient of given values is 12 R 11.
Now, check Reasonable. The estimate quotient value is 15 which is approximately to 12 R 11.
Question 8.
Answer: The quotient of 790/29 is 27 R 7.
Check Reasonable, the estimate value is 26 which is approximately to 27 R 7.
Explanation: Given that, the value is 790 and 29.
The estimation of given values nearest to tens is 780/30 = 26
The divison process is,
Therefore, the quotient of given values is 27 R 7.
Next, check Reasonable. The estimate quotient value is 26 which is approximately to 27 R 7.
Question 9.
Answer: The quotient is 23 R 2.
Next check Reasonable, the estimate value is 21 which is approximately to 23 R 2.
Explanation: As given in the question, the value is 416 and 18.
The estimation of given values nearest to tens is 420/20 = 21.
The 416 by 18 divison is,
So, the quotient of given values is 23 R 2.
Now, check Reasonable. The estimate quotient value is 21 which is approximately to 23 R 2.
Question 10.
Answer: The quotient of 624 and 42 is 14 R 36.
Check Reasonable, the estimate value is 15 which is approximately to 14 R 36.
Explanation: As given in the question, the value is 624 and 42.
Now, we will find the estimation quotient value and real quotient value.
The estimation of given values nearest to tens is 600/40 = 15
The divison process is,
Hence, the quotient of given values is 14 R 36
Now, check Reasonable. The estimate quotient value is 15 which is approximately to 14 R 36.
Algebra. Divide to find the variable in each equation.
Question 11.
840 ÷ 24 = h
h = ______________
Answer: h = 35
Explanation: Given that, the value is 840 and 24.
Now, we will find the quotient value.
The divison process is,
Therefore, the quotient value is 35 i.e., h = 35.
Question 12.
528 ÷ 12 = b
b = ______________
Answer: b = 44
Explanation: Given that, the value is 528 and 12.
Now, we will find the b value.
First, find the divison process,
The quotient is 44. So, the value of b = 44.
Question 13.
952 ÷ 28 = w
w = _______________
Answer: w = 34
Explanation: As given in the question, the values are 952 and 28.
Now, we will find the w value, which is nothing but quotient value.
So, the divison process is,
Therefore, the quotient value is 34. So, the value of w is 34.
Problem Solving
Question 14.
Mr. Calzada buys flags for his store. Each flag costs $28. How many flags can he buy for $350? What does the remainder represent?
Answer: 12 flags can he buy for $350.
Explanation: Given that,
Mr. Calzada buys flags for his store.
The cost of each flag is $28.
Now, we will find out how many flags can he buy for $350.
So, the values are $350/$28.
Now, divide it. We get the quotient and remainder.
i.e., 350/28 = 12(14/28) = 12(1/2).
So, he buys 12 flags for $350. In this , the remainder represents how much money is less for buying 13th flag.
Question 15.
The area of a rectangle is 384 square feet and the width is 24 feet. Find the length.
Answer: The length of a rectangle is 16 feet.
Explanation : As given that,
The area of a rectangle is 384 square feet
The width of the rectangle is 24 feet.
Now, we will find the length of a rectangle.
We know the formula for area of a rectangle.
The area of a rectangle is, l x w.
But, we will find the length.
So, the formula is A = l x w.
A/w = l
Substitute the values in above formula.
i.e., 384/24 = l
16 = l
Therefore, the length of a rectangle is 16 feet.
Question 16.
Dreanne uploads 292 pictures to her online album. Her online album shows 12 pictures on each page. How many pages does she scroll through to see all 292 pictures? What does the remainder represent?
Answer: She scroll 24(1/3) pages to see all 292 pictures.
The remainder means the last number remaining after the completion of the division process. So, 12 is the remainder value
Explanation: As given in the question,
Dreanne uploads 292 pictures to her online album.
Her online album shows 12 pictures on each page.
Now, we will find out how many pages does she scroll through to see all 292 pictures.
So, the values are 292 and 12.
Now, divide it.
The value 292 is divided by 12. to get the quotient is 24 (4/12) = 24(1/3).
So, 24(1/3) pages does she scroll through to see all 292 pictures.
Question 17.
Mathematical PRACTICE Identify Structure In 31 days, Gwen’s dog sleeps 496 hours. If she sleeps the same number of hours each night, how many hours does she sleep per night? Find the unknown number in the equation 496 ÷ 31 = h.
Answer: If she sleeps the same number of hours each night, the she sleeps 16 hours per night.
Next, the number for the h is 16.
Explanation: Given that, the data is
Gwen’s dog sleeps 496 hours in 31 days.
If she sleeps the same number of hours each night then find out how many hours does she sleep per night.
Also, find the unknown number in the equation 496 ÷ 31 = h.
So, the values are 496 and 31.
Now divide it, to get the h value.
So, the value of h = 16.
Therefore, she sleep 16 hours per night.
HOT Problems
Question 18.
Mathematical PRACTICE Make a Plan Write a division problem that has a two-digit quotient that is greater than 40 but less than 50.
Answer: Given the question, we will write the two-digit quotient that is greater than 40 and less than 50.
Let x – dividend, y – divisor and the q – quotient.
We know that, Q = x/y
i.e., x = Q x y
So, 40 < Q < 50.
Now, consider thatm Q = 45 and y = 4.
Then x = 45 x 4 = 180.
A division problem is equal to x / y = 180 / 4 = 45.
Therefore, the two-digit quotient is 45.
Question 19.
Building on the Essential Question What is a standard procedure for dividing by a two-digit divisor? Explain.
Answer: The standard procedure for dividing by a two-digit divisor is, divide the first number of the dividend by the first digit of the divisor. Next, write the result of this division in the space of the quotient. Multiply the digit of the quotient by the divisor, then write the result beneath the dividend and subtract it.
McGraw Hill My Math Grade 5 Chapter 4 Lesson 3 My Homework Answer Key
Practice
Divide. Check for reasonableness.
Question 1.
874 ÷ 23 = _______________
Answer: The quotient is 38.
Check Reasonable, the estimate value is 40 which is approximately to 38.
Explanation: Given that, the value is 874 and 23.
The estimation of given values nearest to tens is 800/20 = 40.
The divison process is,
Hence, the quotient of given values is 38
Now, check Reasonable. The estimate quotient value is 40 which is approximately to 38.
Question 2.
988 ÷ 96 = _______________
Answer: The quotient of the given value is 10(7/24).
Check Reasonable, the estimate value is 11 which is approximately to 10(7/24).
Explanation: As given that, the value is 988 and 96.
The estimation of given values nearest to tens is 990/90= 11
Next,the divison process for given values is,
Hence, the quotient of given values is 10(28/96) = 10(7/24)
Now, check Reasonable. The estimate quotient value is 11 which is approximately to 10(7/24).
Question 3.
Answer: The quotient for the given values is 16(6/29).
Explanation: Given that, the value is 940 and 58.
Now, we will find the quotient of the given values.
So, the divison process is,
Hence, the quotient of given values is 16(12/58) = 16(6/29).
Problem Solving
Question 4.
Algebra Find the variable in the equation 803 ÷ 73 = m.
m = _______________
Answer: m = 11
Explanation: Given that, the values are 803 and 7.
Now, we will find the m value, which is nothing but the quotient value.
So, the divide the given values to get the quotient value. The below is the process of division.
Therefore, the quotient of the given values is 11 i.e., m = 11.
Question 5.
Algebra Find the variable in the equation 988 ÷ 76 = d.
d = _____________
Answer: d = 13
Given that, the values are 988 and 76
Now, we will find the d value, which is nothing but the quotient value.
So, the divide the given values. The below is the process of division,
Hence, by dividing 988 by 76, to get the quotient is 13 i.e., d = 13.
Question 6.
Mathematical PRACTICE Stop and Reflect Members of the Bladerunners skating club collected $950 from fundraising activities. They want to buy Ultrablade skates, which are $48 a pair. How many pairs of skates can they buy? What does the remainder represent?
Answer: They can buy19 pairs of skates.
The remainder represents the last number remaining after the completion of the division process. So, 38 is the remainder value
Explanation: As given that, the data is
Members of the Bladerunners skating club collected $950 from fundraising activities.
They want to buy Ultrablade skates, which are $48 a pair.
Now, we will find out how many pairs of skates can they buy.
So, the values are 950 and 48.
Now, divide it. We get the final value.
The below is the division process,
Hence, the quotient is 19(38/48) = 19(19/24)
Question 7.
A theater has 990 total seats. There are a total of 22 rows in the theater. If each row has an equal amount of seats, how many seats are in each row? Find the unknown number in the equation 990 ÷ 22 = s.
Answer: If rach row has an equal amounts of seat, then 45 seats are there in each row.
The number value in the equation s = 45.
Explanation: Given that,
A theater has 990 total seats.
There are a total of 22 rows in the theater. If each row has an equal amount of seats.
Then find out how many seats are in each row. Next, find the unknown number value in the equation is s.
So, the values are 990 and 22.
Now, divide it to get the s value. The process of division is,
Therefore, the quotient of the given values is 45. So, the value of s is 45.
Question 8.
A group of friends equally split the dinner bill shown. If each person paid $16, how many friends paid?
Answer: 14 friends are went. Each person pays $16.
Explanation: Given in the question,
A group of friends equally split the dinner bill.
The bill of the dinner is $224.
If each person paid $16, how many friends paid?
Now, we will find out how many friends are went to the restaurant.
So, the values are $224 and 16.
Now, divide it.
224/16 = 14
So, 14 friends are together to went the restaurant.
Test Practice
Question 9.
Emily loves to read. She read 527 hours in 31 weeks. If she read an equal number of hours each week, how many hours did she read each week?
(A) 10 hours
(B) 14 hours
(C) 15 hours
(D) 17 hours
Answer: D
Explanation: Given that,
Emily loves to read, so she read 527 hours in 31 weeks.
If she read an equal numbers of hours in each week, then how many weeks she read?
Now, we will find out the she read each week in how many hours.
Using the division, to get the value.
So, the values are 527 and 31.
Now, divide it. To get the value is,
527/ 31 = 17
So, she reads 17 hours in each week.