All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 4 Lesson 5 Divide Greater Numbers will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 4 Lesson 5 Divide Greater Numbers
Math in My World
Example 1
A large city has a total of 22500 students that ride a bus to school. There are 75 different schools within the city. How many students are dropped off at each school if an equal number of students are dropped off at each school?
Let s represent the number of students dropped off at each school.
Write an equation to find the value of s.
______________ ÷ _____________ = s
1. Place the first digit.
225 ÷ 75 ≈ 3
Write 3 in the quotient over the hundreds place.
2. Multiply.
75 × 3 = 225
Subtract. 225 – 225 = 0
Compare. 0 < 75
3. 0 ÷ 75 = 0
75 × 0 = O
0 – 0 = 0
0 < 75
4. Divide the ones.
o ÷ 75 = 0
75 × 0 = 0
0 – 0 = 0
0 < 75
So, 22,500 ÷ 75 = _____________. Since s = ____________, ____________ students are dropped off at each school.
Answer: So, 22,500 ÷ 75 = 300. Since s = 300, 300 students are dropped off at each school.
Explanation: Given that, the values are 22500 and 75.
Now, we will find the quotient.
The division of 22500 and 75 is,
Therefore, the quotient is 300 i.e., s= 300. So, 300 students are dropped off at each school.
Example 2
Estimate the quotient of 46,534 and 152. Then divide. Is 36 a reasonable quotient? Explain.
Estimate 45,000 ÷ 150 = _____________
1. Place the first digit.
465 ÷ 152 ≈ 3
Write 3 in the quotient over the hundreds place.
2. Multiply.
152 × 3 = 456
Subtract. 465 – 456 = 9
Compare. 9 < 152
3. Divide the tens.
Ninety-three is not divisible by 152, so put a 0 in the quotient over the tens place.
4. Divide the ones.
934 ÷ 152 ≈ 6
152 × 6 = 912
934 – 912 = 22
22 < 152
Check: Since the estimate is _____________ and the actual quotient is ____________, a quotient of 36 is not reasonable.
Answer: Since the estimate quotient is 300 and the actual quotient is 306 R 22, a quotient of 36 is not reasonable.
Explanation: Given that, the values are 46534 and 152.
Now, we will find the quotient.
First, we will find the estimate quotient.
So, the given values are rounded to nearest ten and hundreds.
The values 46534 and 152 is rounded to 45000 and 150.
Now, divide it. To get the estimated quotient value.
45000/150 = 300
The estimated quotient value is 300.
Next, we need to find the actual quotient.
The division of 46534 and 152 is,
After division, the quotient is 306 R 22.
Guided Practice
Question 1.
Find the missing number in the division problem below.
Answer: The missing in the division is 9. So, the quotient value is 1912.
Explanation: Given that, the values are 47800 and 25.
Now, we will find the quotient value.
So, divide the given values.
After division, the quotient value is 1912.
Therefore, in the given quotient the missing digit is 9.
Talk Math
Explain how estimation can be used before, during, and after a division problem.
Answer: Estimation of a number is a reasonable guess of the actual value to make calculations easier and realistic. Estimation means approximating a quantity to the required accuracy. This is obtained by rounding off the numbers involved in the calculation and getting a quick and rough answer.
Independent Practice
Estimate. Then divide. Check for reasonableness.
Question 2.
Answer: The quotient value is 1803.
Explanation: As given that, the values are 91988 and 51.
Now, we will find the quotient value.
The below is the division process,
Hence, the quotient value is 1803.
Question 3.
Answer: The quotient value is 861.
Explanation: Given that, the values are 14637, 17.
Now, we need to find out the quotient value.
So, the division is,
Therefore, after division. The quotient value is 861.
Question 4.
Answer: The quotient value is 242 R 1
Explanation: Given that, the values are 15489 and 64.
Now, we will find the quotient value.
So, the values are 15489 and 64.
After division, the quotient is 242 R 1.
Question 5.
36,712 ÷ 52 = _____________
Answer: The quotient value is 706.
Explanation: Given the values are 36712, and 52.
Now, we will find the value of the quotient .
The division process is,
By dividing, 36712 and 52. To get the quotient value is 706.
Question 6.
43,803 ÷ 93 = _______________
Answer: The final quotient value is 471.
Explanation: The given values are 43803 and 93.
Now, we need to find out the value of quotient.
The below is the division process,
So, by dividing 43803 by 93. To get the quotient value is 471.
Question 7.
26,208 ÷ 28 = _______________
Answer: The quotient value is 936.
Explanation: As given that, the values are 26208 and 28.
Now, divide it. We will get the quotient value.
The below is the division process,
After division, the quotient value is 936.
Question 8.
Answer: The quotient value is 605 R 25.
Explanation: As given that, the values are 25435 and 42.
Now, we will find the quotient value.
The division process is,
After division, the quotient value is 605 R 25.
Question 9.
Answer: The quotient value of 966 R 4.
Explanation: Given that, the values are 85978 and 89.
Now, we will find the quotient value.
The division process is,
Therefore, the quotient value is 966 R 4.
Question 10.
Answer: The final value is 66 R 378.
Explanation: Given that, the values are 52056 and 783.
Now, divide it. We get the final value.
The division is,
After division, the quotient value is 66 R 378.
Algebra. Divide to find the variable in each equation.
Question 11.
39,788 ÷ 812 = y
y = _____________
Answer: The value of y is 49.
Explanation: Given that, the values are 39788 and 812.
Using the division, we can find the value of ‘y’.
So, the quotient value is 49. Hence, the value of y is 49.
Question 12.
25,696 ÷ 352 = g
g = _____________
Answer: The value of g is 73.
Explanation: As given that, the values are 25696 and 352.
Now, we will find the g value.
The division process is,
After division, the quotient is 73 i,.e., the value of g is 73.
Question 13.
36,557 ÷ 263 = d
d = _______________
Answer: The value of d is 139.
Explanation: Given that, the values are 36557 and 263.
Now, we will find the ‘d’ value using the division.
After division, the quotient is 139. So, the value of d is 139.
Problem Solving
Question 14.
A farmer plows a corn field in the shape of a rectangle that has an area of 15,840 square yards. If the length of the field is 132 yards, what is the width of the field?
Answer: The width of the rectangular field is 120 yards.
Explanation: Given that,
A farmer plows a corn field in the shape of a rectangle that has an area of 15,840 square yards.
The length of the field is 132 yards.
Now, we need to find the value of width of the field.
We know that, the formula for area of a rectangle.
The area of a rectangle is, A = l x w.
15840 = 132 x w
15840/132 = w
Hence, the width of the rectangle is 120 yards.
Question 15.
An average person speaks 35,000 words in one week. Does the average person speak more or less than 2,500 words per day? Find the unknown number in the equation 35,000 ÷ 7 = w.
Answer: The average person speak more than 2500 words per day. The words are 5000.
In a equation, the value of w is 5000 words.
Explanation: Given that, the data is
An average person speaks 35,000 words in one week.
Now, we will find out the average person speak more or less than 2,500 words per day.
Find the value of w.
So, the values are 35000 and 7. Now divide it.
i.e., 35000/7 = 5000.
In a equation, the value of w is 5000.
Therefore average person speak more than 2500 words per day. The words are 5000 words.
Question 16.
Mathematical PRACTICE Use Number Sense The athletic department raised $14,533 to buy new football uniforms. If each uniform costs $258, how many uniforms can they buy? Explain how you interpreted the remainder. How much more money they do need to buy one more uniform?
Answer: 56 uniforms can they buy. The remainder 85 means they have $85 left over.
They need $173 to buy one more uniform.
Explanation: Given that,
The athletic department raised $14,533 to buy new football uniforms.
If each uniform costs $258, then find out how many uniforms can they buy.
Now, divide the given values.
After division, the quotient is 56 R 85. So, based on quotient 56 uniforms can they buy.
The remainder 85 means they have $85 left over. Theerfore they need $173 to buy one more uniform.
HOT Problems
Question 17.
Mathematical PRACTICE Draw a Conclusion Find the unknown number in the equation 30,672 ÷ q = 852. Explain how you found the unknown.
Answer: The q value is 36.
Explanation: Given that, the values are 30682 and 852.
Now, we will find the value of the q.
I divide 30682 by 852, to get the quotient value i.e., q value.
After dividing, the quotient value is 36. So, the value of q is 36.
Question 18.
Building on the Essential Question How can I divide greater numbers using a standard procedure?
Answer: The standard procedure for diving greater number is, take the first digit of the dividend from the left. Check if this digit is greater than or equal to the divisor. Then divide it by the divisor and write the answer on top as the quotient. Subtract the result from the digit and write the difference below. Divide any number by following the same steps and repeated them until get the quotient.
McGraw Hill My Math Grade 5 Chapter 4 Lesson 5 My Homework Answer Key
Practice
Estimate. Then divide. Check for reasonableness.
Question 1.
21,312 ÷ 36 = _____________
Answer: The quotient value is 592.
Explanation: Given that, the values are 21312 and 36.
Now, we need to find the value of quotient value.
By dividing the given values, to get the quotient value is 592.
Question 2.
76,912 ÷ 92 = ______________
Answer: The quotient value is 836.
Explanation: Given that, the values are 76912 and 92.
Now, we will find the quotient value.
After dividing the given values. To get the quotient value is 836.
Question 3.
26,878 ÷ 89 = _______________
Answer: The quotient value is 302.
Explanation: Given that, the values are 26,878 and 89.
Now, we will find the value of quotient.
By dividing, 26878 and 89. To get the quotient is 302.
Problem Solving
Question 4.
Given the area of a rectangle is 14,628 square millimeters, and the width is 12 millimeters, find the length.
Answer: The length of a rectangle is 1219 millimeters.
Explanation: As given in the question,
The area of a rectangle is 14,628 square millimeters.
The width of a rectangle is 12 millimeters.
Now we will find the length of a rectangle.
We know the formula for area of a rectangle.
The area of a rectangle is , A = length x width
14, 628 = l x 12
14628/12 = l
L = 1219 millimeters.
Hence, the length of a rectangle is 1219 millimeters.
Question 5.
Turtles and tortoises have long life spans A tortoise can live for 54,750 days How many years can a tortoise live? (hint 365 days = 1 year)
Answer: 150 years can a tortoise live.
Explanation: Given that,
Turtles and tortoises have long life spans.
A tortoise can live for 54,750 days.
Now, we will find out how many years can a tortoise live.
We know that, 365 days = 1 year.
So, divide 54750/365 to get the value.
i.e, 54750 is equal to 150 years.
Therefore, a tortoise can live 150 years.
Question 6.
Mathematical PRACTICE Use Algebra The new baseball stadium holds 64,506 people. There are 26 gates where people enter the ballpark. The same number of people entered each gate. How many people entered the first gate? Find the unknown number in the equation 64,506 ÷ 26 = p.
Answer: The value of p = 2481.
So, 2481 peoples entered the first gate.
Explanation: As given in the question,
The new baseball stadium holds 64,506 people.
There are 26 gates where people enter the ballpark.
The same number of people entered each gate. Then we will find how many people entered the first gate.
Using the division method, we will find the value of ‘p’
So, the values are 64,506 and 26.
After division of given numbers, the quotient value is 2481 i.e., p = 2481.
Therefore, 2481 people entered the first gate.
Test Practice
Question 7.
Joshua works for a computer company at an annual salary of $38,480. He receives 26 equal paychecks during the year. How much does he receive in each paycheck?
(A) $1,370
(B) $1,480
(C) $1,525
(D) $1,560
Answer: Option-B $1480.
Explanation: Given that, the data is,
Joshua works for a computer company at an annual salary of $38,480.
He receives 26 equal paychecks during the year.
Now, we will find out how much does he receive in each paycheck.
Using the division method, we can find the value.
So, the values are 38480 and 26.
Now divide it.
After, division the quotient is 1480. So, he receive $1480 in each paycheck.