All the solutions provided in McGraw Hill Math Grade 4 Answer Key PDF Chapter 6 Lesson 8 Distributive Property and Partial Quotients will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 4 Answer Key Chapter 6 Lesson 8 Distributive Property and Partial Quotients
Draw It
Jake and his three brothers all went on separate vacations. They traveled 484 miles in all. They each traveled the same distance. How many miles did each person travel?
Find 484 ÷ 4.
1. Model 484 as (400 + 80 + 4).
2. Divide each section by 4. Write each quotient above the bar.
Answer:
3. Add the quotients. _____ + ____ + _____ = _____
484 ÷ 4 = _____
So, each person traveled ____ miles.
Check Use multiplication to check a division problem.
Answer:
The quotients are 100 + 20 + 1 = 121
484 ÷ 4 = 121
So, each person traveled 121 miles.
Explanation:
Partial quotients is a way to divide where you break the dividend into parts that are easier to divide.
Try It
There are 625 bars of soap. Each gift bag will have 5 bars of soap. How many gift bags can be made with the soaps?
Find 625 ÷ 5 using partial quotients.
1. Divide the hundreds.
500 is close to 625 and is compatible with 5. Divide 500 by 5.
____ is a partial quotient.
Subtract 500 from 625.
Answer:
100 is a partial quotient.
625 – 500 = 125
Explanation:
2. Divide the tens. 25
100 is close to 125 and is compatible with 5.
Divide 100 by 5. 0
____ is a partial quotient.
Subtract 100 from 125.
Answer:
The partial quotient is 20.
Now subtract 125 -100 = 25
3. Divide the ones.
Divide 25 by 5.
____ is a partial quotient.
So, ____ gift bags can be made.
Answer:
The partial quotient is 5.
So, 5 gift bags can be made.
4. Add the partial quotients.
_________ + _____ + ____ = _____
625 ÷ 5 = _____
Answer:
100 + 20 + 5 = 125
625 ÷ 5 = 125
Talk About It
Question 1.
Draw an area model that could be used to find 346 ÷ 2 by using the Distributive Property.
Answer:
The answer is 176.
150 + 20 + 3 = 176
346 ÷ 2 = 176.
Explanation:
Question 2.
Mathematical PRACTICE 3 Justify Conclusions How are partial quotients similar to partial products?
Answer:
The number with which the divisor is multiplied is called the partial quotient. Partial products can be used to multiply two or more numbers. Hence partial quotients are similar to partial products.
Practice It
Divide. Use the Distributive Property. Complete the area models.
Question 3.
624 ÷ 2
____ + ____ + ____ = _____
624 ÷ 2
Answer:
312
Explanation:
300 + 10 + 2 = 312
624 ÷ 2 = 312.
Question 3.
848 ÷ 4
______________
848 ÷ 4 = _____
Answer:
212.
Explanation:
200 + 10 + 2 = 212
848 ÷ 4 = 212
Divide. Use the Distributive Property. Draw area models.
Question 5.
669 ÷ 3
Answer:
The answer is 223.
Explanation:
200 + 20 + 3 = 223.
Question 6.
442 ÷ 2
Answer:
221.
Explanation:
200 + 20 + 1 = 221.
442 ÷ 2 = 221.
Divide. Use the Distributive Property or partial quotients.
Question 7.
Answer:
The answer is 118.
Explanation:
Question 8.
Answer:
231.
Explanation:
200 + 30 + 1 = 231
Apply It
Use the Distributive Property or partial quotients to solve Exercises 9-11.
Question 9.
Blake’s dad needs $165 for a new suitcase. If he saves an equal amount for 3 weeks, how much does he save each week?
Answer:
55 dollars is saved each week.
Explanation:
Given,
Blake’s dad needs $165 for a new suitcase.
If he saves an equal amount for 3 weeks.
165 ÷ 3 = $55.
Question 10.
There are 567 people at the basketball game. The bleachers are divided into 9 sections. There are an equal number of people in each section. How many people are in each section?
Answer:
7 bleachers per section.
Explanation:
No of people at the basketball game = 567
The bleachers are divided into 9 sections
567 ÷ 9 = 63 people per section.
63 ÷ 9 = 7 bleachers per section.
Question 11.
Mathematical PRACTICE 5 Use Math Tools Mrs. Schmitt baked 224 cookies in her bakery. She placed them in 2 rows in her display case. How many cookies are in each row?
Answer:
112 cookies are in each row.
Explanation:
Mrs. Schmitt baked 224 cookies in her bakery.
She placed them in 2 rows in her display case.
224 ÷ 2 = 112 cookies are in each row.
Question 12.
In Exercise 10, why can the Distributive Property not be used to solve the problem?
Answer:
Distributive Property can be used to simply division problems by breaking them apart. But in Exercise 10 the division 567 ÷ 9 cannot be used the distributive property.
Question 13.
Mathematical PRACTICE 6 Explain to a Friend When finding 180 ÷ 4, is 40 or 60 a more reasonable partial quotient? Explain your answer to a friend.
Answer:
40 is a more reasonable partial quotient.
Explanation:
When finding the division of the 180 ÷ 4 the partial quotient of 40 is more reasonable to divide.
Write About It
Question 14.
Why are the Distributive Property and partial quotients helpful when dividing?
Answer:
The partial quotient uses the same method as the distributive property. And in the long division method, partial quotients are used to find the terms to make the larger number.
McGraw Hill My Math Grade 4 Chapter 6 Lesson 8 My Homework Answer Key
Practice
Divide. Use the Distributive Property. Complete the area models.
Question 1.
639 ÷ 3
____ + ____ + ____ = ____
639 ÷ 3 = _____
Answer:
213.
Explanation:
200 + 10 + 3 = 213
639 ÷ 3 = 213.
Question 2.
336 ÷ 6
____ + ____ + ____ = ____
336 ÷ 6 = _____
Answer:
56
Explanation:
50 + 5 + 1 = 56
336 ÷ 6 = 56
Problem Solving
Question 3.
Mathematical PRACTICE 5 Use Math Tools A garden store has 868 plants. They are divided equally into two groups. How many plants are in each group?
Answer:
434 plants.
Explanation:
No of plants that a garden store has = 868
They are divided equally into two groups.
868 ÷ 2 = 434 plants.
Hence there are 434 plants in each group.
Divide. Use the Distributive Property or partial quotients.
Question 4.
____ + ____ + ____ = ____
762 ÷ 3 = ____
Answer:
200 + 50 + 4 = 254.
The division for the given number is 254.
Explanation:
Question 5.
____ + ____ + ____ = ____
426 ÷ 2 = ____
Answer:
200 + 10 + 3 = 213.
426 ÷ 2 = 213.
Explanation:
Vocabulary Check
Question 6.
Explain why it can be helpful to use partial quotients when dividing.
Answer:
Partial quotients are helpful because we can break the dividend into parts which is easier to work.