Section C: Practice Problems Multi-digit Division

Section Summary

Details

In this section, we solved different problems that involve dividing whole numbers.

We recalled two ways of thinking about division. For example, suppose $274 \div 8$ represents a situation where 274 markers are put into equal groups. The value of $274 \div 8$ can tell us:

how many markers are in each group if there were 8 groups, or
how many groups can be made if there were 8 markers in each group.

We learned that the 274 in $274 \div 8$ is called the dividend. We then explored different ways to find the value of a quotient (or the result of the division). For $274 \div 8$ , we can:

Divide by place value and think about putting 2 hundred, 7 tens, and 4 ones into 8 equal groups.
Divide in parts and find partial quotients. For example, we can first find $160 \div 8$ (which is 20), and then $80 \div 8$ (which is 10), and then $32 \div 8$ (which is 4).
Think in terms of multiplication. For example, we can think of $8 \times 20 = 160$ , $8 \times 10 = 80$ , and so on.

Here is one way to record division using partial quotients:

Divide. 2 hundred seventy 4 divided by 8, 11 rows.

Sometimes a division results in a leftover that can’t be put into equal groups or is not enough to make a new group. We call the leftover a remainder. Dividing 274 by 8 gives 34 and a remainder of 2.

Problem 1 (Lesson 13)

If 5 pencils cost 95 cents, how much does each pencil cost? Explain or show your reasoning.
If 68 colored pencils are split evenly between 4 students, how many pencils does each student get? Explain or show your reasoning.

Problem 2 (Lesson 14)

Priya writes the multiples of a number and 63 is on her list. Priya’s number is not 1.

What could Priya’s number be? Explain your reasoning.
112 is the last number on Priya’s list. What is Priya’s number? How many numbers are on Priya’s list?

Problem 3 (Lesson 15)

Clare has 194 square tiles. Can Clare put all of her tiles in 6 rows with the same number of tiles in each row? Explain or show your reasoning.

Problem 4 (Lesson 16)

A long, rectangular hallway is 8 feet wide and has an area of 368 square feet. How long is the hallway?

Write a multiplication equation and a division equation that represent the situation.
Find the length of the hallway. Explain or show your reasoning.

Problem 5 (Lesson 17)

Here is 378 represented with base-ten blocks.

base ten diagram. 3 hundreds, 7 tens, 8 ones.

Use words, diagrams, or equations to show how to use the base-ten blocks to find the value of $378 \div 6$ .

Problem 6 (Lesson 18)

Here are two incomplete calculations of $864 \div 4$ . Complete each calculation to find the value of the quotient.

$\begin{aligned} 800 \div 4 & = 200 \\ 40 \div 4 & = \\ 20 \div 4 & = \\ 4 \div 4 & = \\ \overset{―}{864 \div 4} & \overset{―}{=} \end{aligned}$

Problem 7 (Lesson 19)

Use partial quotients to find the value of $637 \div 4$ .
If there are 637 toothpicks and 4 people, what could $637 \div 4$ mean in this situation? What could each step you took in the algorithm mean?
What does the value of the quotient represent in the situation?

Problem 8 (Lesson 20)

There are 875 peaches at the orchard. Each box contains 9 peaches. How many boxes are needed for the peaches? Explain your reasoning.

Problem 9 (Exploration)

Consider the expression $286 \div 5$ .

Write a division story with a question that can be answered by finding the value of $286 \div 5$ . Then, answer the question.
Write a different story with a question that can be answered by finding the value of $286 \div 5$ but with a different answer than your first story. Answer the question.

Problem 10 (Exploration)

Mai has a special way to see that 531 is a multiple of 9. She says, “Each hundred is 11 nines and 1 more and each ten is one nine and 1 more, so 531 is 58 nines and 9 more.”

Make sense of and explain Mai’s reasoning. Is 531 a multiple of 9?
Use Mai’s reasoning to decide if 648 is a multiple of 9.