# Lesson 20

Dividing Decimals by Decimals

Let’s divide decimals by decimals.

### Problem 1

1. Explain why all of these expressions have the same value.

$$4.5 \div 0.09$$

$$45 \div 0.9$$

$$450 \div 9$$

$$4500\div 90$$

2. What is the common value?

### Problem 2

A student said, “To find the value of $$109.2 \div 6$$, I can divide 1,092 by 60.”

1. Do you agree with her? Explain your reasoning.
2. Calculate the quotient of $$109.2 \div 6$$ using any method of your choice.

### Problem 3

Here is how Han found $$31.59 \div 13$$:

1. At the second step, Han subtracts 52 from 55. How do you know that these numbers represent tenths?
2. At the third step, Han subtracts 39 from 39. How do you know that these numbers represent hundredths?
3. Check that Han’s answer is correct by calculating the product of 2.43 and 13.

### Problem 4

1. Write two division expressions that have the same value as $$61.12 \div 3.2$$.
2. Find the value of $$61.12 \div 3.2$$. Show your reasoning.

### Problem 5

Find each difference. If you get stuck, consider drawing a diagram.

$$2.5 - 1.6$$
$$0.72-0.4$$
$$11.3-1.75$$
$$73-1.3$$

(From Unit 3, Lesson 15.)

### Problem 6

At a school, 460 of the students walk to school.

1. The number of students who take public transit is 20% of the number of students who walk. How many students take public transit?
2. The number of students who bike to school is 5% of the number of students who walk. How many students bike to school?
3. The number of students who ride the school bus is 110% of the number of students who walk. How many students ride the school bus?
(From Unit 2, Lesson 23.)