Lesson 13Dividing Decimals by Decimals
Learning Goal
Let’s divide decimals by decimals.
Learning Targets
I can explain how multiplying dividend and divisor by the same power of 10 can help me find a quotient of two decimals.
I can find the quotient of two decimals.
Lesson Terms
- long division
Warm Up: Same Values
Problem 1
Use long division to find the value of
Problem 2
Select all of the quotients that have the same value as
Activity 1: Placing Decimal Points in Quotients
Problem 1
Think of one or more ways to find
Problem 2
Find
Problem 3
Diego said, “To divide decimals, we can start by moving the decimal point in both the dividend and divisor by the same number of places and in the same direction. Then we find the quotient of the resulting numbers.”
Do you agree with Diego? Use the division expression
Are you ready for more?
Problem 1
Can we create an equivalent division expression by multiplying both the dividend and divisor by a number that is not a multiple of 10 (for example: 4, 20, or
Activity 2: Two Ways to Calculate Quotients of Decimals
Problem 1
Here are two calculations of
Work with your partner to answer the following questions.
How are the two calculations alike? How are they different?
Look at Calculation A. Explain how you can tell that the 36 means “36 tenths” and the 18 means “18 hundredths.”
Look at Calculation B. What do the 3600 and 1800 mean?
We can think of
as saying “there are 9 groups of 5.42 in 48.78.” We can think of as saying “there are 900 groups of 5.42 in 4878.” How might we show that both statements are true?
Problem 2
Explain why
has the same value as . Write a division expression that has the same value as
but is easier to use to find the value. Then, find the value using long division.
Activity 3: Practicing Division with Decimals
Problem 1
Find each quotient using a method of your choice. Then discuss your calculations with your group and agree on the correct answers. If someone in your group makes an error, stop and help that person revise their work. If your group is unsure about an answer, consult your teacher.
Problem 2
Mai is making friendship bracelets. Each bracelet is made from 24.3 cm of string. If she has 170.1 cm of string, how many bracelets can she make? Explain or show your reasoning.
Lesson Summary
One way to find a quotient of two decimals is to multiply each decimal by a power of 10 so that both products are whole numbers.
If we multiply both decimals by the same power of 10, this does not change the value of the quotient. For example, the quotient
To calculate