Lesson 30Objective: Divide

decimal dividends by non-unit decimal divisors

By the end of the lesson, you will be able to…

5th Grade Module 4– Lesson 30K. Clauson

Time to Sprint!

Divide Whole Numbers by Fractions and Fractions by Whole Numbers

Divide Decimals

• How many tenths are in 1?

• 2?

• 3?

• 9?

• 10 ÷ 0.1…. Answer how many tenths are in 10

• 20 ÷ 0.1

• 30?

• 70?

75 ÷ 0.1

75.3 ÷ 0.1

Application Problem

Alexa claims that 16 ÷ 4, 32/8 , and 8 halves are all equivalent expressions. Is Alexa correct? Explain how you know.

Problem 1a = 2 ÷ 0.1

• How many tenths are in 2?

• How do you know?

Concept Development

I can count by tenths. 1 tenth, 2 tenths, 3 tenths,… all the way up to 20 tenths, which is 2 wholes. There are 10 tenths in 1, so there are 20 tenths in 2.Dividing by 1 tenth is the same as multiplying by 10, and 2 times 10 is 20.

20

Problem 1a =

• We also know that any division expression can be written as a fraction.

• What is different about this denominator?

• Let’s rename this denominator as a whole number. What have we learned that allows us to rename fractions without changing the value?

Concept Development

20.1

We need to multiply by a fraction equal to 1.

Problem 1a = 2 ÷ 0.1

• What fractions equal to 1 will rename the denominator as a whole number?

• Work with a partner to try some of your suggestions!

What do you notice about all of these division sentences?

They are equivalent expressions. When we multiply by a fraction

equal to 1, we create equal fractions and an equivalent division

expression.

Problem 1a = 2 ÷ 0.1

• FINAL THOUGHT>>>>

Problem 1b = 2 ÷ 0.2

• Let’s use what we just discovered in problem 1a to solve this new problem!

• Once again the denominator is a decimal.

• How will you find equal fractions with a whole number divisor?

20.2

We need to multiply by a fraction equal to 1.Go ahead and try that!!

Problem 1b = 2 ÷ 0.2

Let’s be sure!To check our division’s answer, we multiply the quotient by the divisor.

Show me!

10 x 0.2 = 210 x 2 tenths = 20 tenths

Problem 1c= 2.4 ÷ 0.2

• This time we have a decimal in both the divisor and the whole. Remind me… what will you do to rename the divisor as a whole number?

2.40.2

Problem 1d = 2.4 ÷ 0.4

• Work on this one independently!

Problem 2a = 1.6 ÷ 0.04

• How is this expression different than those we just completed?

• Since our divisor is still not a whole number, what fraction equal to 1 do you think we should use this time? We want to rename this as a whole number!

1.60.04

Problem 2a = 1.6 ÷ 0.04

Let’s be sure!To check our division’s answer, we multiply the quotient by the divisor.

Show me!

40 x 0.04 = 1.640 x 4 hundredths = 160 hundredths

Problem 2b = 1.68 ÷ 0.04

• Work with your partner to solve and check.

Problem 2c = 1.68 ÷ 0.12

• Work independently to find the quotient.

Get Ready to Finish theProblem Set on Your Own!

Work on Problem Set 30.

You will have 10 minutes to work!

-------------------------------------------------------------------Fast finishers:

- Math Center Activities- choice boards, extra Sprint challenge

- CML packets/ worksheets

- Problem Solving pages

5th Grade Module 4– Lesson 30K. Clauson

5th Grade Module 4- Lesson 30K. Clauson

LET’S DEBRIEF

• Take 2 minutes to check your answers with your partner.

• Let’s share any insights you had while solving these problems.

5th Grade Module 4– Lesson 30K. Clauson

EXITTICKETLESSON 30