Taking the Reciprocal of a Fraction

​Vocabulary Words

Some text here about the topic of discussion

​Improper Fraction - Fraction whose numerator is larger than the denominator.

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​Whole Number - A fraction where the denominator is always 1.

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Simplifying Fractions - ​dividing the numerator and denominator by the same number. Placing the fraction in lowest terms.

Denominator - The bottom number of a fraction that tells how many equal parts are in the whole.

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​Numerator - The top number of a fraction that tells how many parts of a whole are being considered.

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​KCF - Keep, Change Flip

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Reciprocal - ​any two numbers whose product is one when multiplied (flipped fraction)

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Mixed Number - ​a number including a whole number and a fraction.

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Steps to follow for dividing fractions

Step 1 - Only have fractions in the division sentence

Make sure you do not have any mixed numbers in the division sentence.

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Step 2 - Keep, Change, Flip

Keep the first fraction the same, change the division sign to multiplication, and flip the second fraction.

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Step 3 - ​Multiply

You will multiply straight across. Simplify if needed and convert to a mixed number. ​

6th Grade| Math

Dividing Fractions

Match

Match the following fraction with the reciprocal

• 1/6

• 3/4

• 2/7

• 9/10

• 3/8

6

4/3

7/2

10/9

8/3

• 6

• 4/3

• 7/2

• 10/9

• 8/3

A reciprocal is a mathematical expression or function so related to another that their product is 1.

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When dealing with fractions, to find the reciprocal all you need to do is flip the numbers in the fraction.

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Look at the example to the right.​

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​Some text here about the topic of discussion.

​Reciprocal

Dividing Fractions

When dividing fractions you

Keep, Change, Flip

Multiple Choice

Rewrite the division sentence:

$$\frac{1}{4}\div\frac{3}{5}$$  

• $$\frac{1}{4}\times\frac{3}{5}$$  

• $$\frac{1}{4}\times\frac{5}{3}$$  

• $$\frac{4}{1}\times\frac{3}{5}$$  

• $$\frac{4}{1}\times\frac{5}{3}$$  

Multiple Choice

Which expression is represented by the model?

• $$\frac{3}{4}\div\frac{1}{3}$$

• $$\frac{1}{4}\div\frac{1}{8}$$

• $$\frac{1}{8}\div\frac{1}{4}$$

• $$\frac{3}{4}\div\frac{1}{8}$$

Multiple Choice

After I "Keep, Change, Flip" what equation would I have? $$\frac{1}{2}\div\frac{2}{5}$$  

• $$\frac{2}{1}\times\frac{2}{5}$$  

• $$\frac{1}{2}\times\frac{5}{2}$$  

Multiple Choice

Solve $$\frac{1}{2}\div\frac{2}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{5}{4}$$  

• $$\frac{2}{10}$$  

Multiple Choice

When dividing fractions, what rule do we use?

• Keep, Change, Flip

• Multiply straight across

• Must have a common denominator

Multiple Choice

What is the reciprocal of 2 ?

• 2/1
• 1/2
• 2
• none of the above

Multiple Choice

What is the reciprocal of $$\frac{2}{3}$$  ?

• $$\frac{2}{3}$$  

• $$\frac{1}{4}$$  

• $$\frac{3}{2}$$  

• $$\frac{4}{6}$$  

Multiple Choice

What is the recriprocal of 5

• 5/1
• 1/5

Multiple Choice

What is the reciprocal of $$2\ \frac{1}{4}$$  ?

• $$\frac{9}{4}$$  

• $$\frac{4}{9}$$  

• 2 $$\frac{2}{8}$$  

• $$\frac{18}{8}$$  

Multiple Choice

$$\frac{7}{8}\div\frac{6}{9}$$   Rewrite as a multiplication problem.

*KCF

• $$\frac{7}{8}\times\frac{6}{9}$$  

• $$\frac{7}{8}\times\frac{9}{6}$$  

• $$\frac{8}{7}\times\frac{9}{6}$$  

Multiple Choice

$$\frac{1}{2}\div\frac{2}{3}$$    Rewrite as a multiplication problem.

• $$\frac{1}{2}\times\frac{2}{3}$$  

• $$\frac{2}{1}\times\frac{2}{3}$$  

• $$\frac{1}{2}\times\frac{3}{2}$$  

• $$\frac{2}{1}\times\frac{3}{2}$$  

Multiple Choice

5 ÷ 3/7

• 15/35

• 11 and 2/3

• 2 and 3/11

• 8 and 5/7

KEEP first fraction

CHANGE​ divide to multiply

FLIP second fraction over​

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You do not need to write this slide down.

​Example

Multiple Choice

$$2\ \div\ \frac{1}{3}$$  

• $$\frac{2}{3}$$  

• 6

• $$1\frac{1}{2}$$

• $$\frac{1}{6}$$  

Multiple Choice

What is a strategy for Dividing Fractions?

• "Keep, Keep, Flip"

• "Keep, Change, Flip"

• Flip-Change-Flip

• Multiply straight across

Multiple Choice

$$\frac{1}{2}\div\frac{2}{3}$$  How can this division sentence be written as multiplication?

• $$\frac{1}{2}\times\frac{2}{3}$$  

• $$\frac{2}{1}\times\frac{2}{3}$$  

• $$\frac{1}{2}\times\frac{3}{2}$$  

• $$\frac{2}{1}\times\frac{3}{2}$$  

Multiple Choice

$$3\ \div\ \frac{1}{6}$$  How can this division sentence be written as multiplication?

• $$\frac{3}{1}\ \times\ \frac{6}{1}$$  

• $$\frac{1}{3}\ \times\ \frac{1}{6}$$  

• $$\frac{3}{1}\ \div\ \frac{1}{6}$$  

Multiple Choice

What is the quotient of these fractions in lowest terms?

• 6/40
• 6/10
• 3/5
• 12/20

Multiple Choice

$$\frac{2}{5}\div3$$  Solve.

• 2/15

• 1/7

• 6/5

• 6/15