Dividing Fractions Lesson

Dividing Fractions

Multiplying a TOTAL Fraction by the reciprocal of another fraction (PART).

Two numbers that when multiplied together will give a product of 1. Also known as the Multiplicative Inverse, or just Inverse.

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Reciprocals

Multiple Choice

A reciprocal is also known as what vocabulary term:

• opposite
• flip
• inverse
• same

To find the reciprocal of a fraction, flip or switch the numerator and denominator

Fractions

To find the reciprocal of a whole number, take the whole number and put a 1 above it in the numerator spot.

Whole Numbers

Reciprocals

Multiple Choice

What is the reciprocal of 7/8?

• 1
• $$\frac{14}{16}$$

• $$\frac{8}{7}$$

• $$\frac{7}{8}$$

Multiple Choice

What is the reciprocal of 2

• 4

• $$\frac{1}{2}$$

• $$\frac{2}{1}$$

• $$\frac{2}{2}$$

To find the reciprocal of a Mixed Number:

1. First change the mixed number into an Improper Fraction
a. Multiply the Denominator by the Whole Number
b. Take the product and multiply it by the Numerator
c. Place the new Numerator over the same Denominator

2. Flip or Switch the Numerator and Denominator

​Reciprocals of Mixed Numbers

Multiple Choice

Convert this mixed number to an improper fraction.

• $$\frac{24}{5}$$

  
  

• $$\frac{10}{5}$$
  

• $$\frac{30}{5}$$
  

• $$\frac{34}{5}$$
  

Multiple Choice

What is the reciprocal of $$3\frac{2}{5}$$

• $$3\frac{5}{2}$$

• $$\frac{5}{6}$$

• $$\frac{17}{5}$$

• $$\frac{5}{17}$$

Dividing Fractions

1. Keep the First Fraction the Same: 2/5

2. Change ÷ to ×

3. Flip the Second Fraction to its Reciprocal: 3/4

​​Example 1:

Example 2:

1. Keep the First Fraction the Same: 1/4

2. Change ÷ to ×

3. Flip the Second Fraction to its Reciprocal: 4/5

Multiple Choice

What is the rule for Dividing Fractions?

• "Keep, Keep, Flip"

• "Keep, Change, Flip"

• "Keep, Change, Keep

• I don't know!

Multiple Choice

$$\frac{1}{2}\div\frac{2}{3}$$   Apply "Keep, Change, Flip" Rule

• $$\frac{1}{2}\times\frac{2}{3}$$  

• $$\frac{2}{1}\times\frac{2}{3}$$  

• $$\frac{1}{2}\times\frac{3}{2}$$  

• $$\frac{2}{1}\times\frac{3}{2}$$  

Multiple Choice

Divide $$\frac{3}{10}$$ by $$\frac{2}{4}$$

• $$\frac{6}{40}$$

• $$\frac{3}{4}$$

• $$\frac{1}{2}$$

• $$\frac{12}{20}$$

Multiple Choice

In Maddie’s garden, 1/3 of her plants are tomatoes. Of those tomatoes, 2/5 of them are ripe. What fraction of the plants are ripe tomatoes?

• 2/8
• 3/15
• 3/8
• 2/15

Multiple Choice

Anijah had 4/5 liter of water. She drank 7/10 liter with lunch. How many liters of water did Anijah have left to drink after lunch?

• 1

• 1/5

• 2

• 1/10

1. Change Whole Numbers to Fractions

2. Keep, Change, Flip

Example 1: Dividing Fractions and Whole Numbers

1. Change Mixed Numbers to Improper Fractions

2. Keep, Change, Flip

Example 2: Dividing Fractions and Mixed Numbers

Multiple Choice

$$\frac{2}{5}\div4$$  

• 1/10

• 10

• 1/20

• 2/20

Multiple Choice

Solve:

$$\frac{1}{2}$$   $$\div$$    $$1\frac{3}{4}$$  

• $$\frac{7}{4}$$  

• $$\frac{3}{8}$$  

• $$\frac{4}{14}$$  

• 5

Multiple Choice

Andrea has 80 coins in her collection. She shared 3/4 of her collection with friends. How many coins did she share?

• 20

• 50

• 60

• 70

Multiple Choice

Kiely is making bracelets for her friends. Kiely needs  $$\frac{1}{3}$$ foot of string for every bracelet.  She has 9 $$\frac{1}{3}$$  feet of string. How many bracelets can Kiely make? 

• 27 bracelets

• $$\frac{1}{27}$$   bracelets 

• 28 bracelets

• $$\frac{1}{28}$$  bracelets