Dividing Fractions

Unit 2 Lesson 1

Math 6

Dividing Fractions

Students will be able to:

Interpret and compute quotients of fractions.

Solve word problems involving division of fractions by fractions.

Dividing Fractions

Key Vocabulary:

Fraction

Divisor

Dividend

Quotient

Dividing Fractions

Dividing by a fraction is the same as multiplying by

its reciprocal.

To divide fractions take the reciprocal (invert the

fraction) of the divisor and multiply the dividend.

Division rule of two fractions

𝒂

𝒃÷

𝒄

𝒅=

𝒂

𝒃∗𝒅

𝒄=

𝒂∗𝒅

𝒃∗𝒄.

Dividing Fractions

Example: How many units of𝟐

𝟓can you see in

𝟒

𝟓?

𝟐

𝟓

𝟐

𝟓

𝟒

𝟓

Dividing Fractions

Example: How many units of𝟐

𝟓can you see in

𝟒

𝟓?

𝟒

𝟓÷𝟐

𝟓=𝟒

𝟓∗𝟓

𝟐=𝟒 ∗ 𝟓

𝟓 ∗ 𝟐=𝟒

𝟐= 𝟐 𝒖𝒏𝒊𝒕𝒔

Dividing Fractions

Sample Problem 1: Draw a model to solve.

a. How many units of 𝟏

𝟒can you see in

𝟑

𝟒?

Dividing Fractions

Sample Problem 1: Draw a model to solve.

a. How many units of 𝟏

𝟒can you see in

𝟑

𝟒?

𝟑

𝟒

𝟏

𝟒𝟏

𝟒

𝟏

𝟒

Dividing Fractions

Sample Problem 1: Draw a model to solve.

a. How many units of 𝟏

𝟒can you see in

𝟑

𝟒?

𝟑

𝟒÷𝟏

𝟒=𝟑

𝟒∗𝟒

𝟏=𝟑 ∗ 𝟒

𝟒 ∗ 𝟏= 𝟑 𝒖𝒏𝒊𝒕𝒔

Dividing Fractions

Sample Problem 1: Draw a model to solve.

b. How many units of 𝟏

𝟖can you see in

𝟕

𝟖?

Dividing Fractions

Sample Problem 1: Draw a model to solve.

b. How many units of 𝟏

𝟖can you see in

𝟕

𝟖?

𝟕

𝟖

𝟏

𝟖

𝟏

𝟖

𝟏

𝟖

𝟏

𝟖

𝟏

𝟖

𝟏

𝟖

𝟏

𝟖

Dividing Fractions

Sample Problem 1: Draw a model to solve.

b. How many units of 𝟏

𝟖can you see in

𝟕

𝟖?

𝟕

𝟖÷𝟏

𝟖=𝟕

𝟖∗𝟖

𝟏=𝟕 ∗ 𝟖

𝟖 ∗ 𝟏= 𝟕 𝒖𝒏𝒊𝒕𝒔

Dividing Fractions

Sample Problem 2: Find each quotient.

a.𝟐

𝟑÷𝟏

𝟐=

Dividing Fractions

Sample Problem 2: Find each quotient.

a.𝟐

𝟑÷𝟏

𝟐=𝟐

𝟑∗𝟐

𝟏=𝟐 ∗ 𝟐

𝟑 ∗ 𝟏=𝟒

𝟑

Dividing Fractions

Sample Problem 2: Find each quotient.

b.𝟏

𝟒÷𝟐

𝟒=

Dividing Fractions

Sample Problem 2: Find each quotient.

b.𝟏

𝟒÷𝟐

𝟒=𝟏

𝟒∗𝟒

𝟐=𝟏 ∗ 𝟒

𝟒 ∗ 𝟐=𝟏

𝟐

Dividing Fractions

Sample Problem 2: Find each quotient.

c.𝟏

𝟑÷𝟐

𝟗=

Dividing Fractions

Sample Problem 2: Find each quotient.

c.𝟏

𝟑÷𝟐

𝟗=𝟏

𝟑∗𝟗

𝟐=𝟏 ∗ 𝟗

𝟑 ∗ 𝟐=𝟑

𝟐

Dividing Fractions

Sample Problem 2: Find each quotient.

d.𝟏

𝟐÷𝟑

𝟒=

Dividing Fractions

Sample Problem 2: Find each quotient.

d.𝟏

𝟐÷𝟑

𝟒=

𝟏

𝟐∗𝟒

𝟑=𝟏 ∗ 𝟒

𝟐 ∗ 𝟑=𝟐

𝟑

Dividing Fractions

Sample Problem 3: Solve each problem.

a. Diana has𝟏

𝟑of a bag of dog food. Her dog eats

𝟏

𝟔of

a bag per week. How many weeks will the food last?

Dividing Fractions

Sample Problem 3: Solve each problem.

a. Diana has𝟏

𝟑of a bag of dog food. Her dog eats

𝟏

𝟔of

a bag per week. How many weeks will the food last?

𝟏

𝟑÷𝟏

𝟔=𝟏

𝟑∗𝟔

𝟏=𝟏 ∗ 𝟔

𝟑 ∗ 𝟏= 𝟐

𝟐 𝐰𝐞𝐞𝐤𝐬

Dividing Fractions

Sample Problem 3: Solve each problem.

b. How many halves are there in six-fourth?

Dividing Fractions

Sample Problem 3: Solve each problem.

b. How many halves are there in six-fourth?

𝟔

𝟒÷𝟏

𝟐=𝟔

𝟒∗𝟐

𝟏=𝟔 ∗ 𝟐

𝟒 ∗ 𝟏=

𝟔 ∗ 𝟐

𝟐 ∗ 𝟐 ∗ 𝟏=𝟔

𝟐

There are 6 halves in six-fourth.