Fractions

Fractions

When you are finished you will be able to:

Multiply Fractions by whole or mixed numbers

Divide Fractions by whole or mixed numbers

Use order of operations to solve problems.

How Many?

Multiplying A Fraction by A Whole Number

Lesson 1 - Monday

Method 1: Using a Model

Determine the Value of

 $\frac{2}{5}$  x 4 by using a model

Solution: The multiplication can be expressed by using repeated addition.

 $\frac{2}{5}\times4=\frac{2}{5}+\frac{2}{5}+\frac{2}{5}+\frac{2}{5}$  

Model the Fractions Using Fraction Strips

Fraction Strips Can be Found in EDWIN under math tools.

Total the shaded number of fraction strips.

 $\frac{2}{5}+\frac{2}{5}+\frac{2}{5}+\frac{2}{5}=\frac{8}{5}$  

Model the answer, and ensure the final answer is in lowest terms.

 $\frac{8}{5}$  

The answer is already in lowest terms.

•  $\frac{2}{5}\times4\ =\ \frac{8}{5}=1\ \frac{3}{5}$  

Refresher: How to convert an improper fraction to a mixed number.

Method 2 - Number Line

Determine

 $\frac{3}{4}\times3$  by using a number line.

Solution

Model the Fractions using a number line.

To use a number line click: https://apps.mathlearningcenter.org/number-line/

Method 3 - Showing the multiplication

Use the following steps to multiply a fraction by a whole number.

• Multiply the whole number by the numerator of the fraction.

• Write the resulting number over the denominator of the fraction.

• Reduce the fraction to lowest terms.

• Rewrite an improper fraction as a mixed number (see slide 9)

Example: Evaluate

 $\frac{2}{5}\times5.$  

• Multiply the whole number by the numerator

• Write the resulting number over the denominator.

• Write in lowest terms.

•  $\frac{2\times5}{3}=\frac{10}{3\ }=3\ \frac{1}{3}$  

Multiple Choice

Multiply then SIMPLIFY (Change from an improper fractions to a mixed number).  4 x $\frac{2}{3}$  =

•  $2\ \frac{2}{3}$  

•  $\frac{8}{12}$  

•  $\frac{2}{3}$  

•  $\frac{6}{8}$  

Multiple Choice

Multiply then SIMPLIFY (Change from an improper fractions to a mixed number). 8 x  $\frac{1}{5}$  =

•  $\frac{9}{5}$  

•  $1\ \frac{3}{5}$  

•  $8\ \frac{1}{5}$  

•  $\frac{7}{5}$  

Multiple Choice

 $8\ \times\ \frac{1}{3}$  

•  $\frac{9}{3}$  

•  $\frac{11}{3}$  

•  $\frac{8}{3}$  

•  $\frac{24}{3}$  

Multiple Choice

 $9\ \times\ \frac{4}{8}$  

•  $\frac{13}{4}$  

•  $\frac{36}{8}$  

•  $\frac{5}{8}$  

•  $\frac{13}{8}$  

Multiple Choice

 $4\ \times\ \frac{2}{3}$  

•  $\frac{6}{3}$  

•  $\frac{8}{3}$  

•  $\frac{2}{3}$  

•  $\frac{12}{3}$  

Multiple Choice

A recipe calls for  ²/₅ of a pound of chicken for each person. If there are 8 people to be fed, how many pounds of chicken are required?

• 10/5
• 3 and 1/5
• 2 and 6/5
• None

Multiple Choice

Arian spent 24 days at Grandma's house last summer. His brother spent ⅜ of that time at Grandma's. How many days did Arian's brother spend at Grandma's house last summer?

• 6

• 9

• 14

• 64

Multiple Choice

What is the product of
⁵/₈ and 6? 

• ⁵/₁₀₈
• 3 ³/₄
• 2 ¹/₃
• 6 ⁵/₁₈

Multiple Choice

Multiply. Simplify. 5 x 6/8=

• 11/8

• 30/40

• 1/8

• 3 3/4

Multiple Choice

Multiply. 5 x 1/8 =

• 51/8

• 5 1/8

• 5/8

• 6/8

Lesson 2 - Multiplying two fractions

Will review Tuesday's Google Meet

Multiply - Straight Across

• Multiply the numerators together.

• Multiply the denominators together.

• Simplify (reduce) the fraction.

Multiple Choice

1/2 x 3/4

• 3/4

• 3/8

• 4/6

• 3/2

Multiple Choice

What is 2/3 x 2/3

• 4/5

• 2/3

• 4/9

• 4/6

Multiple Choice

 $\frac{7}{9}\times\frac{1}{2}=$  
Simplify if needed.

•  $\frac{7}{18}$  
  

•  $\frac{14}{9}$  
  

•  $\frac{8}{11}$  

•  $1\frac{5}{9}$  

Multiple Choice

 $\frac{5}{1}\times\frac{1}{8}=$  
Simplify if needed.

•  $\frac{51}{8}$ 

•  $5\frac{1}{8}$  

•  $\frac{5}{8}$  

•  $\frac{6}{8}$  
  

Multiple Choice

3/4 x 1/6

• 1/8
• 5/24
• 4/10
• 3/10

Multiple Choice

²/₅ x ¹/₃

• 2/15
• 3/8
• 3/15
• 2/8

Multiple Choice

¹/₂ x ³/₄

• 3/8
• 4/6
• 3/4
• 3/6

Multiple Choice

To multiply two fractions...

• multiply the numerators and keep the denominators constant.
• multiply the numerators and multiply the denominators.
• keep the numerators constant and multiply the denominators.
• guess and check.

Multiple Choice

George has 1/3 pan of brownies. He eats 1/4 of them. What fraction did George eat?

• 1/7
• 1/4
• 1/3
• 1/12

Multiple Choice

What is 2/3 x 2/3 

• 4/9
• 2/3
• 4/3
• 4/6

Lesson 3 - Multiplying a Fraction by a Mixed Number

Will review Wednesday's Google Meet

Use the following steps to multiply a fraction by a mixed number.

• Change the mixed number to an improper fraction. (review slide 9 if you forgot how).

• Multiply the improper fraction by the fraction.

• Reduce the Fraction to lowest terms

• Rewrite the improper fraction as a mixed number.

Example: Evaluate

 $\frac{2}{3}\times3\ \frac{1}{4}$  

• Change the mixed number into an improper fraction.  $3\ \frac{1}{4\ }\rightarrow\ \frac{13}{4}$  

• Multiply the given fractions $\frac{2}{3}\times\frac{13}{4}=\frac{26}{12}$  

• Reduce to lowest terms.  $\frac{26\div2}{12\div2}=\frac{13}{6}$  

• Rewrite  $\frac{13}{6}$  as a mixed number.

•  $\frac{13}{6}\rightarrow\ 2\ \frac{1}{6}$  

Still confused? Try this video

https://www.youtube.com/watch?v=qmfXyR7Z6Lk

Lesson 4 & 5

• Complete & Submit Multiplying Fractions Worksheet

• Complete/Play Math Games Posted

• Complete and Submit MathGames Assignments.