Multiplying and Dividing Fractions

​Operations with Fractions

​Review

Multiplying Dividing

Converting

Simplifing

Review Slides with Notes

The next slides are to remind you of the skills. Take notes if needed. ​

​Types of Fractions

​Change an Improper to a Proper

​Divide Denominator by Numerator

​20 ÷ 5 = 4

REMEMBER

​You can convert a whole number into a fraction.

​Whole number is ALWAYS OVER 1

​Multiply Fractions

​Multiply the numerators together then, multiply the denominators together.

​Simplifying Fractions

&

Reducing Fractions

Means to scale down the both terms using a common factor.

One Simplifying Strategy...

Cross Cancel

Divide the diagonal factors by a common factor. Then, multiply across.

In this example, 9 and 3 have a common factor of 3. Both values are divided by 3 to reduce the terms, making it easier to calculate mentally.

Another Simplifying Strategy...

Simplify using GCF

Divide the each terms of the fraction by the greatest common factor after multiplying each term.

In this example, 6 and 12 have the common factors: 1, 2, 3, and, 6. However, the Greatest Common Factor is 6. Therefore, both terms are divided by 6 to reduce the terms into its simplest form.

​ALWAYS ALWAYS ALWAYS

​S I M P L I F Y when you can

​To divide fractions

​Invert (Flip) the second fraction, then multiply

​KCF

Divide Mixed Numbers

• Convert Mixed Numbers or Whole Numbers into Improper Fractions.

• Change the division sign to a multiplication sign.

• Rewrite the second fraction as its reciprocal (flip the fraction).

• Multiply the Numerators.

• Multiply the Denominators.

• Simplify if needed.

Let's Practice!!!

As you practice skills related to multiplying and dividing fractions & mixed numbers. Be sure to use your whiteboard to solve. ***No Calculators allowed!

Multiple Choice

The top number in a fraction is called a...

• Numerator

• Denominator

Multiple Choice

Simplify the fraction:
5/15 =

• 1/3

• 5/30

• 2/3

• 1/4

Multiple Choice

• $$\frac{3}{7}$$  

• $$\frac{3}{12}$$  

• $$\frac{1}{12}$$  

• $$\frac{1}{4}$$  

Multiple Choice

Find the product. Simplify if needed.

• 1/4

• 9/16

• 5/11

• 6/24

Multiple Choice

Gina had $$\frac{1}{4}$$ of a pizza and she shared it with 3 people.  

How much did each person get?

What type of problem is this?

• add

• subtract

• multiply

• divide

Multiple Choice

Which common multiple can be used as a common denominator to solve this problem?

$$\frac{8}{9}-\frac{3}{5}=$$  

• 9

• 20

• 27

• 45

Multiple Choice

• 13/3

• 13/27

• 9/39

• 3/13

Multiple Choice

Convert into an improper fraction.

• $$\frac{15}{2}$$

• $$\frac{10}{5}$$

• $$\frac{17}{5}$$

• $$\frac{11}{2}$$

Multiple Choice

Simplify $$\frac{8}{12}$$  

• $$\frac{2}{3}$$  

• $$\frac{3}{4}$$  

• $$\frac{1}{2}$$  

• $$\frac{4}{6}$$  

Multiple Choice

Simplify $$\frac{12}{15}$$

• $$\frac{4}{5}$$

• $$\frac{3}{5}$$

• $$\frac{6}{10}$$

• $$\frac{2}{3}$$

Multiple Choice

What is the reciprocal of 5?

• 5/1

• 1/5

• -5

• -1/5

Multiple Choice

1 $$\frac{7}{8}$$   $$\div$$   3 =

• $$\frac{7}{24}$$  

• $$\frac{5}{8}$$  

• 3 $$\frac{7}{24}$$  

• 5 $$\frac{5}{8}$$  

Multiple Choice

What is 3 $$\frac{1}{2}$$   $$\times$$  1 $$\frac{1}{4}$$  ?

• 2 $$\frac{4}{5}$$  

• 3 $$\frac{1}{8}$$  

• 4 $$\frac{3}{8}$$  

• 5 $$\frac{5}{6}$$  

Multiple Choice

1 $$\frac{7}{8}$$   $$\div$$   3 =

• $$\frac{7}{24}$$  

• $$\frac{5}{8}$$  

• 3 $$\frac{7}{24}$$  

• 5 $$\frac{5}{8}$$  

Multiple Choice

What is 3 $$\frac{1}{2}$$   $$\times$$  1 $$\frac{1}{4}$$  ?

• 2 $$\frac{4}{5}$$  

• 3 $$\frac{1}{8}$$  

• 4 $$\frac{3}{8}$$  

• 5 $$\frac{5}{6}$$  

Multiple Choice

Mia is working on projects that require 3 $$\frac{1}{2}$$   yards of ribbon per project. Mia has 28 yards of ribbon. What is the greatest number of projects that Mia can complete with this ribbon?

• 98

• 31 $$\frac{1}{2}$$  

• 24 $$\frac{1}{2}$$  

• 8

Multiple Choice

What numbers can I multiply to make a like unit for 3/5 and 2/3?

• 3 X 2 = 6

• 3 X 3 = 9

• 3 X 5 = 15

• I cannot make a like unit.

Multiple Choice

Is $$\frac{3}{4\ }$$  x $$\frac{2}{3}$$   greater than or less than 1?

• Greater than 1

• Less than 1

Multiple Choice

Is $$\frac{3}{4}$$  x $$\frac{2}{3}$$   greater than or less than $$\frac{2}{3}$$  ?

• Greater than

• Less than

Multiple Choice

Is $$\frac{3}{4}$$   x $$\frac{2}{3}$$   greater than or less than $$\frac{3}{4}$$  

• Greater than

• Less than

Fill in the Blanks

How many complete bows can you make from 3 $\frac{2}{3}$   meters of ribbon if $\frac{1}{4}$   of a meter of ribbon makes one bow? (Type your answer)

Multiple Choice

The top number in a fraction is called a...

• Numerator

• Denominator

Multiple Choice

Solve. Write the answer in its simplest form.

• $$\frac{6}{36}$$

• $$\frac{5}{15}$$

• $$\frac{1}{6}$$

• $$\frac{9}{24}$$

Multiple Choice

The bottom number in a fraction is called the...

• Numerator

• Denominator

Multiple Choice

Identify the operation you would use to solve:

Jason is baking cookies for a party. He has a recipe that calls for 2/3 cups flour. If he needs to triple the recipe, how much flour does the recipe require?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

What is the sum of these fractions?

• 4/5

• 3/20

• 17/20

• 4/20

Multiple Choice

What operation would I use to solve?

Marc is decorating for the holidays by placing ribbon along his stair railing. If the railing is 8m long and each ribbon is 3/4 m long, how many ribbons does Marc need to buy to fully cover the railing?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Select

Which of the following are improper fractions?
(Choose all that apply.)

• $$\frac{1}{5}$$  

• $$\frac{22}{5}$$  

• $$3\frac{1}{8}$$  

• $$\frac{13}{11}$$  

Multiple Choice

Convert the mixed fraction to a improper fraction.

• 27 /7

• 21 /7

• 31 /7

• 41/7

Multiple Choice

$$2\times\frac{2}{5}$$    Choose the BEST answer.

• $$\frac{22}{5}$$  

• $$2\frac{2}{5}$$  

• $$\frac{4}{5}$$  

• $$20$$  

Multiple Choice

$$6\div\frac{1}{2}$$  

Solve the expression.

• 6

• 62

• 3

• 12

Multiple Choice

Convert the following mixed number to an improper fraction:

$$2\ \frac{1}{8}$$  

• $$\frac{11}{8}$$  

• $$\frac{17}{8}$$  

• $$\frac{3}{8}$$  

Multiple Choice

Simplify ¹²/₁₆

• ³/₄

• ²/₃

• ¹⁰/₁₂

• ²⁴/₃₂

Multiple Choice

Calculate the following expression.

$$2\ \frac{2}{3}\times2\ \frac{3}{4}$$  

• $$7\ \frac{1}{2}$$  

• $$7\ \frac{1}{3}$$  

• $$7\ \frac{1}{4}$$  

Multiple Choice

Divide. Write in the simplest form.

$$5\frac{1}{2}\ \div\ 2$$  

• $$\frac{1}{4}$$  

• $$3\ \frac{1}{4}$$  

• $$2\ \frac{3}{4}$$  

Multiple Choice

Divide. Write in the simplest form.

$$6\ \frac{1}{2}\ \div\ 3\ \frac{1}{4}$$  

• 7

• 4

• 2

Multiple Choice

Divide. Write in the simplest form.

$$8\ \frac{3}{4}\ \div\ 2\ \frac{1}{6}$$  

• $$4\ \frac{1}{26}$$  

• $$16\ \frac{3}{24}$$  

• $$4\ \frac{3}{4}$$  

Match

Match the following each fraction with its reciprocal.

• $$\frac{1}{6}$$

• $$\frac{3}{4}$$

• $$\frac{2}{7}$$

• $$\frac{9}{10}$$

• $$\frac{3}{8}$$

6

4/3

7/2

10/9

8/3

• 6

• 4/3

• 7/2

• 10/9

• 8/3

Match

Match the following improper fraction with its equivalent mixed number.

• $$\frac{15}{3}$$

• $$\frac{7}{2}$$

• $$\frac{14}{3}$$

• $$\frac{25}{6}$$

• $$\frac{45}{10}$$

5

• 5

• $$3\frac{1}{2}$$

• $$4\frac{2}{3}$$

• $$4\frac{1}{6}$$

• $$4\frac{5}{10}$$