Multiplying and Dividing Fractions

Multiplying and Dividing Fractions

Multiplying and Dividing Fractions

When Multiplying or Dividing fractions, ALWAYS convert Mixed Numbers to Improper Fractions FIRST!

Converting Mixed numbers to Improper fractions:

• Multiply the whole number and the denominator

• Add the numerator to the answer you got

• Put your new number over the old denominator

Poll

What are the steps for converting a mixed number to an improper fraction?

• add and subtract

• multiply then add

• multiply and divide

• divide and subtract

Multiple Choice

What is $5\frac{3}{4}$  as an improper fraction?

•  $\frac{19}{4}$  

•  $\frac{20}{3}$  

•  $\frac{23}{4}$  

•  $\frac{23}{5}$  

Now you are ready to Multiply and Divide

Math Antics - Multiplying Fractions

https://youtu.be/qmfXyR7Z6Lk

ALWAYS SIMPLIFY YOUR ANSWER...either before you multiply by breaking down to prime factors and canceling them or at the end by dividing the numerator and denominator by a common factor.

Remember this rhyme to help you every time:

First is fine,

Switch the sign,

Flip the fraction,

Complete the action!

Multiple Choice

What is the first step to solving this question:

 $3\frac{1}{2}\times2\ \frac{1}{4}$  

• Multiply the whole numbers together

• Ignore the whole numbers and multiply the fractions

• Convert to improper fractions

• Change the denominators so they match

Multiple Choice

Solve this question:


 $\frac{5}{7}\times\frac{3}{4}$  

•  $\frac{8}{11}$  

•  $\frac{15}{28}$  

•  $\frac{15}{11}$  

•  $\frac{20}{21}$  

If you have a whole number, what do you put under it to make it a fraction?

1

Multiple Choice

Solve this question:


 $3\ \times\ \frac{4}{5}$  

•  $\frac{12}{15}$  

•  $\frac{12}{5}$  

•  $\frac{4}{15}$  

•  $\frac{12}{8}$  

Let's Review

Adding and Subtracting Fractions

• Turn mixed numbers into improper fractions

• Find the least common denominator

• Change both fractions so they have a common denominator

• Add or subtract the fractions

• Change back into a mixed number if necessary

Multiplying Fractions

1) Change mixed numbers and whole numbers into improper fractions

2) Cross cancel and multiply across

OR

2) Multiply across and simplify

3) Change back into a mixed number if necessary

Dividing Fractions

Keep, Change, Flip

Keep the first fraction

Change to Multiplication

Flip the last fraction to the reciprocal

Reciprocal? Huh?

A reciprocal, or multiplicative inverse, is simply one of a pair of numbers that, when multiplied together, equal 1. If you can reduce the number to a fraction, finding the reciprocal is simply a matter of transposing the numerator and the denominator. FLIP!! To find the reciprocal of a whole number, just turn it into a fraction in which the original number is the denominator and the numerator is 1.

EXAMPLE

For example, the reciprocal of  $\frac{2}{3}$  is   $\frac{3}{2}$ , because  $\frac{2}{3}\times\frac{3}{2}=1$ .

The reciprocal of 7 is  $\frac{1}{7}$   because  $7\times\frac{1}{7}=1$ .

Multiple Choice

What is the reciprocal of  $\frac{7}{8}$  ?

•  $1$  

•  $\frac{8}{7}$  

•  $\frac{14}{16}$  

•  $\frac{7}{8}$  

Multiple Choice

Find the reciprocal of  $\frac{7}{11}$  .

•  $1\ \frac{1}{7}$  

•  $\frac{11}{11}$  

•  $\frac{11}{7}$  

•  $\frac{7}{7}$  

Multiple Choice

What is the reciprocal of $\frac{4}{5}$  ?

•  $\frac{4}{5}$  

•  $\frac{5}{4}$  

•  $\frac{5}{1}$  

•  $\frac{1}{5}$  

Math Antics - Dividing Fractions

https://youtu.be/4lkq3DgvmJo

Poll

What kind of math do you really do when you are dividing fractions?

• multiplying

• adding

• subtracting

• dividing

Dividing Fractions

1) Change mixed numbers and whole numbers into improper fractions

2) Keep, change, flip

3) Cross cancel and multiply across

OR

3) Multiply across and simplify

4) Change back into a mixed number if necessary

ALWAYS SIMPLIFY YOUR ANSWER...either before you multiply by breaking down to prime factors and canceling them or at the end by dividing the numerator and denominator by a common factor.

Multiple Choice

Solve this question:

 $\frac{4}{7}\ \div\frac{3}{5}$  

•  $\frac{20}{21}$  

•  $\frac{1}{1}$  

•  $\frac{12}{35}$  

•  $\frac{1.1}{1.2}$  

Multiple Choice

Solve:

 $\frac{3}{8}\div\frac{2}{3}$  

•  $\frac{9}{16}$  

•  $\frac{1}{4}$  

•  $\frac{6}{24}$  

•  $\frac{3}{8}$  

Multiple Choice

Simplify. Write your answer as a mixed number when necessary.

 $\frac{9}{10}\div\frac{1}{4}$  

•  $\frac{36}{10}$  

•  $\frac{9}{40}$  

•  $3\ \frac{6}{10}$  

•  $3\ \frac{3}{5}$  

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