Multiplying and Dividing Fractions

Multiplying and Dividing Fractions

6th grade review

​Multiplying Fractions by Whole Numbers

​To multiply a fraction by a whole number, first put the whole number over 1. Next, multiply the numerators across. Then, multiply the denominators across.

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​Try a few on your own.

Multiple Choice

  $$\frac{1}{4}\times3$$  

• $$\frac{1}{2}$$  

• $$\frac{1}{4}$$  

• $$\frac{3}{4}$$  

• $$2$$  

Multiple Choice

$$3\times\frac{3}{10}$$  

• $$\frac{6}{10}$$  

• $$\frac{9}{10}$$  

• $$\frac{6}{30}$$  

• $$\frac{9}{30}$$  

​Multiplying Fractions by Fractions

​Multiply the numerator by the numerator and the denominator by the denominator.

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Let's try some.

Multiple Choice

$$\frac{2}{3}\times\frac{4}{5}$$  

• $$\frac{6}{8}$$  

• $$\frac{6}{15}$$  

• $$\frac{3}{10}$$  

• $$\frac{8}{15}$$  

Multiple Choice

$$\frac{6}{7}\times\frac{1}{5}$$  

• $$\frac{6}{35}$$  

• $$\frac{7}{12}$$  

• $$\frac{7}{30}$$  

​Cross-Reducing

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To cross-reduce, you look at the diagonal numbers. If they have a common factor, you can divide both numbers by that factor. This simplifies the problem so that you don't have to reduce after multiplying. It also helps to make multiplying across more simple.

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​Let's see how we do...

Fill in the Blanks

What is a factor of both 2 and 4?  

Fill in the Blanks

What is a factor of both 5 and 10?

Fill in the Blanks

What is the greatest factor of both 12 and 16?

Try it!

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Now that you have seen some examples, you are going to do a few of these yourself. Make sure to cross-reduce each problem before solving. Your answers should be in simplest form.

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​If you need help, raise your hand!

Multiple Choice

$$\frac{4}{9}\times\frac{1}{8}=$$  

• $$\frac{4}{17}$$  

• $$\frac{1}{18}$$  

• $$\frac{1}{36}$$  

• $$\frac{4}{72}$$  

Multiple Choice

$$\frac{2}{3}\times\frac{6}{7}=$$  

• $$\frac{4}{7}$$  

• $$\frac{12}{21}$$  

• $$\frac{8}{10}$$  

• $$\frac{4}{5}$$  

Multiple Choice

$$\frac{3}{5}\times\frac{5}{8}=$$  

• $$\frac{15}{40}$$  

• $$\frac{8}{13}$$  

• $$\frac{3}{8}$$  

• $$\frac{6}{16}$$  

​Mixed Numbers to Improper Fractions

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When multiplying mixed numbers, you need to make them improper first. Then you can cross reduce, multiply across, and convert them back to a mixed number by dividing.

Multiple Choice

$$3\frac{1}{2}\times2\frac{2}{3}=$$  

• $$6\frac{1}{2}$$  

• $$6\frac{3}{6}$$  

• $$9\frac{1}{3}$$  

• $$9\frac{1}{2}$$  

Multiple Choice

$$4\frac{1}{5}\times1\frac{2}{3}=$$  

• $$4\frac{2}{15}$$  

• $$5\frac{3}{8}$$  

• $$6\frac{1}{3}$$  

• $$7$$  

Multiple Choice

$$2\frac{5}{8}\times3\frac{2}{3}=$$  

• $$6\frac{5}{12}$$  

• $$6\frac{10}{24}$$  

• $$9\frac{5}{8}$$  

• $$9\frac{1}{3}$$  

Now it's time for division!​

Multiple Choice

What are the three magic words used in dividing fractions (in order)?

• Flip, keep, change

• Keep, change, flip

• Change, flip, keep

• Flip, change, keep

Hopefully, you picked this...​

Multiple Choice

What should $$5\div\frac{1}{3}$$  be changed to?

• $$\frac{5}{1}\times\frac{1}{3}$$  

• $$\frac{5}{1}\div\frac{3}{1}$$  

• $$\frac{1}{5}\times\frac{1}{3}$$  

• $$\frac{5}{1}\times\frac{3}{1}$$  

Multiple Choice

What should  $$\frac{3}{5}\div2$$  be changed to?

• $$\frac{3}{5}\times\frac{2}{1}$$  

• $$\frac{3}{5}\times\frac{1}{2}$$  

• $$\frac{3}{5}\div\frac{2}{1}$$  

• $$\frac{3}{5}\div\frac{1}{2}$$  

Multiple Choice

What should $$\frac{2}{3}\div\frac{4}{5}$$  be changed to?

• $$\frac{2}{3}\times\frac{5}{4}$$  

• $$\frac{3}{2}\times\frac{4}{5}$$  

• $$\frac{2}{3}\div\frac{5}{4}$$  

• $$\frac{3}{2}\div\frac{4}{5}$$  

Multiple Choice

$$5\div\frac{1}{3}=$$  

• $$\frac{5}{3}$$  

• $$\frac{1}{15}$$  

• $$\frac{3}{5}$$  

• $$15$$  

Multiple Choice

$$\frac{3}{5}\div2=$$  

• $$\frac{10}{3}$$  

• $$\frac{6}{5}$$  

• $$\frac{3}{10}$$  

• $$3\frac{1}{3}$$  

Multiple Choice

$$\frac{2}{3}\div\frac{4}{5}$$  

• $$\frac{8}{15}$$  

• $$\frac{5}{6}$$  

• $$\frac{12}{10}$$  

• $$1\frac{1}{5}$$  

Multiple Choice

$$2\frac{1}{5}\div3\frac{3}{5}=$$  

• $$1\frac{7}{18}$$  

• $$6\frac{2}{5}$$  

• $$\frac{23}{25}$$  

• $$\frac{11}{18}$$  

Multiple Choice

$$5\frac{1}{2}\div2\frac{3}{4}=$$  

• $$5$$  

• $$2$$  

• $$10\frac{3}{8}$$  

• $$\frac{1}{2}$$  

​You did it!

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If you did well, then you are finished. If you got 15 or less or you would like to improve your score, please try again. Ask for help if needed!

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