Multiply Fractions and Simplify

Multiply Fractions Model

Multiple Choice

What expression is represented by the model?

• 1/5 ✕ 2/3

• 1/3 ✕ 2/5

Multiple Choice

Try another. Remember to cross reduce if possible.  

$$\frac{6}{9}\ x\ \frac{3}{6}$$  

• 1/3

• 9/15

• 18/54

• 1/2

Multiple Choice

$$\frac{2}{3}\ x\ 5$$   Turn 5 into a fraction by placing it over 1 and then multiply

• 15/2

• 7/3

• 10/3

• 8/3

Multiple Choice

$$\frac{9}{10}\ x\ 30$$  

Cross reduce if possible.

• 270

• 9/300

• 9/40

• 27

Multiple Choice

$$\frac{1}{2}\ x\ \frac{3}{7}$$  

• 3/14

• 3/9

• 4/9

• 6/7

• ​Multiply the numerators

• ​Multiply the denominators

• ​Simplify if possible.

• ​Both are even, so divide each by 2.

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​You can simplify BEFORE you multiply by finding "buddies" with common factors.

Multiple Choice

$$\frac{4}{5}\times\frac{5}{6}$$   Remember to simplify.

• $$\frac{9}{11}$$  

• $$\frac{2}{3}$$  

• $$\frac{20}{30}$$  

• $$\frac{4}{6}$$  

Multiple Choice

$$\frac{1}{3}\times\frac{2}{3}$$   Remember to simplify.

• $$\frac{2}{9}$$  

• $$\frac{2}{3}$$  

• $$\frac{3}{6}$$  

• $$\frac{3}{9}$$  

Multiple Choice

$$15\times\frac{3}{5}$$   Remember to simplify.

• $$\frac{18}{5}$$  

• $$\frac{45}{5}$$  

• 9

• $$5\frac{1}{5}$$  

​To Multiply mixed numbers:

* change mixed numbers to improper fractions

(multiply and add)

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​* simplify if possible

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​* multiply numerators

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​* multiply denominators

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​* simplify your answer.

Multiple Choice

$$5\frac{1}{3}\ \times3\text{ }\frac{3}{4}$$  

• 9

• $$15\ \frac{1}{4}$$  

• $$\frac{15}{4}$$  

• 20

Multiple Choice

fIve as a fraction would be

• 5/1

• 5/0

• 5/5

When multiplying factions and whole numbers

• If there are any mixed numbers you turn them into improper fractions

• to turn a mixed number into an improper fraction you must first multiply the denominator by the whole number

• then you add the numerator

• place that answer back over the denominator that was in the original fraction

Multiple Choice

What is the first step in turning a mixed number into an improper fraction?

• Multiply the denominator and the whole number

• adding the numerator to the denominator

Turning an improper fraction into a mixed number

To turn an improper fraction into a mixed number

• you divide the the denominator into the whole number

• the quotient becomes the numerator

• the remainder becomes the numerator

• the denominator stays the same

• Reduce if needed

Multiple Choice

$$\frac{1}{4}\times\ \frac{1}{3}=$$  

• $$\frac{2}{12}$$  

• $$\frac{1}{12}$$  

• $$\frac{6}{12}$$  

Multiple Choice

$$\frac{1}{2}\times\frac{1}{8}=$$  

• $$\frac{1}{4}$$  

• $$\frac{1}{16}$$  

• $$\frac{2}{16}$$  

Multiple Choice

$$\frac{4}{7}\times\frac{1}{2}=$$  

• $$\frac{2}{7}$$  

• $$\frac{5}{14}$$  

• $$\frac{3}{4}$$  

• $$\frac{4}{9}$$  

Multiple Choice

$$\frac{6}{27}$$  

Simplify!

• $$\frac{2}{9}$$  

• $$\frac{1}{3}$$  

• $$\frac{3}{9}$$  

• Already in simplest form. 

• $$\frac{1}{7}$$  

Multiple Choice

Evaluate  $$\frac{2}{11}\times3$$  

remember: we can give any whole number a denominator of 1! 

• $$\frac{6}{33}$$  

• $$\frac{6}{11}$$  

• $$\frac{2}{33}$$  

• $$\frac{5}{16}$$  

• $$\frac{5}{11}$$  

Multiply Fractions Test Review

"Of" means Multiply

1/2 of 12 =

Converting Mixed Numbers and Improper Fractions

Multiply Fractions

Numerator x Numerator

Denominator x Denominator

Put whole numbers over 1

Convert mixed to improper before multiplying

1. Make sure you have basic fractions

This makes things easier for you!

If you have a whole number, you must put a 1 under it.

Open Ended

How do I turn 5 into a fraction?

If you have a mixed number, turn it into an improper fraction

Reminder on Converting Mixed Numbers

• Multiply the denominator and whole number

• Add that product to the numerator

• Denominator stays the same

We want fractions that we can multiply straight across with!

It makes life easier!!

Remember that you multiply fractions straight across

Numerator x Numerator

Denominator x Denominator

Open Ended

$$\frac{2}{3}\degree\ \frac{1}{4}$$  Multiply

Multiple Choice

Find the simplified product:

$$\frac{4}{7}\times28$$  

• 112/7

• 8

• 16

• 112/196

One option to solve for the product is to remember that 28 can be written as 28/1. The algorithm says we should multiply numerator x numerator and denominator x denominator. Then simplify.

Review Explanation #1

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Multiple Choice

Use the Model to help you solve $$\frac{2}{3}\times\frac{3}{8}$$  

• 6/24 = 1/4

• 17/24

• 5/24

• 3/24 = 1/6

If we use the model, we can see that the area where 2/3 and 3/8 overlap is 6/24. This can be simplified because both 6 and 24 are divisible by 6. We can also solve using the algorithm a/b x c/d = (a x c)/(b x d)

Review Explanation #2

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Multiple Choice

Find the area of the rectangle with a length of 5 3/4 feet and a width of 2 2/3 feet.

• 10 5/7 sq. ft.

• 16 5/6 sq. ft.

• 15 1/3 sq. ft.

• 10 1/2 sq. ft.

To find the area of a rectangle, we needed to remember the equation Area = length x width. Which for this question would be 5 3/4 x 2 2/3. One way to solve is to turn the mixed numbers into improper fractions and multiply, then Simplify.

Review Explanation #3

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​Another way to look at it. Challenge/Get ready for Algebra.

Multiple Choice

Which products are greater than 3 5/6?

• $$\frac{3}{8}\times3\frac{5}{6}$$  

• $$\frac{8}{3}\times3\frac{5}{6}$$  

• $$3\frac{5}{6}\times\frac{3}{3}$$  

• $$\frac{7}{8}\times3\frac{5}{6}$$  

We can use what we know about fractions and whole numbers to help us solve this question without solving exactly. I know a fraction is a part of a whole. If I multiply my original number by a fraction, the product will be less (a part of) the original number.

Review Explanation #4

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