Multiplication and Division With Fractions

Objective

Know how to multiply and divide fractions fractions.

Example

Calculate. Express answers in simplest form

Answer:

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Explanation

You've been through several levels of fractions up to this point. Now, we can finally put it all together to do begin performing calculations. To multiply you must

1. Convert all mixed numbers to improper fractions

2. Multiply numerators and denominators

3. Simplify

1. First, we can't multiply with mixed numbers, so convert them to improper fractions

2. Now that we have no mixed numbers, we can multiply

16 x 32 = 512

6 x 9 = 54

3. Now we need to simplify. Reminder, that means

• reduce the fraction part until 1 is the only common denominator

• the fraction can not be improper

It's up to you which part to simplify first. Here, we'll get rid of the improper fraction first

As you can see, our fraction is improper. First, convert it to a mixed number

All that's left to do now is reduce. We can see that 2 is a common factor. Dividing the numerator and denominator by 2, we get.

13 and 27 have no common factors, so we're done

Answer:

There is one extra step when dividing instead of multiplying. We'll show this in the example below

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Examples

Example 1

Here's where the extra step comes in. Instead of dividing, we take the reciprocal of the second fraction, then change the operation to times

Reciprocal just means switching the numerator and denominator

Use 12 as a common factor to reduce

Answer:

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Ready?