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Multiplying and Dividing Fractions

Going against what you would think, when you multiply fractions whose values are less than 1, your answer gets smaller! A simplified reason for this is that when you multiply a small number with a small number, you get a very small number, which makes sense when you compare it with multiplying a big number with a big number to get a very big number.

Let's see one in action:

1/2 * 3/4

To multiply these, simply go across the top number (the numerators) and multiply them. Then do the same for the denominators.

1 * 3 = 3
2 * 4 = 8

Your answer is 3/8! Notice that the answer has a value less than either of the numbers you multiplied with.

Before moving onto division, try a few. (Answers, as always, are below.)

1. 3/4 * 2/3
2. 6/7 * 3/6
3. 2/3 * 5/2

Don't forget to reduce! You can do so at any time, but it is easier to reduce before you do any calculations.

Answers:

1. 3/4 * 2/3
Numerator: 3 * 2 = 6
Denominator: 4 * 3 = 12
Answer: 6/12, which can be reduced to 3/6, and finally to the correct answer of 1/2!

2. 6/7 * 3/6
Numerator: 6 * 3 = 18
Denominator: 7 * 6 = 42
Answer: 18/42, which can be reduced to 6/14 , and finally to the correct answer of 3/7!

3. 2/3 * 5/2
Numerator: 2 * 5 = 10
Denominator: 3 * 2 = 6
Answer: 10/6, which can be reduced to 5/3, and if using improper fractions, 1 2/3!

 

Dividing Fractions
Dividing fractions does not involve any actual division at all. In fact, it is almost exactly the same as multiplication! The one extra step you need to do is to use the reciprocal (the opposite) of the dividing number. Here is an example:

2/5 ÷ 1/3

is the same as

2/5 * 3/1

And that's it! Change the divide sign to a multiply sign, flip the fraction over, and solve! Note: You may see these written a few different ways; the trick is to recognize them and do the same operations.

Try these (Answers below)

1. 3/4 / 2/3
2. 2/1 ÷ 2/1
3. 7/17 ÷ 4/17


The answers below show how to work with both types of how the division problems will look. The calculation you'll do will be the same, of course.

1. 3/4 / 2/3
Write as multiplication (after reciprocal): 3/4 * 3/2
Numerator: 3*3 = 9
Denominator: 4*2 = 8
Answer: 9/8

2. 2/1 ÷ 2/1
Write as multiplication after finding reciprocal: 2/1 * 1/2
Numerator: 2 * 1 = 2
Denominator: 1 * 2 = 2
Answer: 2/2, which can be reduced to 1/1, or simply 1.

3. 7/17 ÷ 4/17
Write as multiplication after finding reciprocal: 7/17 * 17/4
Since we have a multiplication problem with the same number in the numerator and denominator, instead of multiplying the larger numbers, we can just "cancel them out" - that is, make them both equal to one (since 17/17 is equal to 1.)
Note: We could also have done this in example 2!
Cancel values in numerator and denominator that are equal: 7/1 * 1/4
Numerator: 7 * 1 = 7
Denominator: 1 * 4 = 4
Answer: 7/4

The more you try, the easier it becomes!

Always remember that many fractions you may be working with can either be reduced or "cross-cancelled," as shown in example 3. Doing this makes any arithmetic you do on the values later much, much easier!

 

Find another math lesson at the Math Lesson and Tutorial Center!

 

 

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