fraction ops

$: fraction ops$
8/14/2019 fraction ops

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Fraction Operations

Adding, subtracting, multiplying &

dividing

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Mixed Numbers & Improper Fractions

A mixed number is a combination of a wholenumber and a fraction. For example:

An improper fraction is a fraction whosenumerator (top) is bigger than itsdenominator (bottom). Example:

These two forms are completelyinterchangeable. You just have to decidewhich form is the most convenient for you touse.

5

31

5

8

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Mixed Numbers & Improper Fractions

To choose between mixed numbers &improper fractions:

When you are adding or subtracting,mixed numbers are best. (Don’t forget,they must have common denominators.)

When you are multiplying or dividing,

improper fractions will be best.

When you are finished, always leave youranswer in mixed number form.

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Converting Improper Fractions to

Mixed Numbers To convert an improper fraction to a mixed

number, simply divide. If you have a remainder, itwill become the numerator (top) of the new

fraction. The denominator of the improper fractionwill still be the denominator in the mixed number.

3

553

1

-3

2

2/3

3

21

3

5

(Read:

5 divided by 3)

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Converting Mixed Numbers to

Improper Fractions This is just a matter of cutting up the whole units

into the right size pieces and then adding them tothe fractional part of the mixed number.

Real life example: If you had 2 3/4 dollars ($2.75),how many fourths of a dollar (quarters) would youhave?

The $2 would make 8 quarters. That’s 8/4. Thenadd the other 3/4 (the 75 cents) and you have atotal of 11/4. That’s 11 quarters.

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Improper Fractions

517

52

515

52

55

13

523

This is the long way. There is ashorter way, but you need to knowwhy the shortcut works before you

start using it.

Here is an example:

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Improper Fractions For the shortcut, multiply the bottom by

the whole number then add it to the

numerator. The denominator of theimproper fraction is the same as it wasin the mixed number.

7

30

7

24

Multiply:4x7=28

Add:

28+2=30

Denominator didnot change!

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Adding & Subtracting Fractions

Remember that fractionsrepresent pieces of things.Before you can add pieces,

you have to make sure thatthey are the same size.

This means that we have tofind equivalent fractions with

a common denominator. Youhave already learned thisprocess.

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Second, remember that thedenominator tells us about the SIZE of

the pieces – not the amount of pieces. For this reason, the denominator stays

the same when you add.

10

7

10

4

10

3

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Finally, when you do anything withfractions, you should always leave the

answer in simplest form. It’s “good mathmanners” to leave things in simplest form.

2

1

10

5

10

2

10

3

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Sometimes when you add fractions, youcan end up with an answer that is more

than one (an improper fraction). Whenthis happens, you should convert youranswer back to mixed number form.

10

3110

13

10

6

10

7

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Multiplying Fractions

When you multiply fractions, it isusually easier to try to simplify before

you do all the work of multiplying.

63

5

733

5

32273

522

12

5

21

4

When you multiply fractions, justmultiply straight across. You do not

need a common denominator.

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If you do not simplifybefore you start

multiplying, you willwork with some larger-than-necessarynumbers.

You will also have tosimplify your answerwhen you finish.

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To simplify, you can either prime factor thenumbers and cross out any numbers thatappear in both the top & bottom –

Or you can ask yourself, “Are there anynumbers in the top & bottom that can bedivided by the same number?”

28

9

8

3

7

6

Are there any numbers (top & bottom)that can be divided by the same number?Yes: 6 and 8 can both be divided by 2.6 ÷ 2 = 3, and 8 ÷ 2 = 4.

3

4

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Dividing Fractions

Dividing fractions is a lot like multiplying fractions.

You do not need a common denominator.

Instead, you will need to use the reciprocal of a

fraction.

The reciprocal is the “upside down” version of afraction.

7

3Thereciprocal

ofis

3

7

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Dividing Fractions

Any number multiplied by itsreciprocal = 1.

We can use this fact to make ourdividing easier.

112

12

3

4

4

3

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Dividing Fractions

8

5

3

2

8

5

3

2

It turns out that multiplying the top &bottom of this horrible thing by thereciprocal of the bottom number willget rid of the bottom part.

15

1115

16

5

8

3

2

All that’s left when you dothat is:

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Dividing Fractions

So, the bottom line is, in order to divide afraction, you simply multiply the first fractionin the problem by the reciprocal of the

second fraction. Here’s another example:

14

11

10

11

7

5

11

10

7

5

1

2

reciprocals

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Wrap-Up

Basically, when dealing with fractions, youneed to remember:

Adding & subtracting call for commondenominators.

Multiplying & dividing do not.

No matter what you are doing, you should leaveall answers in their most simplified form. Thatmeans mixed numbers if you end up with animproper fraction.

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