Fraction Guide



Fraction Guide

Page 1 Intro to Fractions

Page 2 Three types of Fractions: Improper, proper, and mixed.

Page 3 Changing Fractions

Page 3 Making whole numbers into fractions

Page 4 Equivalent Fractions

Page 4 Comparing Fractions

Page 5 Adding fractions with like denominators

Page 6 Subtracting fractions with like denominators

Page 7 Adding fractions with unlike denominators

Page 8 Subtracting fractions with unlike denominators

Page 9 How to reduce or simply fractions

Page 10 Adding/subtracting mixed numbers

Page 11 Changing a fraction to a percent or decimal

Page 12 Multiplying fractions

Page 13 Dividing fractions

Intro to Fractions

A fraction is a part of a whole

Slice a pizza, and you will have fractions:

|[pic] |[pic] |[pic] |

|1/2 |1/4 |3/8 |

|(One-Half) |(One-Quarter) |(Three-Eighths) |

|  |  |  |

|The top number tells how many slices you have and the bottom number tells how many slices the pizza |

|was cut into. |

Here are some examples:

[pic]

Numerator / Denominator

Top number = Numerator, it is the number of parts you have.

Bottom number = Denominator, it is the number of parts the whole is divided into.

numerator

denominator

Page 1

Three Types of Fractions

There are three types of fractions:

[pic]

Examples of Proper Fractions

(Bottom # is bigger than top #)

Examples of Improper Fractions

(Top # is bigger than bottom #)

Examples of Mixed Numbers

(A whole # and a fraction)

Page 2

Changing Fractions

Multiply the bottom number by the big number, then add the top number. Keep the bottom number the same.

Example: 3 x 2 + 1 = 7 Answer:

Ask a question. How many times can the bottom number go into the top number without going over?

Your answer will be the big number. Put your remainder on top, and the bottom remains the

same.

Example: How many times can 3 go into 17

without going over? (5 times) Then, there is 2 left over, which goes on the top, and 3 stays on the bottom.

Any whole number can be made into a fraction by putting it over 1.

Example: =

Page 3

Equivalent Fractions

Equivalent fractions are fractions that are equal, but use different numbers.

Multiply both the top and bottom number by another number.

Example: I am going to multiply it by 2.

Remember:

What you do to the top of the fraction

you must also do to the bottom of the fraction !

You can use any number you want to multiply it by, but it is usually easier to do low numbers.

Comparing Fractions

When comparing fractions, use the < , > , or = sign.

Since 9 is bigger, that means the fraction on that side is bigger.

Page 4

Adding fractions with like denominators

1. Add the top numbers.

2. Put the answer over the same bottom number.

3. When you are done, you may need to reduce the fraction or change it to a mixed number.

Example:

Now, since it is an improper fraction, I have to change it to a mixed number.

Page 5

Subtracting fractions with like denominators

1. Subtract the top numbers.

2. Put the answer over the same bottom number.

3. When you are done, you may need to reduce the fraction or change it to a mixed number.

Example:

Now, since it is an improper fraction, I have to change it to a mixed number.

Page 6

Adding fractions with unlike denominators

When adding fractions that have unlike denominators, your first step is to get the denominators the same.

Multiply by the opposite bottom number.

x 4 x 3

Now you can add the top numbers.

Your last step is to reduce or change it to a mixed number. In this case, since it is an improper fraction, you have to change it to a mixed number.

Shortcut: If you have a bottom number that goes evenly into the other bottom number, you only have to multiply one side.

Example:

3 can go into six evenly if I multiply it by 2

Page 7

Subtracting fractions with unlike denominators

When subtracting fractions that have unlike denominators, your first step is to get the denominators the same.

Multiply by the opposite bottom number.

x 3 x 4

Now you can subtract the top numbers.

Your last step is to reduce or change it to a mixed number. In this case, you cannot reduce it any further.

Shortcut: If you have a bottom number that goes evenly into the other bottom number, you only have to multiply one side.

Example:

3 can go into six evenly if I multiply it by 2

Page 8

Reducing or Simplifying Fractions

* Can also be called “lowest terms”

When you are ready to put your final answer on paper, you must ask yourself, “Can this fraction be reduced?” Your answer will not be correct unless you reduce the fraction first.

What that means is making the fraction look as small as it can, while still keeping the same value of the fraction.

Steps:

1. Ask: What can both the top and bottom number be divided by?

Example:

In this case, the number that both can be divided by is 3.

2. Do the division.

Once you do your division, check to see if it can be reduced again.

Page 9

Adding and Subtracting Mixed Numbers

When subtracting fractions that are mixed numbers, the same rules apply as when you are adding and subtracting regular fractions. If you forgot how to add and subtract fractions, look at pages 5, 6, 7 and 8 for more help. (

Adding Example:

(like denominator)

1. Add the whole numbers.

2. Then add the fraction.

Adding Example:

(unlike denominator)

1. Get the denominators the same by multiplying.

2. Add the whole numbers.

3. Then add the fractions.

When you are subtracting mixed numbers you can do it exactly the same as adding, EXCEPT WHEN THE FIRST FRACTION IS SMALLER THAN THE SECOND FRACTION. Then, there is a different way. If you are not sure if it is smaller or not, you can do this way and still get the correct answer.

Subtracting Example:

1. Change both numbers to an improper fraction. (page 3)

2. Subtract the numbers.

3. Change back to a mixed number.

Page 10

Changing Fractions to a Percent or Decimal

In order to change a fraction into a

decimal, you must divide.

The top number must go on the INSIDE of the division problem

Example:

4 ) 3

Last, DO the long division. 4) 3

In order to change a decimal into a

percent, you must move the decimal point.

Example: .75 Move the decimal point TWO places to the right.

= 75%

No matter what, you always move it TWO places!

Examples: 1.75 = 175%

.485 = 48.5%

.5826 = 58.26%

25 = 2500%

Page 11

Multiplying Fractions

When you multiply fractions, you DO NOT need to have the same denominator.

Step 1: Multiply across

Step 2: Reduce or simplify if needed.

If you have a mixed number, you should change the mixed number to an improper fraction before starting. (If you forgot how to change a mixed number into an improper fraction, go to page 3.)

Example:

Now you must change it back to a mixed number.

(If you forgot how to do that, look at page 3.)

Now reduce it.

Page 12

Dividing Fractions

When you divide fractions, you DO NOT need to have the same denominator.

Dividing is the same as multiplying, but with some extra steps in the beginning.

Step 1: Get the reciprocal of the SECOND number. A reciprocal is when you flip the fraction upside down.

The reciprocal of

Step 2: Change the division sign to a multiplication sign.

Step 3: Multiply the fraction. (If you forgot how to multiply, see page 12)

Step 4: Reduce or simplify if needed.

If you have a mixed number, you should change the mixed number to an improper fraction before starting. (If you forgot how to change a mixed number into a fraction, go to page 3.)

Page 13[pic][pic]

-----------------------

[pic]

|7|8|

| |9|

Change a mixed number to an improper fraction:

7

2

9

4

2

3

3

4

1

2

5

3

|2|1|

| |3|

|4|2|

| |5|

|2|1|

| |3|

7

3

Change an improper fraction to a mixed number:

17

3

|5|2|

| |3|

Change a whole number into a fraction:

12

1

|12 |

How to find an equivalent fraction:

2

3

4

6

=

2

3

3

4

Cross multiply at an upwards angle and write the number at the top. Do the same for the other side.

8

9

3

4

<

2

3

1

4

1

4

2

4

=

+

3

4

5

4

2

4

=

5

4

=

|1|1|

| |4|

=

2

4

1

4

3

4

5

4

2

4

7

4

-

=

|1|1|

| |4|

=

5

4

+

-

2

3

3

4

+

=

4 x 2

4 x 3

3 x 3

4 x 3

+

+

=

=

9

12

8

12

17

12

17

12

=

|1|5 |

| |12 |

3

6

1

3

2

6

3

6

5

6

+

+

=

x 2

-

=

2

3

3

4

-

3 x 3

4 x 3

4 x 2

4 x 3

=

1

12

8

12

9

12

=

-

9

12

9

12

1

12

1

3

3

6

-

x 2

=

-

1

6

2

6

3

6

(3

(3

=

3

4

=

8

15

x

4

5

2

3

Change a decimal to a percent

=

=

3

4

Change a fraction to a decimal

|1|4 |

| |5 |

+

Reduce

|1|8 |

| |10 |

Change back to mixed #

18

10

=

=

17

10

-

35

10

|1|7 |

| |10 |

-

|3|5 |

| |10 |

|1|5 |

| |12 |

|1|2 |

| |12 |

|2|7 |

| |12 |

=

+

|1|1 |

| |3 |

|1|3 |

| |6 |

|1|5 |

| |6 |

2 x 4

3 x 5

|3|5 |

| |10 |

x

1

2

=

35

10

x

1

2

=

35

20

|1|15 |

| |20 |

|1|3 |

| |4 |

2

3

4

5

(

5

4

4

5

=

2

3

x

5

4

2

3

x

5

4

=

10

12

5

6

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