Download Fraction Guide

Fraction Guide
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Intro to Fractions
Three types of Fractions: Improper, proper, and mixed.
Changing Fractions
Making whole numbers into fractions
Equivalent Fractions
Comparing Fractions
Adding fractions with like denominators
Subtracting fractions with like denominators
Adding fractions with unlike denominators
Subtracting fractions with unlike denominators
How to reduce or simply fractions
Adding/subtracting mixed numbers
Changing a fraction to a percent or decimal
Multiplying fractions
Dividing fractions
Intro to Fractions
A fraction is a part of a whole
Slice a pizza, and you will have fractions:
1
1
/2
(One-Half)
/4
(One-Quarter)
3
/8
(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:
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:
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)
2
3
1
2
3
4
5
3
7
2
9
4
1
23
2
45
8
79
Page 2
Changing Fractions
Change a mixed
number to an
improper
fraction:
Multiply the bottom number by the big number,
then add the top number. Keep the bottom
number the same.
Example:
Change an
improper
fraction to a
mixed number:
3x2+1=7
1
23
7
3
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:
17
3
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.
2
53
Change a whole
number into a
fraction:
Example:
Any whole number can be made into a fraction
by putting it over 1.
12
=
12
1
Page 3
Equivalent Fractions
Equivalent fractions are fractions that are equal, but use different numbers.
How to find an
equivalent
fraction:
Multiply both the top and bottom number by
another number.
Example:
I am going to multiply it by 2.
2
3
Remember:
4
6
=
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.
Cross multiply at an
upwards angle and
write the number at
the top. Do the same
for the other side.
8
9
2
3
3
4
Since 9 is bigger, that means
the fraction on that side is
bigger.
2
3
<
3
4
Page 4
Adding fractions with like denominators
1. Add the top numbers.
2. Put the answer over the same bottom number.
1
4
1
4
+
=
2
4
3. When you are done, you may need to reduce the fraction or
change it to a mixed number.
Example:
3
4
+
2
4
=
5
4
Now, since it is an improper fraction, I have to change it to a mixed
number.
5
4
= 11
4
Page 5
Subtracting fractions with like denominators
1. Subtract the top numbers.
2. Put the answer over the same bottom number.
-
3
4
1
4
=
2
4
3. When you are done, you may need to reduce the fraction or
change it to a mixed number.
Example:
7
4
-
2
4
=
5
4
Now, since it is an improper fraction, I have to change it to a mixed
number.
5
4
= 11
4
Page 6
Adding fractions with unlike denominators
When adding fractions that have unlike denominators, your first step
is to get the denominators the same.
2
3
+
3
4
Multiply by the opposite bottom number.
=
x4
x3
+
4x2
4x3
8
12
+
3x3
4x3
9
12
=
17
12
=
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.
17
12
5
=
112
Shortcut: If you have a bottom number that goes evenly into the other
bottom number, you only have to multiply one side.
Example:
x2
1
3
2
6
+
3
6
+
3
6
3 can go into six evenly if I multiply it by 2
=
5
6
Page 7
Subtracting fractions with unlike denominators
When subtracting fractions that have unlike denominators, your first
step is to get the denominators the same.
-
3
4
2
3
Multiply by the opposite bottom number.
=
x 3
x4
3x3
4x3
9
12
-
4x2
4x3
-
8
12
=
1
12
=
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.
1
12
Shortcut: If you have a bottom number that goes evenly into the other
bottom number, you only have to multiply one side.
Example:
x2
3
6
-
1
3
3
6
-
2
6
3 can go into six evenly if I multiply it by 2
=
1
6
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?
9
12
Example:
In this case, the number that both can be divided by is 3.
2. Do the division.
9
12
3
3
=
3
4
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)
5
112
+
2
112
7
=
212
1. Add the whole numbers.
2. Then add the fraction.
Adding Example:
(unlike denominator)
1
13
+
=
3
16
5
1
= 6
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:
5
310
-
7
110
1. Change both numbers to an improper fraction. (page 3)
2. Subtract the numbers.
3. Change back to a mixed number.
35
10
-
17
10
=
18
10
Change back
to mixed #
8
110
Reduce
4
15
Page 10
Changing Fractions to a Percent or Decimal
Change a
fraction to a
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:
3
4
=
4)3
Last, DO the long division.
Change a
decimal to a
percent
Example:
4) 3
In order to change a decimal into a
percent, you must move the decimal point.
.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
2x4
x
2
3
4
5
=
8
15
3x5
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:
5
310
x
35
10
x
=
1
2
1
2
=
35
20
Now you must change it back to a mixed number.
(If you forgot how to do that, look at page 3.)
15
120 Now reduce it.
3
14
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.

2
3
4
5
Step 1: Get the reciprocal of the SECOND number. A reciprocal is
when you flip the fraction upside down.
The reciprocal of
=
4
5
5
4
Step 2: Change the division sign to a multiplication sign.
2
3
x
5
4
Step 3: Multiply the fraction. (If you forgot how to multiply, see page 12)
2
3
x
5
4
=
10
12
Step 4: Reduce or simplify if needed.
5
6
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.)
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