Three Types of Fractions
Proper Fractions:
The numerator is less than the denominator
Examples: 1/3, 3/4, 2/7
Improper Fractions: The numerator is greater than (or equal to) the denominator
Examples: 4/3, 11/4, 7/7
Mixed Numbers:
A whole number and proper fraction together
Examples: 1 1/3, 2 1/4, 16 2/5
Converting Improper Fractions to Mixed Numbers
To convert an improper fraction to a mixed fraction, follow these steps:



Divide the numerator by the denominator.
Write down the whole number answer
Then write down any remainder above the denominator.
Example: Convert 11/4 to a mixed number.
Divide: 11 ÷ 4 = 2 with a remainder of 3
Write down the 2 and then write down the remainder (3)
above the denominator (4), like this:
2
4 1 1
8
3
= 2
3
4
Converting Mixed Numbers to Improper Fractions
To convert a mixed number to an improper fraction, follow these steps:



Multiply the whole number part by the fraction's denominator.
Add that to the numerator
Then write the result on top of the denominator.
Example: Convert 3 2/5 to an improper fraction.
Multiply the whole number by the denominator: 3 × 5 = 15
Add the numerator to that: 15 + 2 = 17
Then write that down above the denominator, like this:
+
3
x
2
5
=
17
5
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Convert Fractions to Decimals
To convert a Fraction to a Decimal manually, follow these steps:
Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or
100, or 1000, or any 1 followed by 0s.
Step 2: Multiply both top and bottom by that number.
Step 3. Then write down just the top number, putting the decimal point in the correct
spot (one space from the right hand side for every zero in the bottom number)
Example 1: Express 3/4 as a Decimal
Step 1: We can multiply 4 by 25 to become 100
Step 2: Multiply top and bottom by 25:
Step 3: Write down 75 with the decimal point 2 spaces from the right
(because 100 has 2 zeros);
×25
3
75
=
4
100
Answer = 0.75
×25
Convert Fractions to Decimals using Division
To convert a Fraction to a Decimal, follow these steps:
Divide the numerator (top number) by the denominator (bottom number).
For the fraction 3/4, the numeral 4 would be the denominator.
4 3
To continue doing this longhand, put a 0. over the top line of the division
symbol and add .0 to the number under the division symbol
0 
4 3  0
Ignore the decimal point that is inside the division symbol and begin the
process of long division.
0  7
4 3  0
2
8
2
0  7
4 3  0
2
8
2
2
Continue adding 0 inside the division symbol if there is a remainder after
the subtraction.
Stop when the answer of the subtraction is 0.
Now the decimal is exactly equivalent to the fraction. ¾ = 0.75
Repeating Decimals: If the subtraction begins to return the same number over and
over --- for example, 1 ÷ 3 repeatedly returns a remainder of 1 --- you have a repeating
decimal. Write it using a repeat bar.
5
0
0
0
0
_
0.3
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