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Academic Skills Advice
Summary
Fractions
2
3
2
3
means that something has been cut into 3 equal pieces and you have 2 of them.
also means 2 ÷ 3 (written as 3 2.00 when you do the calculation)
2
If the top and bottom number are the same you have a whole one: 2 = 1
3
3
= 1 etc
Finding Fractions of Numbers:




To find  of a number ÷ by 2, to find  ÷ by 3, to find  ÷ by 4, to find  ÷ by 5, etc.
Always divide by the bottom number, then multiply by the top number:
x
Answer
2
3
of 12
12 ÷ 3 = 4
4 x 2 = 8 (to find 1 third ÷3 then x2 to find 2 thirds).
÷
Equivalent Fractions:
Some fractions are exactly the same size as each other. You can times (multiply) or divide
the top and bottom numbers as long as you remember the rule of fractions:
Always do the same to the top as the bottom
Nb. When you divide make sure you use a number that you can divide both the top and
the bottom by. This is called simplifying or cancelling.
Improper Fractions & Mixed Numbers:
An Improper fraction is top heavy (
12
5
).
2
A mixed number has both a whole number and a fraction ( 5 3 ).
Converting from Improper to Mixed:
Divide the bottom number into the top then write the remainder as the fraction.
Example:
13
5
How many 5’s in 13 (2) how many left over? (3) = 2
3
5
Converting from Mixed to Improper:
Multiply the whole number by the bottom number of the fraction then add on the top
number of the fraction.
Example: 4
2
3
4 x 3 = 12 then add the extra 2 on. You have 14 thirds =
© H Jackson 2012 / ACADEMIC SKILLS
14
3
1
Multiplying Fractions:


Cancel first (remember always to cancel a pair – top & bottom)
Multiply top by top and bottom by bottom
1
2
3
10
×
25
=
21
2
(1×2)
The 3 (top) and the 21 (bottom) both divide by 3.
35
(5×7)
The 10 (top) and the 25 (bottom) both divide by 5.
7
5
Dividing Fractions:



Change the divide sign into a multiplication sign.
Turn the second fraction upside down.
Multiply as above.
2
5
÷
3
7
=
2
3
×
7
=
5
14
(2×7)
15
(3×5)
Second fraction is
turned upside down.
÷ becomes x
Adding & Subtracting Fractions:


Make sure the denominators are the same (using equivalent fractions)
Add or subtract the top numbers only.
2
5
+
1
3
2
Top &
bottom x3
5
+
1
3
Top &
bottom x5
6
5
15
15
Now we have:
6
5
11
+
=
(ℎ      ℎ   ℎ )
15 15
15
Nb. Use exactly the same method for take away but subtract the top numbers instead of adding.
6
15
−
5
15
=
1
15
© H Jackson 2012 / ACADEMIC SKILLS
2
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