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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:
𝟏
𝟏
𝟏
𝟏
To find 𝟐 of a number ÷ by 2, to find 𝟑 ÷ by 3, to find 𝟒 ÷ by 4, to find 𝟓 ÷ 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 (𝑒𝑔
12
5
).
2
A mixed number has both a whole number and a fraction (𝑒𝑔 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
+
=
(𝑡ℎ𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑠 𝑐𝑎𝑛 𝑏𝑒 𝑎𝑑𝑑𝑒𝑑 𝑎𝑠 𝑡ℎ𝑒 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟𝑠 𝑎𝑟𝑒 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒)
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