Functional Skills: Fraction Basics
Functional Skills: Fraction Basics Revision
Fraction Basics
Fractions are for when things are divided into equal parts. They are written as a top number, then a horizontal line, then a bottom number, for example \dfrac{3}{4}, which then the same as 3 \div 4.
The top number shows the number of parts you are considering, while the bottom number shows the number of parts in total. For example, if Bob eats 1 slice of cake and the entire cake is 10 slices, he has eaten \dfrac{1}{10} of the cake.
Make sure you are happy with the following topics before continuing.
Some Common Fractions
Fractions as Divisions
Fractions are also another way of writing divisions, for example \dfrac{2}{5}=2\div5
We can use this to turn fractions into decimals. All we do is type the division into the calculator.
\dfrac{2}{5}=2\div5=0.4
Here are our common fractions as decimals using this method:
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Fractions of Something
If you are asked to calculate a fraction “of” an amount, you multiply the fraction by the amount.
Example:Â Find \dfrac{9}{10} of 40.
To do this, we do \dfrac{9}{10}\times40, which is equivalent to 9\div10\times40, which equals 36.
Equivalent Fractions
Equivalent fractions are fractions that have different numbers on the top and the bottom but represent the same value.
Example:Â \dfrac{1}{2} and \dfrac{2}{4} are equivalent, they have the same value.
\dfrac{1}{2}=1\div2=0.5
\dfrac{2}{4}=2\div4=0.5
Two fractions are equivalent if you multiply or divide the top and the bottom by the same number to get from one to the other.
Example:Â \dfrac{1}{5} is equivalent to \dfrac{3}{15} as we multiply both the top and the bottom by 3.
Example 1: Fractions of Something
Find the following:
a) \dfrac{1}{3} of 45
b) \dfrac{8}{10} of 75
c) \dfrac{2}{5} of 100
[3 marks]
a) \dfrac{1}{3}\times45=1\div3\times45=15
b) \dfrac{8}{10}\times 75=8\div 10\times 75=60
c) \dfrac{2}{5}\times100=2\div5\times100=40
Functional Skills: Fraction Basics Example Questions
Question 1:Â Write these fractions as decimals:
a) \dfrac{2}{5}
b) \dfrac{7}{10}
c) \dfrac{4}{5}
d) \dfrac{2}{3}
What is different about the answer to part d)?
[5 marks]
a) \dfrac{2}{5}=2\div5=0.4
b) \dfrac{7}{10}=7\div10=0.7
c) \dfrac{4}{5}=4\div 5=0.8
d) \dfrac{2}{3}=2\div 3 =0.6666...
The answer to part d) is different because it does not stop.
Question 2:Â Find the following:
a) \dfrac{2}{3} of 600
b) \dfrac{1}{3} of 36
c) \dfrac{3}{4} of 540
d) \dfrac{12}{5} of 290
[4 marks]
a) \dfrac{2}{3}\times600=2\div3\times600=400
b) \dfrac{1}{3}\times 36 =1\div 3\times36=12
c) \dfrac{3}{4}\times540=3\div4\times540=405
d) \dfrac{12}{5}\times 290=12\div5\times 290=696
Question 3:Â Are the following pairs of fractions equivalent?
a) \dfrac{1}{2} and \dfrac{3}{6}
b) \dfrac{1}{3} and \dfrac{3}{12}
c) \dfrac{2}{5} and \dfrac{24}{60}
d) \dfrac{3}{10} and \dfrac{6}{18}
e) \dfrac{2}{10} and \dfrac{5}{25}
[5 marks]
a) These are equivalent because we multiply the top and the bottom by 3 to go from \dfrac{1}{2} to \dfrac{3}{6}.
b) These are not equivalent because the top has been multiplied by 3 while the bottom has been multiplied by 4.
c) These are equivalent because we multiply the top and the bottom by 12 to go from \dfrac{2}{5} to \dfrac{12}{60}.
d) These are not equivalent because the top has been multiplied by 2 but the new bottom is 18 while 10\times2=20
e) There is no obvious multiplier for either top or bottom here, so to check we have to turn them into decimals.
\dfrac{2}{10}=2\div10=0.2 and \dfrac{5}{25}=5\div25=0.2, so they are the same, so they are equivalent.
Question 4:Â Which of these fractions is not equivalent to \dfrac{3}{5}?
\dfrac{12}{20},\dfrac{6}{10},\dfrac{24}{35},\dfrac{9}{15},\dfrac{150}{250}
[3 marks]
For \dfrac{12}{20}, both the top and the bottom have been multiplied by 4, so this is equivalent.
For \dfrac{6}{10}, both the top and the bottom have been multiplied by 2, so this is equivalent.
For \dfrac{24}{35}, the top has been multiplied by 8, but 5\times8=40 so the bottom has not been multiplied by 8. So, this is not equivalent.
For \dfrac{9}{15}, both the top and the bottom have been multiplied by 3, so this is equivalent.
For \dfrac{150}{250}, both the top and the bottom have been multiplied by 50, so this is equivalent.
Therefore, the only non-equivalent fraction is \dfrac{24}{35}.
Functional Skills: Fraction Basics Worksheet and Example Questions
