# 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}.