# Functional Skills: Fractions, Decimals and Percentages

## Functional Skills: Fractions, Decimals and Percentages Revision

**Fractions, Decimals and Percentages**

Here we will look at how to convert betweenÂ **fractions**,Â **decimals**, andÂ **percentages**.Â All 3 forms are equivalent ways of saying the same thing, but we normally use the one that is most appropriate in that particular scenario.

For LEVEL 1, you will only need convert between **fractions**,Â **decimals**, andÂ **percentages**, that when converted to a percentage are a multiple of 5\%, e.g. 5\%, 10\%, 50\% etc. For LEVEL 2 you will need to use these skills for more complicated percentages, e.g. 2\%, 12.5\% etc.

Make sure you are happy with the following topics before continuing.

### Question - How do I improve my chances of passing the level 2 maths exam?

Answer – Pre-assessment. This useful tool identifies the key areas of the exam you will need to work on in order to pass your level 2 exam for the first time.

**Common Conversions**

**Fractions**, **decimals**Â and **percentages** conversions are really useful to memorise.

These are some common **fractions**, **decimals**Â and **percentages** you should remember.

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**Converting Fractions to Decimals to Percentages**

**Fractions**** to ****Decimals****:**

Treat the fraction like a division, so divide the top number of the fraction by the bottom number,

e.g. \dfrac{13}{20} = 13 \div 20 = 0.65

**Decimals**** to ****Percentages****:**

Multiply the decimal by 100 (i.e. move the decimal point 2 places to the right) and add a \% sign,

e.g. 0.65 \times 100 = 65\%

**Note:** Convert **fractions** to **percentages** by converting the **fraction** to a **decimal** and then the **decimal** to a **percentage**

e.g. \dfrac{65}{100} = 0.65 = 65\%

**Converting Percentages to Decimals to Fractions**

**Percentages**** to ****Decimals****:**

Divide by 100 (i.e. move the decimal point 2 places to the left) and remove the \% sign,

e.g. 65\% \div 100 = 0.65

**Decimals**** to ****Fractions****:**

Write the decimal as a fraction with 1 on the bottom. Then, repeatedly multiply the top and the bottom of the fraction by 10 until the top number turns into a whole number,

e.g. 0.65 = \dfrac{0.65}{1} = \dfrac{6.5}{10} = \dfrac{65}{100}

Then, you can simplify the fraction if needed: \dfrac{65}{100} = \dfrac{13}{20}

**Note:** To convert straight from **percentages** to **fractions**, write the percentage as a fraction with 100 on the bottom, without the \% sign, and then simplify it

e.g. 65\% = \dfrac{65}{100} = \dfrac{13}{20}

**Comparing Fractions, Decimals and Percentages – Level 1**

For Level 1, you will only need to be able to compare and order **fractions**, **decimals** and **percentages**, that when converted to a percentage are a multiple of 5.

**Example:** Put the following in order from smallest to largest:

25\%Â Â Â Â Â \dfrac{1}{5}Â Â Â Â Â \dfrac{3}{20}Â Â Â Â Â 0.3

**Step 1:** Convert all of the numbers into the same form (converting all to **decimals** is usually the easiest):

25\% = 0.25

\dfrac{1}{5} = 0.2

\dfrac{3}{20} = 0.15

**Step 2:** Rewrite the list as decimals:

0.25Â Â Â Â Â 0.2Â Â Â Â Â 0.15Â Â Â Â Â 0.3

**Step 3:** Put the list in order from smallest to largest, using the technique of ordering decimals:

0.15Â Â Â Â Â 0.2Â Â Â Â Â 0.25Â Â Â Â Â 0.3

**Step 4: **Write down the order, converting the decimals back into their original form:

\dfrac{3}{20}Â Â Â Â Â \dfrac{1}{5}Â Â Â Â Â 25\%Â Â Â Â Â 0.3

**Comparing Fractions, Decimals and Percentages – Level 2**

You will need to be able to compare and order **fractions**, **decimals** and **percentages.**

**Example:** Put the following in order from smallest to largest:

23\%Â Â Â Â Â \dfrac{1}{4}Â Â Â Â Â \dfrac{6}{25}Â Â Â Â Â 0.245

**Step 1:** Convert all of the numbers into the same form (converting all to **decimals** is usually the easiest):

23\% = 0.23

\dfrac{1}{4} = 0.25

\dfrac{6}{25} = 0.24

**Step 2:** Rewrite the list as decimals:

0.23Â Â Â Â Â 0.25Â Â Â Â Â 0.24Â Â Â Â Â 0.245

**Step 3:** Put the list in order from smallest to largest, using the technique of ordering decimals:

0.23Â Â Â Â Â 0.24Â Â Â Â Â 0.245Â Â Â Â Â 0.25

**Step 4: **Write down the order, converting the decimals back into their original form:

23\%Â Â Â Â Â \dfrac{6}{25}Â Â Â Â Â 0.245Â Â Â Â Â \dfrac{1}{4}

**Example 1: Converting Percentages and Decimals**

**a)** Write 47\% as a **decimal**.

**[1 mark]**

Divide by 100 and remove the \%, so,

47 \div 100 = 0.47

**b)** Write 0.548 as a **percentage**.

**[1 mark]**

Multiply by 100 and add a \% sign, so,

0.548 \times 100 = 54.8\%

### Improve your chances of passing your functional skills maths exam.

Take a pre-assessment and understand what topic areas you need to work on to ensure you pass for level 2 maths exam first time.

**Example 2: Converting Fractions and Decimals**

**a)** Write \dfrac{11}{20} as a **decimal**.

**[2 marks]**

For a quick method, notice that 20\times 5=100 and dividing by 100 is easy. So, multiply the top and bottom of the fraction by 5 to get

\dfrac{11\times 5}{20\times 5} =\dfrac{55}{100}=0.55

**b)** Write \dfrac{11}{8} as a **decimal**.

**[2 marks]**

Here, we just need to divide 11 by 8.Â The best way to do this is to use the bus stop method:

So,

\dfrac{11}{8} = 1.375

**c)** Write 3.76 as a **fraction** in its simplest form.

**[2 marks]**

Write the decimal as a fraction with a 1 on the bottom. Then, repeatedly multiply the top and the bottom of the fraction by 10 until the top number turns into a whole number,

\dfrac{3.76}{1}=\dfrac{37.6}{10} = \dfrac{376}{100}

Finally, simplify the fraction:

\dfrac{376}{100} = \dfrac{188}{50} = \dfrac{94}{25}

**Example 3: Converting Percentages and Fractions**

**a)** Write 28.5\% as a **fraction**Â in its simplest form.

**[2 marks]**

Percentages are out of 100, so write it as a fraction with 100 on the bottom:

28.5\%=\dfrac{28.5}{100}

Then, multiply the top and bottom by 10 (to make them whole numbers):

28.5\% = \dfrac{285}{1000}

Finally, simplify the fraction:

\dfrac{285}{1000} = \dfrac{57}{200}

**b) **Write \dfrac{3}{5} as a **percentage**.

**[2 marks]**

Firstly, convert the fraction to a decimal. Notice that,

\dfrac{3}{5}=\dfrac{3\times 2}{5\times 2} = \dfrac{6}{10}

So,

6\div 10 = 0.6

Then, to convert this decimal to a percentage, by multiplying by 100 and adding a \% sign:

0.6 \times 100 = 60\%

**Example 4: Converting Fractions, Decimals and Percentages**

**a) **Write 85\% as a decimal.

**[1 mark]**

Divide by 100 and remove the \%, so,

85\div 100=0.85

**b)Â **Write 0.35 as a percentage.

**[1 mark]**

Multiply by 100 and add a \% sign, so,

0.35\times 100=35\%

**c)Â **Write \dfrac{9}{20} as a decimal.

**[1 mark]**

For this fraction, to work out what it is equivalent as a decimal, we can convert the fraction so the denominator is 100.

\dfrac{9}{20}=\dfrac{45}{100}=0.45

**d) **Write \dfrac{3}{4} as a percentage.

**[2 marks]**

Firstly, convert the fraction to a decimal then to a percentage.

\dfrac{3}{4}=0.75=75\%

## Functional Skills: Fractions, Decimals and Percentages Example Questions

**Question 1:** Write 19.4\% as a decimal.

**[1 mark]**

Divide by 100 and remove the \% sign:

19.4\%\div100=0.194

**Question 2:** Write 12.5\% as a fraction in its simplest form.

**[2 marks]**

Write the percentage as a fraction with 100 on the bottom:

12.5\% = \dfrac{12.5}{100}

Now, multiply the top and bottom by 10 so that both numbers are whole:

\dfrac{12.5}{100} = \dfrac{125}{1000}

Finally, simplify the fraction:

\dfrac{125}{1000} = \dfrac{1}{8}

**Question 3:** Write \dfrac{19}{40} as a decimal.

**[2 marks]**

Treat the fraction as a division and divide 19 by 40,

\;\;\;\;\;0\;0.\;\;4\;\;\;7\;\;\;5\\40\overline{\left)1{}^19.{}^{19}0{}^{30}0{}^{20}0\right.}

So,

\dfrac{19}{40}=0.475

**Question 4:** Write 0.712 as a fraction in its simplest form.

**[2 marks]**

Write this decimal as a fraction with 1 on the bottom:

0.712=\dfrac{0.712}{1}

Make the numbers whole by multiplying the top and bottom of the fraction by 1000:

\dfrac{0.712 \times 1000}{1 \times 1000}=\dfrac{712}{1000}

Finally, simplify the fraction fully:

\dfrac{712}{1000}=\dfrac{89}{125}

**Question 5:** Write the following in order from largest to smallest:

\dfrac{1}{2}Â Â Â Â Â \dfrac{13}{25}Â Â Â Â Â Â 0.51Â Â Â Â Â 51.2\%

**[2 marks]**

Convert all of the numbers into decimals:

\dfrac{1}{2} = 0.5

\dfrac{13}{25} = 0.52

51.2\% = 0.512

Rewrite the list as decimals:

0.5Â Â Â Â Â 0.52Â Â Â Â Â 0.51Â Â Â Â Â 0.512

Put the list in order from largest to smallest, using the technique of ordering decimals:

0.52Â Â Â Â Â 0.512Â Â Â Â Â 0.51Â Â Â Â Â 0.5

Write down the order, converting the decimals back into their original form:

\dfrac{13}{25}Â Â Â Â Â 51.2\%Â Â Â Â Â 0.51Â Â Â Â Â \dfrac{1}{2}

**Question 6:Â **Write the following in order from smallest to largest:

\dfrac{6}{10}Â Â Â Â Â 55\%Â Â Â Â Â 0.65Â Â Â Â Â \dfrac{14}{20}

**[2 marks]**

Convert all of the numbers into decimals:

\dfrac{6}{10}=0.6

55\%=0.55

\dfrac{14}{20}=0.7

Put these decimals in order:

0.55Â Â Â Â Â 0.6Â Â Â Â Â 0.65Â Â Â Â Â 0.7

Write down the order, converting the decimals back into their original form:

55\%Â Â Â Â Â \dfrac{6}{10}Â Â Â Â Â 0.65Â Â Â Â Â \dfrac{14}{20}

**Question 7:Â **Write 115\% as decimal.

**[1 mark]**

Divide by 100 and remove the \% sign:

115\% \div 100=1.15

## Functional Skills: Fractions, Decimals and Percentages Worksheet and Example Questions

### Fractions, Decimals and Percentages L1

FS Level 1NewOfficial PFS### Fractions, Decimals and Percentages L2

FS Level 2NewOfficial PFS[responsive-flipbook id=”pfs_pocket_revision_guide_-_sample”]

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