# Fractions, decimals and percentages

## What are fractions, decimals and percentages?

Fractions, decimals and percentages all represent parts of a whole.

## What is a fraction?

A fraction is a way of representing a part, or parts, of a whole. The numerator shows us how many parts we have.

The denominator shows us how many parts there are in total.

## What is a decimal?

A decimal is a number whose whole part and fractional part are separated by a decimal point. It is a way of writing a number that is not a whole number, but is inbetween two whole numbers.

In the above example, the number is bigger than the whole number 3, but smaller than the whole number 4.

The '3' represents 3 ones. The '6' represents 6 tenths.

## What is a percentage?

A percentage of a number or object is how many parts of it there are out of 100 equal parts.

'Percent' means 'per 100'.

In the above example, if you split an object into 100 parts, 75 of the parts make 75%.

## Converting fractions to decimals

To convert a fraction into a decimal, divide the numerator by the denominator.

The simplest method is to use a calculator, but long division can also be used.

## Converting decimals to fractions

To convert a decimal into a fraction, first you need to write the decimal divided by 1, as shown below:

Then, multiply the top and the bottom by 10 for every number after the decimal point (e.g. if there are two numbers after the decimal point, multiply by 100; if there are three numbers after the decimal point, multiply by 1000).

This fraction can then be simplified if possible:

## Converting decimals to percentages

To convert a decimal to a percentage, multiply the decimal by 100:

## Converting percentages to decimals

To convert a percentage to a decimal, divide the percentage by 100:

## Converting fractions to percentages

To convert a fraction into a percentage, first turn it into a decimal by dividing the numerator by the denominator:

Then multiply this decimal by 100:

## Converting percentages to fractions

To convert a percentage into a fraction, put the percentage over 100, and simplify if possible:

## Fractions KS1

In the National Curriculum for KS1, the focus is on fractions.

In Year 1, pupils should be taught to:

• recognise, find and name a half as one of two equal parts of an object, shape or quantity 
• recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

In Year 2, pupils should be taught to:

• recognise, find, name and write fractions 1/3 , 1/4 , 2/4 and 3/4 of a length, shape, set of objects or quantity 
• write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2 .

## Fractions, Decimals and Percentages KS2

In the National Curriculum for KS2, children continue to learn about fractions, and are introduced to decimals in Year 4, and percentages in Year 5.

In Year 3, pupils should be taught to:

• count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
• recognise, find and write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators
• recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators 
• recognise and show, using diagrams, equivalent fractions with small denominators 
• add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7 ] 
• compare and order unit fractions, and fractions with the same denominators 
• solve problems that involve all of the above.

In Year 4, pupils should be taught to:

• recognise and show, using diagrams, families of common equivalent fractions
• count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• add and subtract fractions with the same denominator
• recognise and write decimal equivalents of any number of tenths or hundredths
• recognise and write decimal equivalents to 1/4 , 1/2 , 3/4
• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
• round decimals with one decimal place to the nearest whole number
• compare numbers with the same number of decimal places up to two decimal places
• solve simple measure and money problems involving fractions and decimals to two decimal places.

## Fractions, Decimals and Percentages Year 5

In Year 5, pupils should be taught to:

• compare and order fractions whose denominators are all multiples of the same number
• identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths
• recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5 ]
• add and subtract fractions with the same denominator and denominators that are multiples of the same number
• multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams
• read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]
• recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
• round decimals with two decimal places to the nearest whole number and to one decimal place
• read, write, order and compare numbers with up to three decimal places
• solve problems involving number up to three decimal places
• recognise the per cent symbol (%) and understand that per cent relates to ‘number of parts per hundred’, and write percentages as a fraction with denominator 100, and as a decimal
• solve problems which require knowing percentage and decimal equivalents of 1/2 , 1/4 , 1/5 , 2/5 , 4/5 and those fractions with a denominator of a multiple of 10 or 25.

## Fractions, Decimals and Percentages Year 6

In Year 6, pupils should be taught to:

• use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• compare and order fractions, including fractions > 1
• add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
• multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 1/4 × 1/2 = 1/8 ]
• divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6 ]
• associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]
• identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
• multiply one-digit numbers with up to two decimal places by whole numbers
• use written division methods in cases where the answer has up to two decimal places
• solve problems which require answers to be rounded to specified degrees of accuracy
• recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.