Home

Maths

Fractions

Simplifying fractions

Select Lesson

Algebra

Simple formulae

Linear number sequences

Missing number problems

Solving equations with two unknowns

Ratio and proportion

Solving ratio problems

Calculating percentages of amounts

Scale factor problems

Unequal sharing

Statistics

Pie charts

Line graphs

Discrete and continuous data

Mean, median, mode and range

Geometry - position and direction

Coordinate polygons

Drawing and reflecting shapes on the coordinate grid

Drawing and translating shapes on the coordinate grid

Describing positions in the four quadrants

Geometry - properties of shapes

2D shapes: Types and properties

3D shapes: Types and properties

Comparing and classifying shapes

3D shape nets

Geometric shapes: Types and properties

Parts of a circle

Drawing and measuring angles with a protractor

Angles around a point and on a straight line

Finding missing angles

Measurement

Calculate and convert between units of measure

Perimeter of composite rectilinear shapes

Area of irregular shapes

Area of parallelograms and triangles

Formulae for the area and volume of shapes

Calculating the volume of cubes and cuboids

Fractions

Finding fractions of amounts

Mixed numbers and improper fractions

Comparing and ordering fractions greater than 1

Simplifying fractions

Add and subtract fractions: Different denominators

Multiplying pairs of proper fractions

Dividing fractions by whole numbers

Equivalent fractions, decimals and percentages

Multiplying decimals by whole numbers

Dividing and expressing the answer as a decimal

Multiplication and division

Times tables up to 12 x 12

Multiplying a 4-digit number by a 1 or 2-digit number

Dividing numbers up to 4 digits by a 2-digit number

Mental maths strategies

Common factors and multiples

Order of operations: BIDMAS

Using estimation to check answers

Addition and subtraction

Adding numbers using mental maths

Using column addition to add numbers

Subtracting numbers using mental maths

Using column subtraction to subtract numbers

Multi-step problems with addition and subtraction

Inverse operations to check calculations

Number and place value

Numbers to 10,000,000

Place value: Four-digit numbers

Representing numbers in different ways

Rounding any number up to 1,000,000

Counting using positive and negative numbers

Counting in powers of 10

Negative numbers

Explainer Video

Tutor: Toby

Summary

Simplifying fractions

In a nutshell

To simplify a fraction, you reduce the fraction to its lowest form. The lowest form of a fraction occurs when the numerator (top number) and denominator (bottom number) have no common factors except $1$ .

Example 1

Below are some examples of fractions in their lowest form.

$\frac{1}{3}, \frac{2}{9}, \frac{13}{20}$ 

Simplifying fractions

The quickest way to simplify a fraction is to divide by the highest common factor (HCF). The highest common factor is the largest factor that the numerator and denominator have in common.

Procedure

1.	Determine the HCF of the numerator and the denominator.
2.	Divide both the numerator and the denominator by the HCF. The resulting fraction is in its simplest form.

Example 2

Give the fraction $\frac{12}{20}$  in its simplest form.

List the factors of the numerator and the denominator:

Numerator: $1, 2, 3, 4, 6, 12$

Denominator: $1, 2, 4, 5, 10, 20$

Identify the largest number that appears on both lists:

$4$

Divide the numerator and denominator by the HCF:

$\frac{12\div4}{20\div4}= \underline{\frac{3}{5}}$

Tip: If the numerator and denominator are even, you can always divide by $2$ .

Expanding fractions

To add, subtract or compare fractions the denominators need to be the same.

procedure

1.	Identify the multiplier needed to give both fractions a common denominator.
2.	Multiply the numerator and denominator by the answer found in Step 1.

Example 3

Which fraction is greater, $\frac{3}{4}$  or $\frac{7}{8}$ ?

Identify the multiplier needed to give each fraction a common denominator:

$4\times2 = 8$ 

Multiply the numerator and denominator by the multiplier:

$\frac{3\times2}{4\times2} = \frac{6}{8}$ 

Compare the two fractions:

$\frac{6}{8}<\frac{7}{8}$ therefore $\underline{\frac{3}{4}<\frac{7}{8}}$ 

Learn with Basics

Length:

$Add and subtract fractions: Same denominator$

Unit 1

Add and subtract fractions: Same denominator

$Add and subtract fractions: Denominators are multiples$

Unit 2

Add and subtract fractions: Denominators are multiples

Jump Ahead

Optional

$Simplifying fractions$

Unit 3

Simplifying fractions

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do I simplify fractions?

1. Determine the highest common factor (HCF) of the denominator and the numerator. 2. Divide both the numerator and the denominator by the HCF. The resulting fraction is in its simplest form.

What is highest common factor?

The highest common factor is the largest factor that the numerator and denominator have in common.

What is a simplified fraction?

To simplify a fraction, you reduce the fraction to its lowest form. The lowest form of a fraction occurs when the numerator and denominator have no common factors except 1.

Home

Maths

Fractions

Simplifying fractions

Videos

Summary

Exercises

Select Lesson

Algebra

Simple formulae

Linear number sequences

Missing number problems

Solving equations with two unknowns

Ratio and proportion

Solving ratio problems

Calculating percentages of amounts

Scale factor problems

Unequal sharing

Statistics

Pie charts

Line graphs

Discrete and continuous data

Mean, median, mode and range

Geometry - position and direction

Coordinate polygons

Drawing and reflecting shapes on the coordinate grid

Drawing and translating shapes on the coordinate grid

Describing positions in the four quadrants

Geometry - properties of shapes

2D shapes: Types and properties

3D shapes: Types and properties

Comparing and classifying shapes

3D shape nets

Geometric shapes: Types and properties

Parts of a circle

Drawing and measuring angles with a protractor

Angles around a point and on a straight line

Finding missing angles

Measurement

Calculate and convert between units of measure

Perimeter of composite rectilinear shapes

Area of irregular shapes

Area of parallelograms and triangles

Formulae for the area and volume of shapes

Calculating the volume of cubes and cuboids

Fractions

Finding fractions of amounts

Mixed numbers and improper fractions

Comparing and ordering fractions greater than 1

Simplifying fractions

Add and subtract fractions: Different denominators

Multiplying pairs of proper fractions

Dividing fractions by whole numbers

Equivalent fractions, decimals and percentages

Multiplying decimals by whole numbers

Dividing and expressing the answer as a decimal

Multiplication and division

Times tables up to 12 x 12

Multiplying a 4-digit number by a 1 or 2-digit number

Dividing numbers up to 4 digits by a 2-digit number

Mental maths strategies

Common factors and multiples

Order of operations: BIDMAS

Using estimation to check answers

Addition and subtraction

Adding numbers using mental maths

Using column addition to add numbers

Subtracting numbers using mental maths

Using column subtraction to subtract numbers

Multi-step problems with addition and subtraction

Inverse operations to check calculations

Number and place value

Numbers to 10,000,000

Place value: Four-digit numbers

Representing numbers in different ways

Rounding any number up to 1,000,000

Counting using positive and negative numbers

Counting in powers of 10

Negative numbers

Explainer Video

Tutor: Toby

Summary

Simplifying fractions

In a nutshell

Example 1

Below are some examples of fractions in their lowest form.

$\frac{1}{3}, \frac{2}{9}, \frac{13}{20}$ 

Simplifying fractions

The quickest way to simplify a fraction is to divide by the highest common factor (HCF). The highest common factor is the largest factor that the numerator and denominator have in common.

Procedure

1.	Determine the HCF of the numerator and the denominator.
2.	Divide both the numerator and the denominator by the HCF. The resulting fraction is in its simplest form.

Example 2

Give the fraction $\frac{12}{20}$  in its simplest form.

List the factors of the numerator and the denominator:

Numerator: $1, 2, 3, 4, 6, 12$

Denominator: $1, 2, 4, 5, 10, 20$

Identify the largest number that appears on both lists:

$4$

Divide the numerator and denominator by the HCF:

$\frac{12\div4}{20\div4}= \underline{\frac{3}{5}}$

Tip: If the numerator and denominator are even, you can always divide by $2$ .

Expanding fractions

To add, subtract or compare fractions the denominators need to be the same.

procedure

1.	Identify the multiplier needed to give both fractions a common denominator.
2.	Multiply the numerator and denominator by the answer found in Step 1.

Example 3

Which fraction is greater, $\frac{3}{4}$  or $\frac{7}{8}$ ?

Identify the multiplier needed to give each fraction a common denominator:

$4\times2 = 8$ 

Multiply the numerator and denominator by the multiplier:

$\frac{3\times2}{4\times2} = \frac{6}{8}$ 

Compare the two fractions:

$\frac{6}{8}<\frac{7}{8}$ therefore $\underline{\frac{3}{4}<\frac{7}{8}}$ 

Learn with Basics

Length:

$Add and subtract fractions: Same denominator$

Unit 1

Add and subtract fractions: Same denominator

$Add and subtract fractions: Denominators are multiples$

Unit 2

Add and subtract fractions: Denominators are multiples

Jump Ahead

Optional

$Simplifying fractions$

Unit 3

Simplifying fractions

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do I simplify fractions?

1. Determine the highest common factor (HCF) of the denominator and the numerator. 2. Divide both the numerator and the denominator by the HCF. The resulting fraction is in its simplest form.

What is highest common factor?

The highest common factor is the largest factor that the numerator and denominator have in common.

What is a simplified fraction?

To simplify a fraction, you reduce the fraction to its lowest form. The lowest form of a fraction occurs when the numerator and denominator have no common factors except 1.