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Maths

Ratio and proportion

Unequal sharing

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Solving ratio problems

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Scale factor problems

Unequal sharing

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Geometry - position and direction

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2D shapes: Types and properties

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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

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Finding fractions of amounts

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Comparing and ordering fractions greater than 1

Simplifying fractions

Add and subtract fractions: Different denominators

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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

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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: Alice

Summary

Unequal sharing

In a nutshell

Ratios can be used in lots of different scenarios - one of the most common being when things are shared unequally.

Ratio vs proportion

Definitions

Ratio	Compares one part to another.
Proportion	Compares one part to the whole thing

Example 1

Look at the squares.

The ratio of shaded to unshaded squares can be written:

$3:1$

The proportion of shaded squares is three (the number shaded) out of four (the total number of squares). Written as a fraction:

$\underline{\frac{3}{4}}$ 

Maths; Ratio and proportion; KS2 Year 6; Unequal sharing

Unequal sharing problems

When things are shared unequally, ratios and proportions can both be used to work out how many things each person gets.

Example 2

For every one slice of pizza that Rachel eats, her older sister Anna eats two. There are six slices in a whole pizza. Work out how many each of them get and write your answer as a ratio.

Write the information as a ratio.

Rachel : Anna

$1:2$

Add up the ratio and work out the proportion eaten by each person.

$1+2=3$

Rachel eats a third: $\frac{1}{3}$

Anna eats two thirds: $\frac{2}{3}$

Work out each fraction of the total amount to find out how much eat person gets.

Rachel: $\frac{1}{3}$ of $6=6\div3=2$

Anna:  $\frac{2}{3}$ of $6=(6\div3)\times2=4$

Therefore, Rachel and Anna get pizza in a ratio of $\underline{2:4}.$

Note: The numbers in the ratio should be given in the same order as the words in the question. Rachel is listed first, so her number in the ratio comes first.

Learn with Basics

Length:

Unit 1

Solving ratio problems

Jump Ahead

Optional

Unit 2

Unequal sharing

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do I answer an unequal sharing problem?

When things are shared unequally, ratios and proportions can both be used to work out how many things each person gets.

What is the difference between ratio and proportion?

The difference between ratio and proportion is that ratio compares one part to another whilst proportion compares one part to the whole thing.

Home

Maths

Ratio and proportion

Unequal sharing

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: Alice

Summary

Unequal sharing

In a nutshell

Ratios can be used in lots of different scenarios - one of the most common being when things are shared unequally.

Ratio vs proportion

Definitions

Ratio	Compares one part to another.
Proportion	Compares one part to the whole thing

Example 1

Look at the squares.

The ratio of shaded to unshaded squares can be written:

$3:1$

The proportion of shaded squares is three (the number shaded) out of four (the total number of squares). Written as a fraction:

$\underline{\frac{3}{4}}$ 

Unequal sharing problems

When things are shared unequally, ratios and proportions can both be used to work out how many things each person gets.

Example 2

For every one slice of pizza that Rachel eats, her older sister Anna eats two. There are six slices in a whole pizza. Work out how many each of them get and write your answer as a ratio.

Write the information as a ratio.

Rachel : Anna

$1:2$

Add up the ratio and work out the proportion eaten by each person.

$1+2=3$

Rachel eats a third: $\frac{1}{3}$

Anna eats two thirds: $\frac{2}{3}$

Work out each fraction of the total amount to find out how much eat person gets.

Rachel: $\frac{1}{3}$ of $6=6\div3=2$

Anna:  $\frac{2}{3}$ of $6=(6\div3)\times2=4$

Therefore, Rachel and Anna get pizza in a ratio of $\underline{2:4}.$

Note: The numbers in the ratio should be given in the same order as the words in the question. Rachel is listed first, so her number in the ratio comes first.

Learn with Basics

Length:

Unit 1

Solving ratio problems

Jump Ahead

Optional

Unit 2

Unequal sharing

Final Test

Create an account to complete the exercises

FAQs - Frequently Asked Questions

How do I answer an unequal sharing problem?

When things are shared unequally, ratios and proportions can both be used to work out how many things each person gets.

What is the difference between ratio and proportion?

The difference between ratio and proportion is that ratio compares one part to another whilst proportion compares one part to the whole thing.