A part to whole (sometimes part to part) comparison. If two things are proportional then the ratio of part to whole is maintained and the multiplicative relationship between parts is also maintained.

A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole.

LCM is an abbreviation for lowest common multiple.

The lowest common multiple is the lowest number that is a multiple of two or more numbers.

Changing ratios

Maths

Checking and securing understanding of simplifying and unitising ratios

Checking and securing understanding of equivalent ratios

Checking and securing understanding of sharing in a ratio

Checking and securing understanding of converting between ratios, percentages and fractions

Checking and securing understanding of real world ratios

Combining ratios

Writing equations from ratios

Algebraic ratios

Problem solving with algebraic ratios

In the compound measures unit, pupils will be exploring the multiplicative relationship between different compound measures. Ratio will be one of the ways in which this is explored and the skills from this unit will aid understanding.

The ratio unit will cover comparing fractions, percentages and ratios and being able to move fluently between them. The percentages unit ensured pupils had the opportunity to work with finding the percentage of an amount and the opportunity to calculate interest.

In this unit pupils will learn how to combine ratios, interpret algebraic ratios, and investigate quantity changes and their effect on ratios.

Ratio

Which of the following is used as a separator in a ratio?

There are 30 cans of drink and bags of sweets in a vending machine. The ratio of cans : bags is 2 : 1. 5 cans and 1 packet is sold.  What is the ratio of cans : bags now? (In its simplest form)

There are 24 vehicles in a car park.  The ratio of cars : vans is 5 : 1.  4 more cars enter the car park.  What is the ratio of cars : vans now?  (Give your answer in its simplest form)

The ratio of adults to children at an athletics club is 7 : 5.  2 more children join, the ratio is now 4 : 3.  How many adults are members of the club?

3 bags contain counters in the ratio 3 : 2 : 4. Some counters are taken out of 1 bag and put into the other 2. The ratio of counters is now 1 : 1 : 2.  What is the minimum number of counters removed?

The ratio of the number of £1 coins to £2 in Sam’s money box is 2 : 3.  Their gran gives them 4 more £1 coins, the ratio is now 5 : 6.  How much money was in Sam’s money box originally?

To combine ratios they must have a {{ }} component.

Given these bar models.  What is the ratio of hearts to suns?

Given that squares : circles = 6 : 5 and circles : triangles = 1 : 3.  Find the ratio of squares : triangles.

a : b = 3 : 4, b : c = 5 : 9.  Find the ratio a : b : c

A box contains 185 sweets which are either hearts (h), stars (s) or bottles (b).  The ratio of hearts to stars is 2 : 3. The ratio of stars to bottles is 5 : 4.  How many bottles are in the box?

Changing ratios

Lesson outcome