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Students learn how to simplify and use equivalent ratios to calculate proportionate amounts. They use this knowledge to share an amount using a ratio.

This unit takes place in Year 9 Term 2 and leads on to Indices and Standard Form.

- solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
- solve problems involving the calculation of percentages
- solve problems involving unequal sharing and grouping using knowledge of fractions and multiples

- use ratio notation, including reduction to simplest form
- express a multiplicative relationship between two quantities as a ratio
- understand and use proportion as equality of ratios
- relate ratios to fractions
- express the division of a quantity into two parts as a ratio
- apply ratio to real contexts and problems (such as those involving conversion, comparison, scaling, mixing, concentrations)
- understand and use proportion as equality of ratios

- It is important for students to visualise equivalent and ratios by categorising objects and breaking them down into smaller groups.
- It is important to apply equivalent ratios when solving problems involving proportion. Including the use of the unitary method.
- To share amount given a ratio it is necessary to find the value of a single share.
- When two or more measurements increase at a linear rate they are in direct proportion. Inverse proportion is when one increases at the same rate the other decreases.

- Ratios amounts are often confused with fractions involving the same digits. For instance 2 : 3 is confused with 2⁄3 or 1 : 2 = 1⁄2.
- When solving problems involving proportion students tend to struggle with forming a ratio. For instance, 3 apples cost 45p would form the ratio apples : cost.
- When writing ratios into the form 1 : n students incorrectly assume that n has to be an integer or greater than 1.

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## Dewi Williams says:

You’re right about common misconceptions between ratios and fractions – pupils will often confuse the ratio 2 : 3 with the fraction 2/3.

However, I also think that there is a lot of value in pointing out the similarities between ratios and fractions. Equivalent ratios is conceptually very similar to equivalent fractions, and it is worth pointing out those similarities.

Thanks for sharing!

## mrmath_admin says:

Hi Dewi

Thanks for the comment. I completely agree about the need to understand a ratio as a proportion. These questions are becoming much more common nowadays in exam papers. Students continue to find them difficult.

It is also common to see ratio and proportion problems linked with the lowest common multiple.

Thanks again

Jonathan