Ratio and Proportion GCSE Resit Guide

A GCSE Maths resit can make familiar topics feel strangely unfamiliar. You may remember seeing ratios, recipes and best-buy questions before, yet still hesitate over the first step. The encouraging truth is that ratio and proportion GCSE questions rely on a small collection of repeatable methods.

You need to recognise what is being compared, make units consistent and decide whether to divide, multiply or find the value of one part. This guide explains those decisions through worked examples covering sharing in a ratio, scaling recipes, best buys and direct proportion.

MathsGenie has free GCSE Maths revision resources for Edexcel, AQA, OCR, Eduqas and other exam boards, so you can follow each method with exam-style practice.

Your ratio and proportion GCSE checklist

Before attempting a question, ask:

• What quantities are being compared?
• Are the units the same?
• Does the question involve sharing, scaling or comparing value?
• Can I find the value of one part or one unit?
• Does one quantity increase at a constant rate with the other?
• Have I answered in the units requested?

These questions matter because ratio and proportion is not one isolated technique. It is a way of describing relationships. Once you identify the relationship, the calculation becomes much more manageable.

Understanding ratios

A ratio compares quantities. For example, if the ratio of red counters to blue counters is $3:5$, there are three red counters for every five blue counters.

The order matters. Red to blue is $3:5$, while blue to red is $5:3$.

Ratios can be simplified in the same way as fractions. To simplify $18:30$, divide both parts by their highest common factor, $6$:

$$18:30=3:5$$

The relationship has not changed. Each number has simply been divided by the same amount.

If this foundation needs strengthening, use the Edexcel ratio revision lesson or the corresponding OCR ratio resources. The exam board presentation may vary, but the underlying mathematics remains the same.

Sharing in a ratio

When sharing in a ratio, the numbers in the ratio represent equal-sized parts, not the amounts themselves. The reliable method is:

• add the ratio parts;
• divide the total by that number;
• multiply by each part of the ratio.

Worked example: dividing money

Share £84£84£84 in the ratio $3:4$.

First, find the total number of parts:

$$3+4=7$$

Now find the value of one part:

£84÷7=£12£84\div 7=£12£84÷7=£12

Multiply by each number in the ratio:

3×£12=£363\times £12=£363×£12=£36 4×£12=£484\times £12=£484×£12=£48

Therefore, the two shares are £36£36£36 and £48£48£48.

Always check that the shares return to the original total:

£36+£48=£84£36+£48=£84£36+£48=£84

That final check takes only a few seconds and catches many calculator slips.

A variation gives one share rather than the total. If £36£36£36 represents three parts, one part is:

£36÷3=£12£36\div 3=£12£36÷3=£12

The other share, representing four parts, is then:

4×£12=£484\times £12=£484×£12=£48

This is the same structure approached from a different starting point. The MathsGenie ratio revision guide provides further notes and examples when you are ready to practise both forms.

Scaling recipes with proportion

Recipe questions test proportional reasoning. If every ingredient is multiplied by the same scale factor, the taste and consistency stay in proportion.

Worked example: scaling up a recipe

A recipe for $4$ people uses:

• $300g$ of flour;
• $200ml$ of milk;
• $2$ eggs.

Find the quantities needed for $10$ people.

The scale factor is:

$$10÷4=2.5$$

Multiply every ingredient by $2.5$:

$$300\times 2.5=750$$ $$200\times 2.5=500$$ $$2\times 2.5=5$$

The recipe for $10$ people needs $750g$ of flour, $500ml$ of milk and $5$ eggs.

An alternative is the unitary method. Divide each quantity by $4$ to find the amount for one person, then multiply by $10$. Both methods are correct. A scale factor is often faster, while the unitary method can feel clearer when the multiplier is not obvious.

The key is consistency. Multiplying one ingredient by $2.5$ and another by $2$ would change the recipe because the quantities would no longer remain proportional. You can develop this skill using the MathsGenie proportion lesson and its accompanying exam-style questions.

A GCSE student investigates a suspicious best-buy question with a detective calculator

Solving best buy questions

Best buy questions compare value for money. The lowest displayed price is not necessarily the best value because the products may contain different quantities.

To compare fairly, calculate the price for the same amount. Common choices include the cost per item, per gram, per kilogram or per litre.

Worked example: comparing packet sizes

Packet A contains $450g$ and costs £2.70£2.70£2.70.

Packet B contains $800g$ and costs £4.40£4.40£4.40.

Compare the cost per $100g$.

For Packet A:

£2.70÷450=£0.006 per gram£2.70\div 450=£0.006\text{ per gram}£2.70÷450=£0.006 per gram £0.006×100=£0.60 per 100 g£0.006\times 100=£0.60\text{ per }100\text{ g}£0.006×100=£0.60 per 100 g

For Packet B:

£4.40÷800=£0.0055 per gram£4.40\div 800=£0.0055\text{ per gram}£4.40÷800=£0.0055 per gram £0.0055×100=£0.55 per 100 g£0.0055\times 100=£0.55\text{ per }100\text{ g}£0.0055×100=£0.55 per 100 g

Packet B is the best buy because it costs £0.55£0.55£0.55 per $100g$, compared with £0.60£0.60£0.60 for Packet A.

You could instead compare how many grams each pound buys. That method is valid, but the interpretation reverses: a larger quantity per pound is better, whereas a smaller cost per gram is better. Cost per unit is often easier to explain clearly.

Write a conclusion in context. A page of correct calculator work without identifying the best option may not fully answer the question.

Direct proportion

Two quantities are in direct proportion when they increase or decrease by the same scale factor. If one quantity doubles, the other doubles. If one is divided by three, the other is also divided by three.

For variables $y$ and $x$, direct proportion is written as:

$$y\propto x$$

This means:

$$y=kx$$

where $k$ is the constant of proportionality.

Worked example: finding the constant

Suppose $6$ cinema tickets cost £18£18£18, with every ticket costing the same amount.

Let the total cost be $y$ and the number of tickets be $x$. Since the cost is directly proportional to the number of tickets:

$$y=kx$$

Substitute $y=18$ and $x=6$:

$$18=6k$$ $$k=3$$

The equation is therefore:

$$y=3x$$

For $11$ tickets:

$$y=3\times 11=33$$

The total cost is £33£33£33.

Here, $k$ has a practical meaning: it is the cost of one ticket. This link between an equation and a unit rate is useful across direct proportion questions. Higher-tier questions may use forms such as $y\propto x^2$, so always copy the stated relationship carefully rather than assuming it is $y\propto x$.

The proportion revision guide can help you move from numerical scaling to algebraic proportion.

Common mistakes that cost resit marks

Treating ratio parts as actual amounts

In a $3:4$ split, the total is divided into $7$ parts, not $4$. Add all ratio numbers before dividing the total.

Changing only one side of a ratio

Equivalent ratios require every part to be multiplied or divided by the same number. Changing $3:5$ to $6:5$ changes the relationship.

Mixing units

Do not compare a price per kilogram directly with a price per gram. Convert both to the same unit before deciding which option is better.

Choosing the cheapest packet

Best buy means best value, not the lowest purchase price. Compare equal quantities and state which option wins.

Using additive reasoning for a multiplicative problem

If a recipe grows from $4$ portions to $10$, adding $6$ to every ingredient is not valid. Proportion uses multiplication by a common scale factor.

Rounding too early

Keep the full calculator value during intermediate steps and round only the final answer when necessary. Early rounding can alter a best-buy comparison when prices are close.

Forgetting the context

Include money signs, units and a written conclusion. Your working should lead to the answer the question actually requested.

A focused revision plan for a GCSE Maths resit

Resit revision is most effective when mistakes determine what you practise next. Begin with one short ratio lesson, answer a set of practice questions, then check the mark scheme. Separate method errors from arithmetic slips.

A useful sequence is:

• simplify ratios and find equivalent ratios;
• practise sharing in a ratio;
• scale recipes and other quantities;
• compare unit prices in best-buy questions;
• write and use direct proportion equations;
• finish with mixed exam questions under timed conditions.

Use the free MathsGenie revision planner to spread these tasks across the time available. Once individual methods feel secure, move to GCSE past papers and revision materials. Past papers reveal whether you can recognise a ratio problem when the question does not announce the topic.

If you follow Edexcel, predicted GCSE Maths papers can provide further exam-style practice, with mark schemes and worked solutions. Use predicted papers as practice rather than as a promise of what will appear.

Turn the method into marks

Ratio and proportion becomes less intimidating when you stop treating every question as new. Sharing questions ask for the value of one part. Recipes use a common scale factor. Best buys require a common unit. Direct proportion expresses the same scaling relationship through an equation.

Start with the relevant MathsGenie revision lesson, complete the practice questions and mark them honestly. Then return to the questions you missed without looking at the solution. That second attempt is where recognition begins to become reliable, and reliable methods are what turn resit preparation into marks.