# Ratio, proportion and scale · Grade 8

> Ratio, proportion and scale, Grade 8: The ratio of two quantities, Scale and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Ratio, proportion and scale (Grade 8) you practise 4 skills: The ratio of two quantities · Proportion: the missing term · Sharing in a given ratio · Scale.

A ratio compares two amounts by division. If a bag holds 4 red balls and 6 blue balls, the ratio of red to blue is 4 : 6. Divide both parts by the same number, just as you simplify a fraction, and you get 2 : 3: for every two red balls there are three blue ones.

A proportion says that two ratios are equal, for example 3 : 5 = 12 : 20. In every proportion the cross products are equal: 3 times 20 equals 5 times 12. That is how you find a missing number.

To share an amount in the ratio 2 : 3, add the numbers of the ratio: there are 5 equal parts. Divide the amount by 5, and each share gets its own number of parts.

On a map with the scale 1 : 100,000, each centimetre on the map is 100,000 centimetres in real life, which is one kilometre. A party recipe works the same way: to make three times as much, multiply every amount by three, and the ratio between the amounts stays the same.

**Tip:** Watch the order: the ratio of red to blue is not the ratio of blue to red.

## What you learn

### The ratio of two quantities

- Example: A class has 12 boys and 3 girls. What is the ratio of boys to girls? Write it in its simplest form.
- Answer: 4 : 1
- Solution: Divide both parts by 3: 12 : 3 = 4 : 1

### Proportion: the missing term

- Example: Find x: 3 : 10 = 9 : x
- Answer: 30
- Solution: 9 is 3 times 3, so the missing number is 3 times 10 too: x = 10 × 3 = 30

### Sharing in a given ratio

- Example: Share 88 shekels between two people in the ratio 3 : 5 . How much money is in the smaller share?
- Answer: 33 shekels
- Solution: The number of equal parts: 3 + 5 = 8 Each part is: 88 ÷ 8 = 11 The smaller share has 3 of these parts: 11 × 3 = 33

### Scale

- Example: The scale of the map is 1 : 100 . On the map, two points are 20 cm apart. How far apart are they in real life, in metres?
- Answer: 20 m
- Solution: Each centimetre on the map is 100 cm in real life. 20 × 100 = 2,000 2,000 cm is 20 m.

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education's grade 8 transition maths curriculum (2026–27).

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