Ratio, proportion and scale · Grade 8
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
For example: A class has 12 boys and 3 girls. What is the ratio of boys to girls? Write it in its simplest form.
Answer and solution
The answer: 4 : 1
Divide both parts by 3: 12 : 3 = 4 : 1
Proportion: the missing term
For example: Find x: 3 : 10 = 9 : x
Answer and solution
The answer: 30
9 is 3 times 3, so the missing number is 3 times 10 too: x = 10 × 3 = 30
Sharing in a given ratio
For example: Share 88 shekels between two people in the ratio 3 : 5 . How much money is in the smaller share?
Answer and solution
The answer: 33 shekels
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
For 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 and solution
The answer: 20 m
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, so there are new exercises every time. The topic follows the Israeli Ministry of Education's grade 8 transition maths curriculum (2026–27).