- Maths
- Classes 6-8
- 4 min read
Ratio and proportion
Compare quantities with ratios, simplify them, check proportion and use the unitary method to solve everyday problems.
Let us begin
The big idea
When you mix sharbat, scale a recipe or share sweets, you are using ratios. A ratio compares two quantities, and proportion says two ratios are equal.
A ratio compares two quantities of the same kind. If a sharbat has 2 glasses of syrup for every 3 glasses of water, the ratio of syrup to water is 2 : 3. The order matters.
Like a fraction, a ratio can be simplified by dividing both numbers by the same number. 12 : 18 becomes 2 : 3 when both are divided by 6. We can also multiply both numbers by the same number to get equivalent ratios.
Four numbers are in proportion when the two ratios are equal. 3 : 4 and 9 : 12 are in proportion because both simplify to 3 : 4. A quick check: the product of the outer numbers should equal the product of the inner numbers, 3 × 12 = 4 × 9.
The unitary method finds the value of one unit first and then the value of many. To share an amount in a ratio, add the parts to find the total number of parts, find one part, and then multiply.
Worked examples
See how it works
Simplify 12 : 18
The biggest number that divides both 12 and 18 is 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3. So 12 : 18 = 2 : 3.
Are 3 : 4 and 9 : 12 in proportion?
3 × 3 = 9 and 4 × 3 = 12, so 3 : 4 = 9 : 12. Check with cross products: 3 × 12 = 36 and 4 × 9 = 36. They are equal, so yes.
Unitary method
5 notebooks cost Rs 120. One notebook costs 120 ÷ 5 = Rs 24. So 8 notebooks cost 8 × 24 = Rs 192.
Sharing in a ratio
Share Rs 500 in the ratio 2 : 3. Total parts = 2 + 3 = 5. One part = 500 ÷ 5 = 100. Shares are 2 × 100 = Rs 200 and 3 × 100 = Rs 300. Check: 200 + 300 = 500.
Try it at home
Sharbat ratio
You will need
- Any fruit syrup or squash
- Water
- Two glasses or cups
- A spoon
- A small cup to use as a measure
What to do
- In glass 1 put 1 cup of syrup and 3 cups of water. Write the ratio 1 : 3.
- In glass 2 put 2 cups of syrup and 6 cups of water. Write the ratio 2 : 6.
- Simplify 2 : 6. It becomes 1 : 3, the same as glass 1.
- Taste both. They should taste the same because the ratio is the same.
- Predict how much syrup you need for 12 cups of water, keeping the ratio 1 : 3.
Ask a grown-up: An adult should help with pouring and supervise tasting, and check that nobody has an allergy to the syrup.
Practice sheet
Check what you learned
Practice sheet: Ratio and proportion (Classes 6-8, Maths)
- Write the ratio of 4 red marbles to 6 blue marbles in simplest form.
- Simplify 15 : 25.
- Fill in the blank: 2 : 5 = 6 : ___.
- Are 4 : 5 and 12 : 15 in proportion?
- 3 kg of rice costs Rs 150. What do 5 kg cost?
- A class has 18 boys and 12 girls. Find the ratio of boys to girls in simplest form.
- Share 60 sweets between Asha and Ravi in the ratio 1 : 2.
- A recipe uses 2 cups of rice and 5 cups of water. How much water is needed for 6 cups of rice?
- A car goes 120 km in 2 hours at a steady speed. How far does it go in 5 hours?
- Red and white paint are mixed in the ratio 3 : 7 to make 40 ml. How much red paint is there?
Answer key
Answers: Ratio and proportion
- 2 : 3 (divide both by 2).
- 3 : 5 (divide both by 5).
- 15 (2 × 3 = 6, so 5 × 3 = 15).
- Yes. Multiply 4 : 5 by 3 to get 12 : 15.
- Rs 250 (one kg costs Rs 50, so 5 kg cost 5 × 50).
- 3 : 2 (divide both by 6).
- Asha gets 20 sweets and Ravi gets 40 (3 parts, 1 part = 20).
- 15 cups (6 cups is 3 times 2 cups, so 3 × 5 = 15).
- 300 km (speed 60 km per hour, 60 × 5 = 300).
- 12 ml (10 parts, 1 part = 4 ml, red = 3 × 4 = 12 ml).