Proportional Reasoning-1
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Ratios and Proportional Change
A ratio a : b says that for every a units of one quantity there are b units of the other. To reduce a ratio to its simplest form, divide both terms by their HCF. Two ratios are proportional when their simplest forms are the same, which means both terms change by the same multiplying factor. Adding or subtracting the same number to both terms does not keep a ratio proportional.
Why it matters. Ratio and proportion are used in recipes, maps, scaling photographs and comparing prices. Children who understand that proportional change is multiplicative can avoid the common mistake of adding the same number to both terms.
Try it in two minutes
- Ask your child: a recipe uses 2 cups of rice and 3 cups of water. What is the ratio? What if we double the recipe?
- Ask what happens if we add 1 cup to both (3 : 4). Is this the same taste or thickness?
- Ask them to reduce 12 : 18 to its simplest form.
Try at home. Ask your child to find the ratio of boys to girls in the family or class and write it in simplest form.
Solving Problems with Proportions
If a : b :: c : d then a × d equals b × c, which is called cross multiplication. This is the Rule of Three: given three of the four numbers, the fourth can be found. Both ratios must use the same units, for example minutes with minutes. Not every situation is proportional: if speed rises, the time taken falls, so 50 : 2 :: 75 : ? does not work.
Why it matters. The Rule of Three is used in shopping, cooking, travel and scaling. Learning to check units and to ask whether a situation is really proportional prevents common mistakes.
Try it in two minutes
- Ask: 4 pens cost ₹ 36. How much do 7 pens cost? Let your child find the cost of one pen first and then use cross multiplication.
- Ask: a car goes 60 km in 90 minutes. How far in 2 hours? Watch for the unit change.
- Ask why more speed does not mean more time.
Try at home. Ask your child to scale a recipe for 6 people up to 15 people and explain each ingredient.
Sharing in a Ratio and Mixtures
To divide a quantity x in the ratio m : n, split it into m + n equal groups. The first part is m of those groups and the second part is n of them, so each group is x ÷ (m + n). For example, 42 shared in the ratio 4 : 3 has 7 groups of 6, giving 24 and 18. For mixtures, keep the part that does not change and use proportion to find the new total.
Why it matters. Sharing profits, dividing money fairly and mixing paints or recipes all use this idea. It teaches children to think in parts and wholes rather than guess.
Try it in two minutes
- Ask your child to share 20 sweets between two people in the ratio 3 : 2. How many groups in total? How big is each group?
- Ask what happens if there are 30 sweets in the same ratio.
- Ask how to mix 2 parts red and 3 parts white to make 30 mL of paint.
Try at home. Ask your child to share ₹100 between two cousins in the ratio 2 : 3 and check that the shares add up to ₹100.
Unit Conversions and Comparing Prices
To compare quantities or solve a proportion, both must use the same unit. Some conversions are 1 litre = 1000 mL, 1 hectare = 10,000 square metres, 1 acre = 43,560 square feet and 1 metre = 3.281 feet. Temperature uses Fahrenheit = 9/5 × Celsius + 32. To compare prices fairly, find the price for the same amount, such as the price of 1 kg.
Why it matters. Mixing units is a common reason for wrong answers in shopping, cooking and measuring. Converting first and comparing prices per unit helps in everyday decisions.
Try it in two minutes
- Ask your child to compare a 500 g pack of biscuits at ₹40 with a 1 kg pack at ₹70. Which is cheaper per kg?
- Ask how many mL are in a 2.5 litre bottle.
- Ask them to change 20 °C to Fahrenheit with the rule.
Try at home. Ask your child to compare the price per unit of two sizes of the same product in a shop.
What your child will practise
- Ratios and Proportional Change: Desert Quick Fire (Quick Fire)
- Ratios and Proportional Change: Mission Control Sort (Sort It Out)
- Sharing in a Ratio and Mixtures: Ocean Puzzle (Clue Puzzle)
- Solving Problems with Proportions: Lab Explorer Quest (Collect the Answer)
- Unit Conversions and Comparing Prices: Space Quick Fire (Quick Fire)
- Quiz: Ratios and Proportional Change (8 questions)
- Quiz: Sharing in a Ratio and Mixtures (8 questions)
- Quiz: Solving Problems with Proportions (8 questions)
- Quiz: Unit Conversions and Comparing Prices (8 questions)