Proportional Reasoning-1
CBSE · Class 8 · Mathematics
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What is a ratio and how is it written?
Answer
A ratio is a comparison of two quantities using division. It is written as a:b, where 'a' and 'b' are called the terms of the ratio. For example, if there are 60 mm width and 40 mm height, the ratio i…
What does the ratio 5:3 mean?
Answer
The ratio 5:3 means that for every 5 units of the first quantity, there are 3 units of the second quantity. For example, if boys to girls ratio is 5:3, then for every 5 boys, there are 3 girls.
How do you find the simplest form of a ratio?
Answer
To find the simplest form of a ratio, divide both terms by their HCF (Highest Common Factor). For example, 60:40 has HCF = 20, so dividing both terms: 60÷20 : 40÷20 = 3:2.
When are two ratios said to be proportional?
Answer
Two ratios are proportional when they are equal in their simplest forms. We use the symbol '::' to show proportion. For example, 6:4 :: 9:6 because both simplify to 3:2.
What is cross multiplication and when is it used?
Answer
Cross multiplication is used to check if two ratios are proportional or to find missing terms. If a:b :: c:d, then a×d = b×c. For example, in 3:4 :: 6:8, we get 3×8 = 4×6 = 24.
Solve: 12:15 :: 8:?
Answer
Using cross multiplication: 12 × ? = 15 × 8 12 × ? = 120 ? = 120 ÷ 12 = 10 Therefore, 12:15 :: 8:10…
What is the Rule of Three (Trairasika)?
Answer
The Rule of Three is an ancient method to solve proportion problems with four quantities where three are known and one is unknown. If a:b :: c:d, then d = (b×c)/a. This method was used by ancient Indi…
A car travels 120 km in 2 hours. How far will it travel in 5 hours at the same speed?
Answer
Set up proportion: 120:2 :: ?:5 Using cross multiplication: 2 × ? = 120 × 5 2 × ? = 600 ? = 300 km The car will travel 300 km in 5 hours.
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- NCERT Official — ncert.nic.in
- CBSE Academic — cbseacademic.nic.in
- CBSE Official — cbse.gov.in
- National Education Policy 2020 — education.gov.in
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