Fractions in Disguise | Mathematics Grade 8 CBSE

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The many faces of a fraction

A fraction can disguise itself as an equivalent fraction, a decimal, a ratio or a percentage — yet keep the same value. Tap each idea to see how the disguise works.

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The three big ideas

Equivalent fractions — multiply (or divide) the numerator and denominator by the same non-zero number and the value does not change: 1/2 = 2/4 = 3/6 = 50/100.
Lowest terms — divide top and bottom by their HCF until they share no common factor. 18/24 → divide by 6 → 3/4.
Rational number — any number that can be written as p/q with p, q integers and q ≠ 0. This includes whole numbers (5 = 5/1) and negatives (−3/4).
Every rational number has a place on the number line; 2/3 sits two-thirds of the way from 0 to 1.

Common mistake: writing a fraction "in lowest terms" but stopping too early — 6/8 → 3/4, not 6/8 → 3/4 → done; always check the HCF really is 1.

Fraction → decimal — divide the numerator by the denominator: 3/4 = 3 ÷ 4 = 0.75. Some give a terminating decimal (0.75), others a recurring one (1/3 = 0.333…).
Add / subtract — first make the denominators the same, then add the numerators: 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
Multiply — multiply tops together and bottoms together: 2/3 × 3/5 = 6/15 = 2/5.
Divide — multiply by the reciprocal (flip the second fraction): 4/5 ÷ 2/3 = 4/5 × 3/2 = 12/10 = 6/5.

Worked example. Add 2/3 and 1/4.

1. The denominators are 3 and 4. Their LCM is 12.

2. Rewrite each fraction over 12: 2/3 = 8/12 and 1/4 = 3/12.

3. Add the numerators: 8/12 + 3/12 = 11/12.

4. 11 and 12 share no common factor, so 11/12 is already in lowest terms. Answer: 11/12.

Common mistake: adding denominators — writing 2/3 + 1/4 = 3/7. Denominators are never added; only the numerators, once the bottoms match.

As a ratio — the fraction a/b is the ratio a : b. So 3/4 means "3 parts for every 4", written 3 : 4.
As a percentage — a fraction out of 100. Multiply by 100 and add the % sign: 3/4 = 75/100 = 75%.
As a decimal — divide out: 3/4 = 0.75. So 3/4 = 3 : 4 = 0.75 = 75% — all the same quantity.
Comparing — to compare fractions, turn them into decimals (or a common denominator): 1/2 = 0.50, 2/3 ≈ 0.67, 3/4 = 0.75, so 1/2 < 2/3 < 3/4.

Where you'll meet it

Disguised fractions in daily life

Discounts & offers

A "25% off" sticker is the fraction 1/4 in disguise. On a ₹800 shirt that is 1/4 × 800 = ₹200 off, so you pay ₹600. Recognising the percentage as a fraction makes the mental maths quick.

Recipes & sharing

A recipe for 4 people needs 3/4 cup of rice; for 8 people you double it to 6/4 = 1½ cups. Equivalent fractions let you scale a recipe up or down without spoiling the proportions.

Cricket strike rate

A batter who scores 45 runs off 60 balls has a strike rate of 45/60 = 3/4 = 75 (runs per 100 balls). The same ratio, shown as a "per-100" figure, is how commentators compare players.

Check yourself

Competency quiz

Modelled on the competency-based pattern — MCQ, assertion–reason and a case study, testing whether you can use the ideas, not just recall them.

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