04. Comparison & Ordering of Numbers

Numbers compare aur order kaise karein: integers, fractions, decimals, negative numbers, number line, cross-multiplication, LCM method, SSC CGL tricks + practice questions with answers.

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1) Comparison ka golden rule (Number Line)

Number line par jo number right side hota hai woh bada hota hai. Aur jo left side hota hai woh chhota hota hai.

• Example: 5 > 2
• Example: -1 > -3 (kyunki -1 zero ke closer hai)

2) Integers compare (Positive vs Negative)

• Positive always > negative: 3 > -100
• Negative numbers me: jo absolute value me bada, wo actually smaller hota (zero se door): -9 < -2

3) Decimals compare (simple method)

1. Integer part compare karo.
2. Equal ho to decimal digits left-to-right compare karo.
3. Need ho to trailing zeros add karo: 2.5 = 2.50

• Example: 3.09 > 3.008 (0.09 > 0.008)
• Example: 12.4 < 12.40? (No) — actually equal: 12.4 = 12.40

4) Fractions compare (SSC favourite)

Method A: Cross-multiplication (fastest)

Compare a/b and c/d (b, d > 0): a×d aur c×b compare karo.

• Example: 3/7 vs 4/9 → 3×9 = 27, 4×7 = 28 ⇒ 4/9 is bigger

Method B: Same denominator (LCM method)

Fractions ko same denominator me convert karo, phir numerators compare karo.

• Example: 5/12 vs 7/18 → LCM(12,18)=36 → 5/12=15/36, 7/18=14/36 ⇒ 5/12 bigger

Method C: Same numerator shortcut

Agar numerator same ho, to jiska denominator chhota, wo fraction bada.

• Example: 5/8 vs 5/11 → 5/8 bigger

5) Ordering kya hota hai?

Ordering ka matlab numbers ko sequence me arrange karna: Ascending (small to big) ya Descending (big to small).

• Ascending: -5, -2, 0, 1, 3
• Descending: 3, 1, 0, -2, -5

6) Mixed comparison (Fraction vs Decimal)

Mixed case me easiest: fraction ko decimal me convert kar lo (or vice-versa).

• Example: 3/4 = 0.75, so 0.8 > 3/4
• Example: 1.2 = 6/5, so 6/5 > 7/6? (compare: 6×6=36, 7×5=35 ⇒ 6/5 bigger)

7) Common traps

• Negative numbers me sign confuse mat karo: -1 > -9
• Decimals compare karte time digits align karo: 2.09 vs 2.1 → 2.09 < 2.10
• Fractions me cross-multiplication me sign ka dhyan (especially negative fractions)

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8) Practice (SSC CGL level) + Answers

1. Arrange ascending: -3, 2, -10, 0, 5
2. Which is bigger: 7/12 or 5/9?
3. Compare: 3.056 and 3.56
4. Which is bigger: -7 or -2?
5. Arrange descending: 0.7, 3/5, 0.65, 2/3
6. Which is bigger: 11/15 or 0.73?

Show Answers

1. -10, -3, 0, 2, 5
2. 7/12 vs 5/9 → 7×9=63, 5×12=60 ⇒ 7/12 bigger
3. 3.056 < 3.56 (because 3.056 < 3.560)
4. -2 is bigger
5. 0.7, 2/3(≈0.666...), 0.65, 3/5(=0.6)
6. 11/15≈0.7333..., so 11/15 > 0.73