Fractions

₹9,000

Step 1: Money spent on rent = 1/3 of ₹18,000 = ₹6,000. Step 2: Remaining money = ₹18,000 - ₹6,000 = ₹12,000. Step 3: Money spent on food = 1/4 of ₹12,000 = ₹3,000. Step 4: Money left = ₹12,000 - ₹3,000 = ₹9,000. A common mistake is taking 1/4 of the total ₹18,000 instead of 1/4 of the remaining ₹12,000.

5/6

Step 1: To divide fractions, multiply the first fraction by the reciprocal of the second. Step 2: Reciprocal of 3/4 is 4/3. Step 3: 5/8 × 4/3 = (5×4)/(8×3) = 20/24. Step 4: Reduce 20/24 to lowest terms: HCF of 20 and 24 is 4. So 20/24 = 5/6. A common error is to divide numerators and denominators separately, giving 5/6... wait — some students multiply without simplifying, getting 20/24 and forgetting to reduce.

5/7

Step 1: To find an equivalent fraction in lowest terms, find HCF of 20 and 28. Step 2: 20 = 2×2×5 and 28 = 2×2×7. HCF = 4. Step 3: Divide both by 4: 20÷4 = 5 and 28÷4 = 7. Step 4: So 20/28 = 5/7. To verify: 5×28 = 140 and 7×20 = 140. Cross products are equal, confirming equivalence.

5/7

Step 1: Use cross-multiplication to compare 5/7 and 8/11. Step 2: Multiply 5 × 11 = 55 (numerator of first × denominator of second). Step 3: Multiply 8 × 7 = 56 (numerator of second × denominator of first). Step 4: Since 55 < 56, we conclude 5/7 < 8/11. So 5/7 is the smaller fraction. This method avoids computing LCM and gives a quick comparison.