Fractions and Decimals

133.20 km

Step 1: Distance in 2.4 litres = 55.5 × 2.4. Step 2: Multiply 555 × 24 = 13320 (ignoring decimals). Step 3: Count decimal digits: 55.5 has 1, 2.4 has 1. Total = 2 places. Step 4: Place decimal: 13320 becomes 133.20. Final Answer: 133.20 km. Common mistake: Miscounting the decimal places.

18

Step 1: 'of' means multiplication. So we need ⅔ × 27. Step 2: Multiply the numerator with the whole number: 2 × 27 = 54. Step 3: Divide by the denominator: 54 ÷ 3 = 18. Step 4: Verification: ⅓ of 27 = 9, so ⅔ of 27 = 9 × 2 = 18. ✓ Final Answer: 18. Common mistake: Dividing 27 by 2 instead of multiplying.

0.846

Step 1: When dividing a decimal by 100, the decimal point shifts 2 places to the LEFT (since 100 has 2 zeros). Step 2: 84.6 → move decimal 2 places left → 0.846. Step 3: Verify: 0.846 × 100 = 84.6. ✓ Final Answer: 0.846. Common mistake: Shifting the decimal to the right instead of left when dividing.

2/3

Step 1: To divide fractions, multiply the first fraction by the reciprocal of the second. Step 2: Reciprocal of 15/16 is 16/15. Step 3: 5/8 × 16/15 = (5×16)/(8×15) = 80/120. Step 4: Simplify 80/120: divide both by 40 → 2/3. Final Answer: 2/3. Common mistake: Multiplying by the fraction directly instead of its reciprocal.