1. a. 4 x 14 = 56 b. 50 x 200 = 10 000 (But 50 x 190 = 9500 is wrong) c. 34 x 400 = 13 600 d. 11 x 80 = 880 e. 13 x 4 = 52 f. 100 / 20 = 5 g. 40 / 2 =20 h. 70 / 7 =10 i. 12 / 6 = 2 (But 10 / 6 = 1.67 is wrong!) 2. a. 4 20 80 20 16 4 (Note: Actual value is 4.011) 4 4 b. 82 7 2 64 49 113 121 11 (Note: Actual value is 10.918) c. 64 20 64 4 8 2 16. THIS IS CORRECT! 5 BUT 60 20 1200 240 16 15 4 15 15.49 IS WRONG! We can't have decimal. 5 5 (Note: Actual value is 15.587) d. 10 20 200 50 49 7 4 4 (Note: Actual value is 7.70) 3. a. 15 x 400 = 6000 which means that James' answer is approximately one tenth of the correct value. b. 14.62 x 401 = 5862.62. James has put the decimal point in the wrong place. 4. a. This calculation is incorrect! Since 15 x 6000 = 90 000 (exact is 93 024 not 930 240) b. This calculation is correct! The answer 5 or 6 is close to 5.26. 60 / 12 = 5 or 60 / 10 = 6 (exact is 5.26 which is given) But 70 / 10 = 7 is wrong. This is higher than 5.26. c. This is correct! Since 200 x 4600 = 920 000. or 190 x 4600 = 874 000. (exact is 880 704 which is given) d. This calculation is incorrect! Since 350 / 2 = 175 which is higher than 14.7. (exact is 147) 5. a. 4 x 800 = 3200. So the correct answer must be 2988.16. b. 3000 / 10 = 300. So the correct answer must be 301 c. 7 2 82 4 d. 80 70 150 75. So the correct answer must be 71.73 2 2 49 64 113 28.25 25 5 . So the correct answer must be 5.4187 4 4 6. Number of seconds in December = 31×24×60×60 ≈ 2 400 000 The correct number of seconds in December = 2 678 400 7. π × 20.5 ≈ 3 × 20 = 60 cm 8. Number of words in book = 326 × 268.4 ≈ 300 × 300 = 90 000 words 9. Total spent in canteen = 1264 × £1.42 ≈ 1200 × £1.50 = £1800 10. Area = π × 6.27² ≈ 3 × 6² = 3 × 36 = 108 cm² 11. (28 x 4) - 22 ≈ (30 x 4) - 20 ≈ 120 - 20 ≈ 100