Simplification & Approximation — Practice

Question 1

3/4 × 240 + 37.5% of 160 − 12² = ?
(a) 84  (b) 96  (c) 108  (d) 120

Accepted Answer

180 + (3/8 × 160) − 144 = 180 + 60 − 144 = 96.

Answer: (b) 96. 37.5% = 3/8 straight from the table.

Question 2

(63² − 37²) / 26 = ?
(a) 26  (b) 74  (c) 100  (d) 130

Accepted Answer

(63+37)(63−37)/26 = (100 × 26)/26 = 100.

Answer: (c) 100. Factor instead of squaring.

Question 3

23.97% of 1249 + 15.02 × 8.03 ≈ ?
(a) 405  (b) 433  (c) 460  (d) 388

Accepted Answer

≈ (1/4)(1250) + 15 × 8 = 312.5 + 120 = 432.5 ≈ 433.

Answer: (b) 433. Round each term to clean numbers first.

Question 4

36 ÷ 4 × 3 + 5 = ?
(a) 8  (b) 14  (c) 32  (d) 41

Accepted Answer

(36 ÷ 4) × 3 + 5 = 9 × 3 + 5 = 32.

Answer: (c) 32. Left-to-right for ÷ and ×; the trap (a) 8 comes from doing 36 ÷ (4 × 3).

Question 5

? × 8 = 15% of 800 + 4³
(a) 21  (b) 23  (c) 25  (d) 28

Accepted Answer

RHS = 120 + 64 = 184. ? = 184 ÷ 8 = 23.

Answer: (b) 23. Isolate the unknown and treat it as one-step algebra.

Question 6

√626 + ∛1330 + 19.9% of 250 ≈ ?
(a) 71  (b) 86  (c) 96  (d) 61

Accepted Answer

√626 ≈ 25 (25²=625); ∛1330 ≈ 11 (11³=1331); 20% of 250 = 50.

25 + 11 + 50 = 86.

Answer: (b) 86. Anchor roots to the nearest known square/cube.

Practice — Simplification & Approximation