Question 16 of 22intermediate🔍 AnalyzeShort Answer8 marks

Compare the following pairs of expressions using '<', '>' or '=' or by reasoning. (a) 49 - 7 + 8 ☐ 49 - 7 + 8 (b) 83×4283 \times 42 - 18 ☐ 83×4083 \times 40 - 18 (c) 145 - 17×817 \times 8 ☐ 145 - 17×617 \times 6 (d) 23×4823 \times 48 - 35 ☐ 23 × (48 - 35) (e) (16 - 11) × 12 ☐ -11×1211 \times 12 + 16×1216 \times 12 (f) (76 - 53) × 88 ☐ 88 × (53 - 76) (g) 25 × (42 + 16) ☐ 25 × (43 + 15) (h) 36 × (28 - 16) ☐ 35 × (27 - 15)

(a)
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=

(b)
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(c)
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<

(d)
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(e)
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=

(f)
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(g)
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=

(h)
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Explanation

(a) Both expressions are identical (b) 83×4283 \times 42 > 83×4083 \times 40, so LHS > RHS (c) 17×817 \times 8 > 17×617 \times 6, so subtracting more gives smaller result (d) LHS = 1069, RHS = 299. LHS > RHS (e) By distributive property: (16-11)×12 = 16×1216 \times 12 - 11×1211 \times 12 = -11×1211 \times 12 + 16×1216 \times 12 (f) LHS = 23×8823 \times 88 = 2024. RHS = 88 × (-23) = -2024. Positive > Negative (g) 42 + 16 = 58 and 43 + 15 = 58. Both equal 25×5825 \times 58 (h) LHS = 36×1236 \times 12 = 432. RHS = 35×1235 \times 12 = 420. 432 > 420

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