Find the product:
- (i) 23 × 310
- (ii) 711 × 58
- (iii) −47 × 514
Answer: (i) 15 (ii) 3588 (iii) −1049
Step-by-step solution
Idea: ab × cd = acbd: multiply numerators together and denominators together, then simplify. No common denominator is needed.
(i) 23 × 310
- 2 × 33 × 10 = 630.½ mark
- Divide top and bottom by 6: 15.½ mark
15
(ii) 711 × 58
- 7 × 511 × 8 = 3588.½ mark
- 35 = 5 × 7 and 88 = 23 × 11 share no factor, so 3588 is in lowest terms.½ mark
3588
(iii) −47 × 514
- Negative × positive = negative: −4 × 57 × 14 = −2098.½ mark
- Divide top and bottom by 2: −1049.½ mark
−1049
(i) 1/5 (ii) 35/88 (iii) −10/49
Check: (i) 23 × 0.3 = 0.2 = 15 ✓ (iii) −0.5714 × 0.3571 ≈ −0.2041 ≈ −1049 ✓.
Answer to write in the exam
(i)
23 × 310 = 630
= 15
(ii)
711 × 58 = 3588
(iii)
−47 × 514 = −2098
= −1049
Common mistakes that cost marks
- Making a common denominator first, as for addition. Not needed for multiplication.
- In (iii), writing a positive answer. One negative factor makes the product negative.
- Leaving (i) as 630 without simplifying.
How this can come in the exam
MCQ (1 mark)
−916 × −827 =
- −16
- 16
- 13
- −1743
Show answer
(B) 16
Negative × negative is positive; 72432 = 16.
Short answer (2 marks)
A rectangular plot is 154 m long and 85 m wide. Find its area.
Show answer
Area = 154 × 85 = 12020 (1 mark) = 6 m2 (1 mark).Try one yourself
Find −625 × 158.
Show answer
−90200 = −920.