Find the sum:
- (i) 25 + 310
- (ii) 712 + 58
- (iii) −47 + 314
Answer: (i) 710 (ii) 2924 (iii) −514
Step-by-step solution
Idea: Make the denominators equal using the LCM, then add the numerators: ab + cb = a + cb. Simplify at the end.
(i) 25 + 310
- LCM of 5 and 10 is 10. 25 = 410.½ mark
- 410 + 310 = 710.½ mark
710
(ii) 712 + 58
- LCM of 12 and 8 is 24. 712 = 1424 and 58 = 1524.½ mark
- 1424 + 1524 = 2924 (= 1524).½ mark
2924
(iii) −47 + 314
- LCM of 7 and 14 is 14. −47 = −814.½ mark
- −814 + 314 = −8 + 314 = −514 = −514.½ mark
−514
(i) 7/10 (ii) 29/24 (iii) −5/14
Check: Decimals: (i) 0.4 + 0.3 = 0.7 ✓ (ii) 0.5833 + 0.625 = 1.2083 = 2924 ✓ (iii) −0.5714 + 0.2143 = −0.3571 = −514 ✓.
Answer to write in the exam
(i)
25 + 310 = 410 + 310
= 710
(ii)
712 + 58 = 1424 + 1524
= 2924
(iii)
−47 + 314 = −814 + 314
= −514
Common mistakes that cost marks
- Adding numerators and denominators separately: 25 + 310 = 515. Wrong: the denominators must be made equal first.
- In (ii), using 96 (= 12 × 8) as the denominator and then forgetting to simplify. The LCM 24 is easier.
- In (iii), losing the minus sign: −8 + 3 = −5, not 5 or −11.
How this can come in the exam
MCQ (1 mark)
34 + −56 =
- −112
- 112
- −210
- 1912
Show answer
(A) −112
912 + −1012 = −112.
Short answer (2 marks)
Find 59 + 715 + −25.
Show answer
LCM of 9, 15, 5 is 45 (½ mark). 2545 + 2145 − 1845 (1 mark) = 2845 (½ mark).Try one yourself
Find 1118 + 512.
Show answer
LCM 36: 2236 + 1536 = 3736.