Find the difference:
- (i) 56 − 14
- (ii) 118 − 34
- (iii) −79 − (−23)
Answer: (i) 712 (ii) 58 (iii) −19
Step-by-step solution
Idea: Make the denominators equal using the LCM, then subtract the numerators. Subtracting a negative number is the same as adding the positive number.
(i) 56 − 14
- LCM of 6 and 4 is 12: 56 = 1012, 14 = 312.½ mark
- 1012 − 312 = 712.½ mark
712
(ii) 118 − 34
- LCM of 8 and 4 is 8: 34 = 68.½ mark
- 118 − 68 = 58.½ mark
58
(iii) −79 − (−23)
- Subtracting a negative is adding: −79 − (−23) = −79 + 23. And 23 = 69.½ mark
- −7 + 69 = −19 = −19.½ mark
−19
(i) 7/12 (ii) 5/8 (iii) −1/9
Check: Add back: (i) 712 + 312 = 1012 = 56 ✓ (ii) 58 + 68 = 118 ✓ (iii) −19 + (−69) = −79 ✓.
Answer to write in the exam
(i)
56 − 14 = 1012 − 312
= 712
(ii)
118 − 34 = 118 − 68
= 58
(iii)
−79 − (−23) = −79 + 69
= −19
Common mistakes that cost marks
- In (iii), writing −79 − 23 = −139: the second minus sign was ignored. Minus a negative becomes plus.
- Subtracting denominators too: 118 − 34 = 84. Only numerators are subtracted.
- Getting 712 in (i) but writing it as 42 from 5 − 1 over 6 − 4.
How this can come in the exam
MCQ (1 mark)
−310 − 25 =
- −110
- 110
- −710
- −515
Show answer
(C) −710
−310 − 410 = −710.
Short answer (2 marks)
What should be subtracted from 34 to get −16?
Show answer
34 − x = −16 gives x = 34 + 16 (1 mark) = 912 + 212 = 1112 (1 mark).Try one yourself
Find −512 − (−38).
Show answer
−512 + 38 = −1024 + 924 = −124.