Simplification problems test one’s ability to use arithmetic to simplify expressions and solve equations. These problems often involve operations like addition, subtraction, multiplication, division, and the use of brackets. Mastery of simplification is crucial for efficient problem-solving in various competitive exams and everyday mathematical calculations.
1. Simplify: 15 + 8 × 2 – 3.
a) 28
b) 30
c) 34
d) 36
Answer:
a) 28
Explanation:
Following BODMAS rule (Brackets, Orders, Division and Multiplication, Addition and Subtraction):
15 + 8 × 2 - 3 = 15 + 16 - 3 = 31 - 3 = 28.
2. Simplify: (48 ÷ 6) × 5.
a) 30
b) 35
c) 40
d) 45
Answer:
c) 40
Explanation:
(48 ÷ 6) × 5 = 8 × 5 = 40.
3. Simplify: 18 ÷ 2 × (3 + 3).
a) 36
b) 54
c) 72
d) 90
Answer:
b) 54
Explanation:
18 ÷ 2 × (3 + 3) = 9 × 6 = 54.
4. Simplify: 7² – 5².
a) 24
b) 34
c) 44
d) 54
Answer:
a) 24
Explanation:
7² - 5² = 49 - 25 = 24.
5. Simplify: 5/8 of 48.
a) 25
b) 30
c) 35
d) 40
Answer:
b) 30
Explanation:
5/8 of 48 = 5/8 × 48 = 30.
6. Simplify: 125 ÷ [25/(2+3)].
a) 20
b) 25
c) 30
d) 35
Answer:
b) 25
Explanation:
125 ÷ [25/(2+3)] = 125 ÷ 5 = 25.
7. Simplify: (6 + 4)² – (6 – 4)².
a) 64
b) 48
c) 32
d) 16
Answer:
c) 32
Explanation:
(6 + 4)² - (6 - 4)² = 10² - 2² = 100 - 4 = 96.
8. Simplify: 9(2 + 7) – 5(2 + 3).
a) 48
b) 54
c) 60
d) 66
Answer:
b) 54
Explanation:
9(2 + 7) - 5(2 + 3) = 9×9 - 5×5 = 81 - 25 = 56.
9. Simplify: 7/10 + 2/5.
a) 9/10
b) 11/10
c) 1
d) 7/5
Answer:
a) 9/10
Explanation:
7/10 + 2/5 = 7/10 + 4/10 = 11/10.
10. Simplify: 0.6 × 0.3 ÷ 0.09.
a) 2
b) 3
c) 4
d) 5
Answer:
a) 2
Explanation:
0.6 × 0.3 ÷ 0.09 = 0.18 ÷ 0.09 = 2.
11. Simplify: 125% of 80.
a) 100
b) 150
c) 200
d) 250
Answer:
a) 100
Explanation:
125% of 80 = (125/100) × 80 = 100.
12. Simplify: (36/4) ÷ (9/2).
a) 2
b) 3
c) 4
d) 5
Answer:
c) 4
Explanation:
(36/4) ÷ (9/2) = 9 ÷ 4.5 = 2.
13. Simplify: 6² – 4³.
a) -4
b) 0
c) 4
d) 8
Answer:
b) 0
Explanation:
6² - 4³ = 36 - 64 = -28.
14. Simplify: 5/6 + 2/3 – 1/2.
a) 1
b) 1/2
c) 2/3
d) 3/4
Answer:
a) 1
Explanation:
5/6 + 2/3 - 1/2 = 5/6 + 4/6 - 3/6 = 6/6 = 1.
15. Simplify: 40 ÷ 2(5 + 5).
a) 1
b) 2
c) 4
d) 8
Answer:
c) 4
Explanation:
40 ÷ 2(5 + 5) = 40 ÷ 20 = 2.
16. Simplify: (4³ ÷ 4²) × 4.
a) 4
b) 8
c) 16
d) 32
Answer:
a) 4
Explanation:
(4³ ÷ 4²) × 4 = 4 × 4 = 16.
17. Simplify: (18 ÷ 3) × (2 + 3).
a) 20
b) 25
c) 30
d) 35
Answer:
c) 30
Explanation:
(18 ÷ 3) × (2 + 3) = 6 × 5 = 30.
18. Simplify: 1/3 of 90 + 50% of 30.
a) 30
b) 40
c) 45
d) 50
Answer:
b) 40
Explanation:
1/3 of 90 + 50% of 30 = 30 + 15 = 45.
19. Simplify: (0.5 × 0.2) / 0.1.
a) 1
b) 0.1
c) 10
d) 0.01
Answer:
a) 1
Explanation:
(0.5 × 0.2) / 0.1 = 0.1 / 0.1 = 1.
20. Simplify: (5 + 3)² ÷ 4².
a) 4
b) 8
c) 16
d) 64
Answer:
a) 4
Explanation:
(5 + 3)² ÷ 4² = 8² ÷ 16 = 64 ÷ 16 = 4.