MCQs on Simplifications & Approximations

[Set - 3]

1. Simplify $10^2 + 5 \times 4 - 8^2$

A) 52
B) 54
C) 56
D) 58

Show Answer

Correct Answer: C) 56
Explanation:
First, calculate the exponents:
$10^2 = 100$
$8^2 = 64$
Then, multiply:
$5 \times 4 = 20$
Now, add and subtract:
$100 + 20 - 64 = 56$

2. Approximate $843.7 + 139.5 - 214.6 + 561.2$

A) 1329.7
B) 1329.8
C) 1329.9
D) 1330.0

Show Answer

Correct Answer: B) 1329.8
Explanation:
First, add and subtract in sequence:
$843.7 + 139.5 = 983.2$
$983.2 - 214.6 = 768.6$
$768.6 + 561.2 = 1329.8$

3. Calculate $13^2 - 8^3 + 9^2$

A) -260
B) -261
C) -262
D) -263

Show Answer

Correct Answer: C) -262
Explanation:
First, calculate the exponents:
$13^2 = 169$
$8^3 = 512$
$9^2 = 81$
Now, perform the subtraction and addition:
$169 - 512 + 81 = -262$

4. Estimate $192.3 + 75.4 - 49.8 + 613.9$

A) 831.8
B) 831.7
C) 831.6
D) 830.8

Show Answer

Correct Answer: A) 831.8
Explanation:
First, add and subtract in sequence:
$192.3 + 75.4 = 267.7$
$267.7 - 49.8 = 217.9$
$217.9 + 613.9 = 831.8$

5. Simplify $5 \times 6 + \frac{45}{9} - 4^2$

A) 8
B) 20
C) 19
D) 18

Show Answer

Correct Answer: C) 19
Explanation:
First, multiply:
$5 \times 6 = 30$
Then, divide:
$\frac{45}{9} = 5$
Then, calculate the exponent:
$4^2 = 16$
Now, add and subtract:
$30 + 5 - 16 = 19$

6. Approximate $1786.4 + 629.5 - 398.6 + 715.2$

A) 2732.2
B) 2732.3
C) 2732.4
D) 2732.5

Show Answer

Correct Answer: D) 2732.5
Explanation:
First, add and subtract in sequence:
$1786.4 + 629.5 = 2415.9$
$2415.9 - 398.6 = 2017.3$
$2017.3 + 715.2 = 2732.5$

7. Calculate $9^3 - 7 \times 4 + 5^2$

A) 725
B) 726
C) 727
D) 728

Show Answer

Correct Answer: B) 726
Explanation:
First, calculate the exponents:
$9^3 = 729$
$5^2 = 25$
Then, multiply:
$7 \times 4 = 28$
Now, perform the subtraction and addition:
$729 - 28 + 25 = 726$

8. Approximate $245.8 + 123.4 - 87.2 + 321.6$

A) 603.4
B) 603.5
C) 603.6
D) 603.7

Show Answer

Correct Answer: C) 603.6
Explanation:
First, add and subtract in sequence:
$245.8 + 123.4 = 369.2$
$369.2 - 87.2 = 282.0$
$282.0 + 321.6 = 603.6$

9. Solve $4 \times (8 + 6) - 2^5$

A) 23
B) 24
C) 34
D) 33

Show Answer

Correct Answer: B) 24
Explanation:
First, calculate inside the parentheses:
$8 + 6 = 14$
Then, multiply:
$4 \times 14 = 56$
Then, calculate the exponent:
$2^5 = 32$
Now, subtract:
$56 - 32 = 24$

10. Estimate $672.9 + 514.7 - 209.8 + 143.2$

A) 1120.9
B) 1121.0
C) 1121.1
D) 1121.9

Show Answer

Correct Answer: B) 1121.0
Explanation:
First, add and subtract in sequence:
$672.9 + 514.7 = 1187.6$
$1187.6 - 209.8 = 977.8$
$977.8 + 143.2 = 1121.0$

11. Simplify $8^2 - 4 \times 6 + 3^3$

A) 37
B) 47
C) 57
D) 67

Show Answer

Correct Answer: D) 67
Explanation:
First, calculate the exponents:
$8^2 = 64$
$3^3 = 27$
Then, multiply:
$4 \times 6 = 24$
Now, perform the addition and subtraction:
$64 - 24 + 27 = 67$

12. Approximate $1489.67 + 589.45 - 278.23 + 695.12$

A) 2495.99
B) 2496.00
C) 2496.01
D) 2496.02

Show Answer

Correct Answer: C) 2496.01
Explanation:
First, add and subtract in sequence:
$1489.67 + 589.45 = 2079.12$
$2079.12 - 278.23 = 1800.89$
$1800.89 + 695.12 = 2496.01$

13. $5 \times (7 + 9) - 12^2 =$

A) -64
B) -74
C) 64
D) 74

Show Answer

Correct Answer: A) -64
Explanation:
First, calculate inside the parentheses:
$7 + 9 = 16$
Then, multiply:
$5 \times 16 = 80$
Then, calculate the exponent:
$12^2 = 144$
Now, subtract:
$80 - 144 = -64$

14. Approximate $852.75 + 763.14 - 491.36 + 223.57$

A) 1348.0
B) 1348.1
C) 1348.2
D) 1348.3

Show Answer

Correct Answer: B) 1348.1
Explanation:
First, add and subtract in sequence:
$852.75 + 763.14 = 1615.89$
$1615.89 - 491.36 = 1124.53$
$1124.53 + 223.57 = 1348.10$

15. Simplify $\frac{(48 + 36)}{6} \times 5 - 7^2$

A) 19
B) 20
C) 21
D) 22

Show Answer

Correct Answer: C) 21
Explanation:
First, calculate inside the parentheses:
$48 + 36 = 84$
Then, divide:
$\frac{84}{6} = 14$
Then, multiply:
$14 \times 5 = 70$
Then, calculate the exponent:
$7^2 = 49$
Now, subtract:
$70 - 49 = 21$

16. Approximate $2147.92 + 1342.5 - 763.6 + 891.45$

A) 3617.27
B) 3618.27
C) 3618.37
D) 3619.37

Show Answer

Correct Answer: A) 3618.27
Explanation:
First, add and subtract in sequence:
$2147.92 + 1342.5 = 3490.42$
$3490.42 - 763.6 = 2726.82$
$2726.82 + 891.45 = 3618.27$

17. Solve $6^2 - 3^3 + 4 \times 7$

A) 57
B) 47
C) 27
D) 37

Show Answer

Correct Answer: D) 37
Explanation:
First, calculate the exponents:
$6^2 = 36$
$3^3 = 27$
Then, multiply:
$4 \times 7 = 28$
Now, perform the addition and subtraction:
$36 - 27 + 28 = 37$

18. Approximate $1094.84 + 856.32 - 498.25 + 347.91$

A) 1800.80
B) 1800.81
C) 1800.82
D) 1800.83

Show Answer

Correct Answer: C) 1800.82
Explanation:
First, add and subtract in sequence:
$1094.84 + 856.32 = 1951.16$
$1951.16 - 498.25 = 1452.91$
$1452.91 + 347.91 = 1800.82$

19. Simplify $7^3 - 5 \times (4 + 3) + 9$

A) 306
B) 307
C) 317
D) 327

Show Answer

Correct Answer: C) 317
Explanation:
First, calculate the exponent:
$7^3 = 343$
Then, calculate inside the parentheses:
$4 + 3 = 7$
Then, multiply:
$5 \times 7 = 35$
Now, subtract and add:
$343 - 35 + 9 = 317$

20. Approximate $643.25 + 421.9 - 297.6 + 180.4$

A) 947.93
B) 947.94
C) 947.95
D) 947.96

Show Answer

Correct Answer: C) 947.95
Explanation:
First, add and subtract in sequence:
$643.25 + 421.9 = 1065.15$
$1065.15 - 297.6 = 767.55$
$767.55 + 180.4 = 947.95$

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MCQs on Simplifications & Approximations

[Set - 3]

1. Simplify 10^2 + 5 \times 4 - 8^2

2. Approximate 843.7 + 139.5 - 214.6 + 561.2

3. Calculate 13^2 - 8^3 + 9^2

4. Estimate 192.3 + 75.4 - 49.8 + 613.9

5. Simplify 5 \times 6 + \frac{45}{9} - 4^2

6. Approximate 1786.4 + 629.5 - 398.6 + 715.2

7. Calculate 9^3 - 7 \times 4 + 5^2

8. Approximate 245.8 + 123.4 - 87.2 + 321.6

9. Solve 4 \times (8 + 6) - 2^5

10. Estimate 672.9 + 514.7 - 209.8 + 143.2

11. Simplify 8^2 - 4 \times 6 + 3^3

12. Approximate 1489.67 + 589.45 - 278.23 + 695.12

13. 5 \times (7 + 9) - 12^2 =

14. Approximate 852.75 + 763.14 - 491.36 + 223.57

15. Simplify \frac{(48 + 36)}{6} \times 5 - 7^2

16. Approximate 2147.92 + 1342.5 - 763.6 + 891.45

17. Solve 6^2 - 3^3 + 4 \times 7

18. Approximate 1094.84 + 856.32 - 498.25 + 347.91

19. Simplify 7^3 - 5 \times (4 + 3) + 9

20. Approximate 643.25 + 421.9 - 297.6 + 180.4

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1. Simplify $10^2 + 5 \times 4 - 8^2$

2. Approximate $843.7 + 139.5 - 214.6 + 561.2$

3. Calculate $13^2 - 8^3 + 9^2$

4. Estimate $192.3 + 75.4 - 49.8 + 613.9$

5. Simplify $5 \times 6 + \frac{45}{9} - 4^2$

6. Approximate $1786.4 + 629.5 - 398.6 + 715.2$

7. Calculate $9^3 - 7 \times 4 + 5^2$

8. Approximate $245.8 + 123.4 - 87.2 + 321.6$

9. Solve $4 \times (8 + 6) - 2^5$

10. Estimate $672.9 + 514.7 - 209.8 + 143.2$

11. Simplify $8^2 - 4 \times 6 + 3^3$

12. Approximate $1489.67 + 589.45 - 278.23 + 695.12$

13. $5 \times (7 + 9) - 12^2 =$

14. Approximate $852.75 + 763.14 - 491.36 + 223.57$

15. Simplify $\frac{(48 + 36)}{6} \times 5 - 7^2$

16. Approximate $2147.92 + 1342.5 - 763.6 + 891.45$

17. Solve $6^2 - 3^3 + 4 \times 7$

18. Approximate $1094.84 + 856.32 - 498.25 + 347.91$

19. Simplify $7^3 - 5 \times (4 + 3) + 9$

20. Approximate $643.25 + 421.9 - 297.6 + 180.4$