MCQs on Simplifications & Approximations

[Set - 6]

1. Simplify $8^2 - 5 \times 4 + 3^3$

A) 69
B) 70
C) 71
D) 72

Show Answer

Correct Answer: C) 71
Explanation:
First, calculate the exponents:
$8^2 = 64$
$3^3 = 27$
Then, multiply:
$5 \times 4 = 20$
Now, perform the addition and subtraction:
$64 - 20 + 27 = 71$

2. Approximate $1548.76 + 678.34 - 294.67 + 431.89$

A) 2364.22
B) 2362.32
C) 2363.32
D) 2364.32

Show Answer

Correct Answer: D) 2364.32
Explanation:
First, add and subtract in sequence:
$1548.76 + 678.34 = 2227.10$
$2227.10 - 294.67 = 1932.43$
$1932.43 + 431.89 = 2364.32$

3. Simplify $7 \times (9 + 5) - 6^2$

A) 61
B) 62
C) 63
D) 64

Show Answer

Correct Answer: B) 62
Explanation:
First, calculate inside the parentheses:
$9 + 5 = 14$
Then, multiply:
$7 \times 14 = 98$
Then, calculate the exponent:
$6^2 = 36$
Now, subtract:
$98 - 36 = 62$

4. Approximate $876.43 + 543.21 - 312.54 + 198.78$

A) 1305.86
B) 1305.87
C) 1305.88
D) 1305.89

Show Answer

Correct Answer: C) 1305.88
Explanation:
First, add and subtract in sequence:
$876.43 + 543.21 = 1419.64$
$1419.64 - 312.54 = 1107.10$
$1107.10 + 198.78 = 1305.88$

5. Simplify $\frac{(45 + 15)}{3} \times 8 - 7^2$

A) 109
B) 110
C) 111
D) 112

Show Answer

Correct Answer: C) 111
Explanation:
First, calculate inside the parentheses:
$45 + 15 = 60$
Then, divide:
$60 \div 3 = 20$
Now, multiply:
$20 \times 8 = 160$
Then, calculate the exponent:
$7^2 = 49$
Now, subtract:
$160 - 49 = 111$

6. $2154.23 + 789.41 - 534.12 + 312.89 =$

A) 2722.01
B) 2722.11
C) 2722.21
D) 2722.41

Show Answer

Correct Answer: D) 2722.41
Explanation:
First, add and subtract in sequence:
$2154.23 + 789.41 = 2943.64$
$2943.64 - 534.12 = 2409.52$
$2409.52 + 312.89 = 2722.41$

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

A) 746
B) 747
C) 748
D) 749

Show Answer

Correct Answer: C) 748
Explanation:
First, calculate the exponents:
$9^3 = 729$
$4^2 = 16$
Then, multiply:
$7 \times 5 = 35$
Now, perform the subtraction and addition:
$729 - 16 + 35 = 748$

8. Approximate $431.67 + 367.56 - 212.45 + 145.87$

A) 732.63
B) 732.64
C) 732.65
D) 732.66

Show Answer

Correct Answer: C) 732.65
Explanation:
First, add and subtract in sequence:
$431.67 + 367.56 = 799.23$
$799.23 - 212.45 = 586.78$
$586.78 + 145.87 = 732.65$

9. Solve $10^2 - 6 \times (4 + 5) + 9^2$

A) 126
B) 127
C) 128
D) 129

Show Answer

Correct Answer: B) 127
Explanation:
First, calculate inside the parentheses:
$4 + 5 = 9$
Then, multiply:
$6 \times 9 = 54$
Then, calculate the exponents:
$10^2 = 100$
$9^2 = 81$
Now, perform the addition and subtraction:
$100 - 54 + 81 = 127$

10. Approximate $1234.56 + 678.98 - 432.56 + 876.43$

A) 2355.41
B) 2356.41
C) 2357.31
D) 2351.11

Show Answer

Correct Answer: B) 2357.41
Explanation:
First, add and subtract in sequence:
$1234.56 + 678.98 = 1913.54$
$1913.54 - 432.56 = 1480.98$
$1480.98 + 876.43 = 2357.41$

11. Simplify $\frac{(64 + 36)}{10} \times 9 - 5^3$

A) -35
B) -45
C) -55
D) -25

Show Answer

Correct Answer: A) -35
Explanation:
First, calculate inside the parentheses:
$64 + 36 = 100$
Then, divide:
$100 \div 10 = 10$
Now, multiply:
$10 \times 9 = 90$
Then, calculate the exponent:
$5^3 = 125$
Now, subtract:
$90 - 125 = -35$

12. Approximate $1987.23 + 876.45 - 543.21 + 214.87$

A) 2535.32
B) 2535.33
C) 2535.34
D) 2535.35

Show Answer

Correct Answer: C) 2535.34
Explanation:
First, add and subtract in sequence:
$1987.23 + 876.45 = 2863.68$
$2863.68 - 543.21 = 2320.47$
$2320.47 + 214.87 = 2535.34$

13. $8^3 - 7 \times (5 + 4) + 2^3 =$

A) 427
B) 437
C) 447
D) 457

Show Answer

Correct Answer: D) 457
Explanation:
First, calculate inside the parentheses:
$5 + 4 = 9$
Then, multiply:
$7 \times 9 = 63$
Then, calculate the exponents:
$8^3 = 512$
$2^3 = 8$
Now, perform the subtraction and addition:
$512 - 63 + 8 = 457$

14. Approximate $543.89 + 312.56 - 213.45 + 112.34$

A) 755.32
B) 755.33
C) 755.34
D) 755.35

Show Answer

Correct Answer: C) 755.34
Explanation:
First, add and subtract in sequence:
$543.89 + 312.56 = 856.45$
$856.45 - 213.45 = 643.00$
$643.00 + 112.34 = 755.34$

15. Simplify $6^3 - 5 \times (8 + 7) + 4^2$

A) 156
B) 157
C) 158
D) 159

Show Answer

Correct Answer: B) 157
Explanation:
First, calculate inside the parentheses:
$8 + 7 = 15$
Then, multiply:
$5 \times 15 = 75$
Then, calculate the exponents:
$6^3 = 216$
$4^2 = 16$
Now, perform the addition and subtraction:
$216 - 75 + 16 = 157$

16. Approximate $1567.89 + 864.32 - 452.78 + 239.45$

A) 2218.58
B) 2218.68
C) 2218.78
D) 2218.88

Show Answer

Correct Answer: D) 2218.88
Explanation:
First, add and subtract in sequence:
$1567.89 + 864.32 = 2432.21$
$2432.21 - 452.78 = 1979.43$
$1979.43 + 239.45 = 2218.88$

17. Simplify $9 \times (5 + 6) - 4^3$

A) 34
B) 35
C) 36
D) 37

Show Answer

Correct Answer: B) 35
Explanation:
First, calculate inside the parentheses:
$5 + 6 = 11$
Then, multiply:
$9 \times 11 = 99$
Then, calculate the exponent:
$4^3 = 64$
Now, subtract:
$99 - 64 = 35$

18. Approximate $1789.56 + 123.45 - 589.12 + 437.89$

A) 1761.76
B) 1761.77
C) 1761.78
D) 1761.79

Show Answer

Correct Answer: C) 1761.78
Explanation:
First, add and subtract in sequence:
$1789.56 + 123.45 = 1913.01$
$1913.01 - 589.12 = 1323.89$
$1323.89 + 437.89 = 1761.78$

19. Simplify $12^2 - 3^3 + 5 \times 8$

A) 157
B) 167
C) 257
D) 267

Show Answer

Correct Answer: A) 157
Explanation:
First, calculate the exponents:
$12^2 = 144$
$3^3 = 27$
Then, multiply:
$5 \times 8 = 40$
Now, perform the addition and subtraction:
$144 - 27 + 40 = 157$

20. Approximate $2356.78 + 564.23 - 387.65 + 123.89$

A) 2657.24
B) 2657.25
C) 2657.26
D) 2657.27

Show Answer

Correct Answer: B) 2657.25
Explanation:
First, add and subtract in sequence:
$2356.78 + 564.23 = 2921.01$
$2921.01 - 387.65 = 2533.36$
$2533.36 + 123.89 = 2657.25$

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MCQs on Simplifications & Approximations

[Set - 6]

1. Simplify 8^2 - 5 \times 4 + 3^3

2. Approximate 1548.76 + 678.34 - 294.67 + 431.89

3. Simplify 7 \times (9 + 5) - 6^2

4. Approximate 876.43 + 543.21 - 312.54 + 198.78

5. Simplify \frac{(45 + 15)}{3} \times 8 - 7^2

6. 2154.23 + 789.41 - 534.12 + 312.89 =

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

8. Approximate 431.67 + 367.56 - 212.45 + 145.87

9. Solve 10^2 - 6 \times (4 + 5) + 9^2

10. Approximate 1234.56 + 678.98 - 432.56 + 876.43

11. Simplify \frac{(64 + 36)}{10} \times 9 - 5^3

12. Approximate 1987.23 + 876.45 - 543.21 + 214.87

13. 8^3 - 7 \times (5 + 4) + 2^3 =

14. Approximate 543.89 + 312.56 - 213.45 + 112.34

15. Simplify 6^3 - 5 \times (8 + 7) + 4^2

16. Approximate 1567.89 + 864.32 - 452.78 + 239.45

17. Simplify 9 \times (5 + 6) - 4^3

18. Approximate 1789.56 + 123.45 - 589.12 + 437.89

19. Simplify 12^2 - 3^3 + 5 \times 8

20. Approximate 2356.78 + 564.23 - 387.65 + 123.89

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1. Simplify $8^2 - 5 \times 4 + 3^3$

2. Approximate $1548.76 + 678.34 - 294.67 + 431.89$

3. Simplify $7 \times (9 + 5) - 6^2$

4. Approximate $876.43 + 543.21 - 312.54 + 198.78$

5. Simplify $\frac{(45 + 15)}{3} \times 8 - 7^2$

6. $2154.23 + 789.41 - 534.12 + 312.89 =$

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

8. Approximate $431.67 + 367.56 - 212.45 + 145.87$

9. Solve $10^2 - 6 \times (4 + 5) + 9^2$

10. Approximate $1234.56 + 678.98 - 432.56 + 876.43$

11. Simplify $\frac{(64 + 36)}{10} \times 9 - 5^3$

12. Approximate $1987.23 + 876.45 - 543.21 + 214.87$

13. $8^3 - 7 \times (5 + 4) + 2^3 =$

14. Approximate $543.89 + 312.56 - 213.45 + 112.34$

15. Simplify $6^3 - 5 \times (8 + 7) + 4^2$

16. Approximate $1567.89 + 864.32 - 452.78 + 239.45$

17. Simplify $9 \times (5 + 6) - 4^3$

18. Approximate $1789.56 + 123.45 - 589.12 + 437.89$

19. Simplify $12^2 - 3^3 + 5 \times 8$

20. Approximate $2356.78 + 564.23 - 387.65 + 123.89$