Simplification and Approximation

A. 6 1/8
B. 5 3/4
C. 6 3/4
D. 5 7/8
Explanation:
6 of 5/8 / 5/8 – 1/8
30/8 * 8/5 – 1/8 = 6 – 1/8 = 5 7/8

A. 1
B. 2
C. 69/28
D. 66/17
Explanation:
(22 * 495 + 891 * 44) / (33 * 176 + 55 * 264) = (22 * 33 * 15 + 9 * 99 * 2 * 22) / (33 * 22 * 8 + 5 * 11 * 22 * 12)
= (22 * 33 * 15 + 22 * 33 * 54) / (33 * 22 * 8 + 33 * 22 * 20) = [22 * 33(15 + 54)] / [33 * 22(8 + 20)] = 69/28

A. 1 17/38
B. 1 38/17
C. 2 38/17
D. None of these
Explanation:
[(62.25/2.5) + (12.5/0.5)] / [(0.75 * 9) + (3.5 * 3.5)]
= [(6225/250) + (125/5)] / (6.75 + 12.25)
= (249/10 + 25) / 19 = 499/190 = 2 119/190

A. 2
B. 1
C. 4
D. 3
Explanation:
[(523 + 27) * (187 – 35) / (424 + 16)] / [110/22 of (2 * 38)]
= [(550 * 152) / 440] / [(110/44) * 38]
= (5 * 38)/(5/2 * 38) = 2

A. 1350
B. 1450
C. 1550
D. 1421
Explanation:
(50 – ?/29)% of 4200 = 3√196

A. 12 3/88
B. 24 21/24
C. 12 25/224
D. 12 1/224
Explanation:
7 + 5 – (3/2 * 1/4) of 2/7 + 7/2 * 1/16
= 7 + 5 – (3/2 * 1/4) * 2/7 + 7/2 * 1/16 = 7 + 5 – 3/28 + 7/32
= 12 + 3/28 + 7/32 = 12 + (7 * 7 – 3 * 8)/224
= 12 + 25/224 = 12 25/224

A. 9
B. 3
C. 0.3
D. 0.03
Explanation:
0.003 * ? * 0.0003 = 0.00000027
3/1000 * ? * 3/10000 = 3/1000 * 3/1000 * 3/100
? = 3/10 = 0.3

A. 4
B. 60
C. 1.75
D. None of these
Explanation:
[(7 * 9) + (2 * 12) + 3]/[(12 * 3) + (81/9)] = (63 + 24 + 3)/(36 + 9) = 90/45 = 2

A. 150 1/3
B. 150 2/3
C. 149 2/3
D. 149 1/3
Explanation:
6 2/3 * 9 3/5 * 2 1/3 + 1 1/3 = 20/3 * 48/5 * 7/3 + 4/3
= 448/3 + 4/3 = 452/3 = 150 2/3

A. 1500
B. 1750
C. 9000
D. 7500
Explanation:
9000 + 16 2/3 % of ? = 10500 => 9000 + 50/3 % of ? = 10500
50/(3 * 100) of ? = 1500 => ? = 1500 * 6
? = 9000