Decimals & Fractions

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1. (c)

6202.5 + 620.25 + 62.025 + 6.2025 + 0.62025
⇒ 6822.75 + 68.84775
⇒ 6891.59775

2. (d)

9.044 + 0.7036 = 9.7476

 9.7476 + 7.6 = 17.3476

 17.3476 + 0.3 = 17.6476       

17.6476 + 2 = 19.6476 

3. (a) 

31.004 − 17.2368 = 13.7654

4. (b)

6.3204 × 100 = 632.04

5. (a)

6. (b)

2.68 × 0.74 = 1.9832

7. (b) 

0.0204 ÷ 17 = 0.0012

8. (b)

1 / 0.0003718 = 10000 / 3.718 

⇒ 10000 * 1 / 3.718

⇒  10000 * 0.2689 = 2689.

9. (b)

2/7 – 3(4/7) +18(1/2) = x/7 +15(1/2)

2/7 – 25/7 + 37/2 = x/7 + 31/2

213/14 = x/7 + 31/2

213 = 2x + 217

213 – 2x = 217

– 2x = 217 – 213

– 2x = 4

x = -2

10. (a)

4 (7/12) + 6 (5/6) – 8 (3/4) = ? + 1 (2/3)

55/12 + 41/6 – 35/4 = ? + 5/3

55/12 + 82/12 – 105/12 = 32/12 = ? + 5/3

32/12 = ? + 5/3

8/3 – 5/5 = ?

(8-5)/ 3 = ? 

3/3 = ?

1

11. (c)

Combine the fractions.
13(1/6) + 6(5/6) = 13+1/6+6+5/6 
13 + 1/ 6 + 6 + 5/6 = 19 + 6/6     

19 + 6/6 = 19 + 1 = 20

Put the value of fraction,
? + 20 = 24
? = 24 – 20 = 4
 
12. (d)
Simplify the fractions.
5(1/ 2) − 4(1/3) = ?-4
⇒ 5/2 − 4/3 = ? – 4
⇒ 15/6 − 8/6 = ? – 4
⇒ 7/6 = ? – 4
⇒ (7/6) + 4 = ? 
⇒ (7/6) + 4 = ? 
⇒  7/6 + 24/6 = ?
⇒  31/6
⇒  5(1/6)
 
13. (a)
60/7 + 36/4 – ? = 187/28
240/28 + 273/28 – ? = 187/28
513/28 – ? = 187/28
513/28 – 187/28 = ?
326/28 = ?
163/14 =?
= 11 (9/14)
 
14. (a)

8 (3/4) + 4 (1/4) – 3 (1/2) = ? + 7(1/3)

24/4 + 4/4 – 3/2 = ? + 7(1/3)

6 + 1 – (3/2) = ? + 7(1/3)

7 – (3/2) = ? + 7(1/3)

11/2 = ? + 7(1/3)

11/2 – 7/3 = ?

(33-14)/ 6 = ?

= 19/6 

15. (b)

3 (1/4) + ? = 7(1/8) + 2 (1/12) 

13/4 + ? = 57/8 + 25/12

13/4 + ? = 171/24+ 50/24

13/4 + ? = 221/24

? = 221/24 – 13/4

? = 221/24 – 78/24

= 143/24 = 5 (23/24)

16. (b)

17. (c)

18. (a)

The denominator of all fractions are 3, 4, 5 and 6.

LCM of 3, 4, 5 and 6 is 60.

No equation all denominators with 60 get.

2/3 = (2×20)/ (3×20) = 40/60

3/4 = (3×15)/ (4×15) = 45/60

4/5 = (4×12)/ (5×12) = 48/60

5/6 = (5×10)/ (6×10) = 50/60

Now. 50>48>45>40

⇒ 50/60 > 48.60 > 45/60 > 40/60

⇒ 5/6 > 4/5 > 3/4 > 2/3

The biggest number is 5/6 and the smallest number is 2/3.

The difference between them is 5/6 – 2/3 = 1/6

19. (d)

(3 + 87/99) – (2 + 59/99)

(3 + 0.87) – (2 + 0.59) 

3.89 – 2.59 = 1.28

20. (c)

0.346767 + 0.133333 = 0,4801/9900 = 0.48‾01

 

 

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Dhalendra Kothale

Dhalendra Kothale

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