RS Aggarwal Solutions: Integers (Exercise 2D) | Mathematics (Maths) Class 7 PDF Download

Q.1. Which of the following is a vulgar fraction?
(a) 3/10
(b) 13/10
(c) 10/3
(d) none of these
Ans. (c) 10/3
10/3 is a vulgar fraction, because its denominator is other than 10, 100, 1000, etc.

Q.2. Which of the following is an improper fraction?
(a) 7/10
(b) 7/9
(c) 9/7
(d) none of these
Ans. (c) 9/7
9/7 is an improper fraction, because its numerator is greater than its denominator.

Q.3. Which of the following is a reducible fraction?
(a) 105/112
(b) 104/121
(c) 77/72
(d) 46/63
Ans. (a) 105/112
A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor.
(105÷7)/(112÷7) =15/16
Thus, 105/112 is a reducible fraction.

Q.4. 2/3, 4/6, 6/9, 8/12 are
(a) like fractions
(b) irreducible fractions
(c) equivalent fractions
(d) none of these
Ans. (c) equivalent fractions
Equivalent fractions are those which are the same but look different.
Thus, 2/3, 4/6=2/3, 6/9=2/3, 8/12=2/3 are equivalent fractions.

Q.5. Which of the following statements is true?
(a) 9/16 = 13/24
(b) 9/16 < 13/24
(c) 9/16 > 13/24
(d) none of these
Ans. (c) 9/16 > 13/24
The two fraction are 9/16 and 13/24.
By cross multiplication, we have:
9 × 24 = 216 and 13 × 16 = 208
However, 216 > 208
∴ 9/16 > 13/24

Q.6. Reciprocal ofis
(a)
(b)
(c)
(d) none of these
Ans. (d) none of these
Reciprocal of= Reciprocal of 7/4 = 4/7

Q.7. (3/10+8/15)=?
(a) 11/10
(b) 11/15
(c) 5/6
(d) none of these
Ans. (c) 5/6
(3/10+8/15) =(9+16) / 30 [∵ LCM of 10 and 15 = 30]
= 25/30
= 5/6

Q.8.= ?
(a)
(b) 1/12
(c)
(d) 11/12
Ans. (d) 11/12
= (13/4−7/3)
= (39−2812)39-2812 [∵ LCM of 4 and 3 = 12]
= 11/12

Q.9. 36÷1/4=?
(a) 9
(b) 1/9
(c) 1/144
(d) 144
Ans. (d) 144
36÷1/4=36×4 [∵ Reciprocal of 1/4 = 4]
= 144

Q.10. By what number shouldbe multiplied to get?
(a)
(b) 5/7
(c)
(d) 1/7
Ans. (b) 5/7
Required number =
= 13/7÷13/5
= 13/7×5/13 [∵ Reciprocal of 13/5 = 5/13]
= 5/7

Q.11. By what number shouldbe divided to get 2/3?
(a)
(b)
(c) 4/9
(d)
Ans. (d)
Required number =÷2/3
= 3/2÷2/3
= 3/2×3/2 [∵ Reciprocal of 2/3 = 3/2]
= 9/4
=

Q.12. ÷2/3=?
(a)
(b)
(c)
(d) none of these
Ans. (c)
÷2/3=8/5÷2/3
= 8/5×3/2 [∵ Reciprocal of 2/3 = 3/2]
= (4×3)/5
= 12/5
=

Q.13.= ?
(a) 1
(b) 2
(c)
(d)
Ans. (d)
= 11/5÷6/5
= 11/5×5/6 [∵ Reciprocal of 6/5 = 5/6]
= 11/6
=

Q.14. The reciprocal ofis
(a)
(b)
(c)
(d) 3/5
Ans. (d) 3/5
Reciprocal of 123123 = Reciprocal of 5353 = 3535

Q.15. Which one of the following is the correct statement?
(a) 2/3 < 3/5 < 14/15
(b) 3/5 < 2/3 < 14/15
(c) 14/15 < 3/5 < 2/3
(d) none of these
Ans. (b) 3/5 < 2/3 < 14/15
The given fractions are 3/5, 2/3 and14/15.
LCM of 5, 3 and 15 = 15
Now, we have:
2/3×5/5=10/15, 3/5×3/3=9/15 and 14/15×1/1=14/15
Clearly, 9/15 <10/15<14/15
∴ 3/5 < 2/3 < 14/15

Q.16. A car runs 16 km using 1 litre of petrol. How much distance will it cover inlitres of petrol?
(a) 24 km
(b) 36 km
(c) 44 km
(d)km
Ans. (c) 44 km
Distance covered by the car onL of petrol =(16 ×) km
= (16 × 11/4) km
= (4 × 11) km = 44 km

Q.17. Lalit reads a book forhours every day and reads the entire book in 6 days. How many hours does he take to read the entire book?
(a)hours
(b)hours
(c)hours
(d)hours
Ans. (a)hours
Time taken by Lalit to read the entire book = (6 × ) h
= (6×7/4) h
= (21/2) h
=h