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

Q: 1. What are integers and how are they represented in mathematics?

Ans.Integers are whole numbers that can be positive, negative, or zero. They are represented on the number line and include numbers like -3, -2, -1, 0, 1, 2, 3, and so forth. Integers do not include fractions or decimals.

Q: 2. How do you add and subtract integers?

Ans.To add integers, you combine their values. If both integers are positive or both are negative, you add their absolute values and keep the common sign. For example, 3 + 5 = 8 and -3 + (-5) = -8. To subtract integers, you can add the opposite. For instance, 3 - 5 can be rewritten as 3 + (-5) = -2.

Q: 3. What are the rules for multiplying and dividing integers?

Ans.When multiplying or dividing integers, the rules are straightforward: if both integers have the same sign (both positive or both negative), the result is positive. If the integers have different signs (one positive and one negative), the result is negative. For example, 4 × 3 = 12 and -4 × -3 = 12, while 4 × -3 = -12.

Q: 4. How do you solve word problems involving integers?

Ans.To solve word problems involving integers, first, read the problem carefully to identify the quantities involved and their signs (positive or negative). Next, translate the words into mathematical expressions using integers and then perform the required operations (addition, subtraction, multiplication, or division) to find the solution.

Q: 5. Can you give an example of comparing integers?

Ans.Comparing integers involves determining which integer is greater or lesser. For example, to compare -3 and 2, we see that -3 is less than 2. On a number line, -3 is located to the left of 2, illustrating that it has a lesser value.

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 RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT) = 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
RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT) = (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 = RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT)
= 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
= RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT)

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
= RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT)

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 on RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT) L 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) RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT) hours
Time taken by Lalit to read the entire book = (6 × ) h
= (6×7/4) h
= (21/2) h
=h

The document RS Aggarwal Solutions: Fractions (Exercise 2D) | Mathematics (Maths) Class 7 (Old NCERT) is a part of the Class 7 Course Mathematics (Maths) Class 7 (Old NCERT).

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FAQs on RS Aggarwal Solutions: Fractions (Exercise 2D) - Mathematics (Maths) Class 7 (Old NCERT)

1. What are integers and how are they represented in mathematics?

Ans.Integers are whole numbers that can be positive, negative, or zero. They are represented on the number line and include numbers like -3, -2, -1, 0, 1, 2, 3, and so forth. Integers do not include fractions or decimals.

2. How do you add and subtract integers?

Ans.To add integers, you combine their values. If both integers are positive or both are negative, you add their absolute values and keep the common sign. For example, 3 + 5 = 8 and -3 + (-5) = -8. To subtract integers, you can add the opposite. For instance, 3 - 5 can be rewritten as 3 + (-5) = -2.

3. What are the rules for multiplying and dividing integers?

Ans.When multiplying or dividing integers, the rules are straightforward: if both integers have the same sign (both positive or both negative), the result is positive. If the integers have different signs (one positive and one negative), the result is negative. For example, 4 × 3 = 12 and -4 × -3 = 12, while 4 × -3 = -12.

4. How do you solve word problems involving integers?

Ans.To solve word problems involving integers, first, read the problem carefully to identify the quantities involved and their signs (positive or negative). Next, translate the words into mathematical expressions using integers and then perform the required operations (addition, subtraction, multiplication, or division) to find the solution.

5. Can you give an example of comparing integers?

Ans.Comparing integers involves determining which integer is greater or lesser. For example, to compare -3 and 2, we see that -3 is less than 2. On a number line, -3 is located to the left of 2, illustrating that it has a lesser value.

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