RS Aggarwal Solutions Class 7 Maths Chapter 4 Ex 4.4 (Updated For 2021-22)

RS Aggarwal Solutions Class 7 Maths Chapter 4 Exercise 4.4: You can easily finish your class assignments and start your exam preparation with RS Aggarwal Solutions Class 10 Maths. The solutions of RS Aggarwal Solutions Class 7 Maths Chapter 4 Exercise 4.4 are prepared by the subject matter experts that are very well-explained and accurate.

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RS Aggarwal Solutions Class 7 Maths Chapter 4 Exercise 4.4

RS Aggarwal Solutions Class 7 Maths Chapter 4 Exercise 4.4 – Overview

Subtraction Of Rational Numbers

There are 2 cases in the Subtraction Of Rational Numbers, mentioned below:

• Having The Same Denominator

There are two random numbers, i.e., 7/4 and 5/4. Subtraction between the two rational numbers in the following way given below:

7/4 − 5/4 = (7−5) / 4 = 2/4 which can be further reduced to 1/2.

• Having Different Denominators

In case of having 2 different denominators, you should follow these steps:

1. Find the L.C.M of the given denominator Values and make them even i.e., same, just like you did in the addition of rational numbers with different denominators.
2. Once the values are the same, you can subtract the rational numbers.

Properties Of A Rational Number

There are 4 properties of a rational number, i.e. associative property,  closure property, commutative property, and distributive property. 

• Closure Property

According to this property, the difference that comes while performing the subtraction operation between the two rational numbers will always produce a rational number as a result.

Hence Q is closed under subtraction.

Take two different rational numbers such as a/b and c/d, here as per the statement above (a/b) – (c/d) will yield to a rational number only.

Eg: (3/7) – (2/7)  = 1/7 which is a rational number yield as a result.

• Commutative Property

According to the property, the Subtraction of two rational numbers can never be said as commutative.

Here,  (a/b) – (c/d)  ≠  (c/d) – (a/b)

Eg: 5/6 – 1/6 =  4/6  =  2/3

1/6 – 5/6  =  -4/6  =  -2/3 

Hence, 5/6 – 1/6  ≠  1/6 – 5/6

Therefore, we can say that the Commutative property is not true at all in the case of subtraction operation.

• Associative Property

As per this property, the Subtraction done between the two rational numbers is never associative.

If a/b, c/d and e/f  are any three rational numbers,

then a/b – (c/d – e/f)  ≠  (a/b – c/d) – e/f

Eg: 2/7 – (5/7 – 1/7)  =  2/7 – 4/7  =  -2/7

(2/7 – 5/7) – 1/7  =  -3/7 – 1/7  =  -4/7

Here, from the above example we can see that,  -2/7  ≠ -4/7

Therefore, 2/7 – (5/7 – 1/7)  ≠  (2/7 – 5/7) – 1/7.

Hence, it is proved that the Associative property is not true at all for the subtraction operation.

• Distributive Property

In this property, the Multiplication operation done between the two given rational numbers is always going to be distributive over the subtraction.

Consider the three rational numbers like a/b, c/d, and e/f,

In such a case, a/b x (c/d – e/f)  =  a/b x c/d  –  a/b x e/f

Eg: 5/3 x (3/7 – 1/7)  =  5/3 x 2/7  =  10/21

5/3 x (3/7 – 1/7)  =  (5/3 x 3/7) –  (5/3 x 1/7) =  (15/21 – 5/21) = 10/21

Hence, 5/3 x (3/7 – 1/7)  =  (5/3 x 3/7) –  (5/3 x 1/7) 

This example states that the multiplication operation is distributive over the subtraction operation.

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