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NCERT solution class 8 Exercise1.2-
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NCERT solution class 8 Exercise1.2-How to do subtraction of rational numbers
Subtracting rational numbers is similar to adding them. Rational numbers are numbers that can be expressed as fractions, and when you subtract them, you follow these steps:
- Ensure a Common Denominator: If the rational numbers you want to subtract have different denominators, find a common denominator. The common denominator is typically the least common multiple (LCM) of the denominators.
- Express Fractions with the Common Denominator: Rewrite each fraction so that they all have the same denominator (the common denominator). To do this, multiply the numerator and denominator of each fraction by the same number to make them share the common denominator.
- Subtract the Numerators: Once you have all the fractions with the same denominator, subtract the numerators. The denominator remains the same.
- Simplify (if necessary): If the resulting fraction can be simplified, simplify it by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.
- Here’s an example of subtracting rational numbers:
- Let’s subtract 5/8 from 7/8.
- Find the common denominator, which is 8 (since both fractions already have 8 as the denominator).
- Express the fractions with the common denominator:
- 7/8 (no need to change it)
- 5/8 (no need to change it)
- Subtract the numerators: 7/8 – 5/8 = 2/8.
- Simplify (if necessary). 2/8 can be simplified by finding the GCD of 2 and 8, which is 2. Divide both the numerator and denominator by 2: (2/2) / (8/2) = 1/4.
- So, 7/8 – 5/8 = 1/4.
NCERT solution class 8 Exercise1.2- Commutative property of subtraction of rational numbers-
The commutative property does not hold for subtraction as it does for addition. The commutative property of addition states that changing the order of numbers in an addition expression does not affect the result, but this property does not apply to subtraction.
In other words, for rational numbers a and b:
a – b is not necessarily equal to b – a.
Subtraction is not commutative, meaning that changing the order of the numbers in a subtraction expression can change the result. For example, if you have the rational numbers 3/4 and 1/4:
3/4 – 1/4 is not equal to 1/4 – 3/4.
3/4 – 1/4 = 2/4 = 1/2 1/4 – 3/4 = (-2/4) = -1/2
The results are not the same, so the commutative property does not apply to subtraction for rational numbers.
The associative property of subtraction does not exist as a standalone property in the same way that the associative property does for addition. The associative property specifically refers to the ability to group numbers and perform the same operation regardless of how they are grouped. For subtraction, this property is not relevant because subtraction does not exhibit associativity.
The associative property for addition is written as:
(a + b) + c = a + (b + c)
However, when it comes to subtraction, changing the grouping of numbers can significantly change the result. For example, consider three rational numbers: a, b, and c. The associative property does not hold for subtraction: