Simplification of Rational Numbers
Simplification of Rational Numbers
Simplification of Rational Numbers:
In order to simplify rational expressions involving the sum or difference of three or more rational numbers, we may use the following steps:
Step I: Find the LCM of the denominator of all the numbers involved.
Step II: Write a rational number whose denominator is the LCM obtained in Step I and numerator is computed as follows:
Divide the LCM obtained in step I by the denominator of first rational number and get a quotient. Multiply the numerator of first rational number by this quotient. Repeat this procedure for all rational numbers. Retain the given signs of addition and subtraction between the given rational numbers and get an expression involving integers. Simplify this expression to get an integer as the numerator.
Step III: Reduce the rational number obtained in step II to the lowest form if it is not already so. This rational number so obtained is the required rational number.
Simplify: -3/4 + 9/8 - (-5)/6
Solution:
We have,
-3/4 + 9/8 - (-5)/6 = -3/4 + 9/8 + 5/6, [Since, -(-5)/6 = 5/6]
Clearly, denominators of the three rational numbers are positive. We now re-write them so that they have a common denominator equal to the LCM of the denominators.
In this case the denominators are 4, 8 and 6.
The LCM of 4, 8 and 6 is 24.
Now, -3/4 = (-3) × 6/4 × 6 = -28/24,
9/8 = 9 × 3/8 × 3 = 27/24 and
5/6 = 5 × 4/6 × 4 = 20/24
Therefore, -3/4 + 9/8 - (-5)/6
= -3/4 + 9/8 + 5/6
= -28/24 + 27/24 + 20/24
= (-28 + 27 + 20)/24
= 19/24
Thus, -3/4 + 9/8 - (-5)/6 = 19/24
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| Right Option : B | |||
| View Explanation | |||
By what rational number should | |||
| Right Option : B | |||
| View Explanation | |||
What is the reciprocal of | |||
| Right Option : D | |||
| View Explanation | |||
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