# Rational Expressions Involving Addition and Subtraction

How to simplify rational expressions involving addition and subtraction of three or more rational numbers?

1. Evaluate 3/5 + 7/3 + -11/5 + -2/3

Solution:

Using the commutative and associative law, it follows that we may arrange the terms in any manner suitably. Using this rearrangement property, we have:

3/5 + 7/3 + -11/5 + -2/3

= (3/5 + -11/5) + (7/3 + -2/5)

= {(3 + (-11)}/5 + {7 + (-2)}/3

= -8/5 + 5/3

= (-24 + 25)/15

= 1/15

2. Simplify: (4/7 + -8/9 + -5/21 + 1/3)

Solution:

Using the rearrangement property, we have:

4/7 + -8/9 + -5/21 + 1/3 = (4/7 + -5/21) + (-8/9 + 1/3)

= {12 + (-5)}/21 + {-8 + 3}/9

= (7/21 + -5/9)

= {21 + (-35)}/63

= -14/63

= -2/9

3. What should be subtracted from -5/7 to get -1?

Solution:

Let the required number be x. Then,

-5/7 – x = -1

-5/7 = x - 1

x = (-5/7 + 1)

= (-5 + 7)/7

= 2/7

Hence, the required number is 2/7.

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Negative Rational Number

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