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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