Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.1 - Real Numbers - 1.1 Exercises: 18

Answer

Associative property and distributive property

Work Step by Step

In the case of 7(a + b + c) = 7(a + b) + 7c, it would not matter whether the first step was to add up a, b and c or to multiply them all by 7 and then add up the results. This is because the distributive property states that if we multiply a number (7) by a sum of two (or, in this case, three) numbers (a, b, c), we get the same result as we get if we multiply the number by each of the terms and then add the results. Similarly, it doesn't matter whether we first add up a and b, or b and c, etc., because the associative property states that when we add three numbers, it doesn’t matter which two we add first. In this sense, 7(a + c) + 7b would have yielded the same result as 7(a + b) + 7c.
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