Basic College Mathematics (10th Edition)

Published by Pearson
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Chapter 2 - Multiplying and Dividing Fractions - 2.6 Applications of Multiplication - 2.6 Exercises - Page 158: 30

Answer

Both statements are true.

Work Step by Step

Multiplication of whole numbers can also be written as repeated addition. For example, multiplying a number by 2 is the same as adding that number to itself. Multiplying by 3 is the same as adding the number together 3 times. Since adding two numbers always results in a result that is larger than either of the two numbers, multiplying whole numbers also gives a result that is larger than either of the two numbers, Multiplying by a proper fraction is a way of dividing a number into smaller (fractional) parts. If x and y are both proper fractions, multiplying x times y can be seen as dividing x into the smaller parts represented by y or, because of the commutative property of multiplication, can be seen as dividing y into the smaller parts represented by x. For this reason the product of multiplying two proper fractions will be smaller than either of the numbers being multiplied.
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