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Exercises Expressions, exponents and radicals

Example 7.12 from Prealgebra, 7.2 Commutative and Associative Properties

Commutative and Associative Properties: example 7.12

Simplify: $(\frac{5}{13} + \frac{3}{4}) + \frac{1}{4} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Notice that the second and third terms have a common denominator, so this work will be easier if we change the grouping.

$(\frac{5}{13} + \frac{3}{4}) + \frac{1}{4}$

Group the terms with a common denominator. $\frac{5}{13} + (\frac{3}{4} + \frac{1}{4})$

Add in the parentheses first. $\frac{5}{13} + (\frac{4}{4})$

Simplify the fraction. $\frac{5}{13} + 1$

Add. $1 \frac{5}{13}$

Convert to an improper fraction. $\frac{18}{13}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: $(\frac{7}{15} + \frac{5}{8}) + \frac{3}{8} .$

How did it go?

PreviousCommutative and Associative Properties: example 7.11 Next Commutative and Associative Properties: example 7.13

From Prealgebra (1st edition) by OpenStax (Rice University), section 7.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.