Problem 67 Simplify each series of addition... [FREE SOLUTION]

91影视

Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 67

Simplify each series of additions and subtractions. $$-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)$$

Short Answer

Expert verified

The simplified form of the given series of addition and subtraction is $-\frac{3}{8}$

Step by step solution

Identify and Separate Subtractions and Additions

The given expression is $-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)$. The subtraction sign before $\frac{5}{8}$ becomes an addition because of the negative sign within its brackets.

Simplify

The expression now changes to $-\frac{3}{4}-\frac{1}{4}+\frac{5}{8}$. Now, compute the subtraction and addition operations. The Least Common Multiple (LCM) of 8 and 4 is 8. The expressions $-\frac{3}{4}$ and $-\frac{1}{4}$ are made to have the same denominator as $\frac{5}{8}$ to simplify the calculation.

Resolve Fractions to have same denominator

Multiplying each of the fractions -3/4 and -1/4 by 2/2 to make the denominator 8, they therefore become $-\frac{6}{8}$ and $-\frac{2}{8}$ respectively. The expression will now be $-\frac{6}{8} -\frac{2}{8} + \frac{5}{8}$

Perform Arithmetic Operations

Next, add and subtract as described, from left to right: $-\frac{6}{8} - \frac{2}{8} = -\frac{8}{8}$ and then $-\frac{8}{8} + \frac{5}{8} = -\frac{3}{8}$

Write the Final Answer

The simplified form of the given expression is $-\frac{3}{8}$

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91影视

Simplify each series of additions and subtractions. $$-\frac{3}{4}-\frac{1}{4}-\left(-\frac{5}{8}\right)$$

Short Answer

Step by step solution

Identify and Separate Subtractions and Additions

Simplify

Resolve Fractions to have same denominator

Perform Arithmetic Operations

Write the Final Answer

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