Problem 63 Simplify each series of addition... [FREE SOLUTION]

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Introductory Algebra for College Students

Robert Blitzer

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 63

Simplify each series of additions and subtractions. $$1-\frac{2}{3}-\left(-\frac{5}{6}\right)$$

Short Answer

Expert verified

The simplified expression is $\frac{7}{6}$

Step by step solution

Interpret the negative before the bracket

The bracket contains a negative fraction. Remember that a negative sign in front of a bracket negates all the elements inside. Change $-\left(-\frac{5}{6}\right)$ to $+\frac{5}{6}$ thus rewriting the expression as: $1-\frac{2}{3}+\frac{5}{6}$

Finding a common denominator

To add or subtract fractions, a common denominator is required. Here, $3$ and $6$ appear in the denominators. The least common multiple (LCM) of $3$ and $6$ is $6$, therefore, convert all fractions to have $6$ as the denominator. The expression becomes: $1-\frac{4}{6}+\frac{5}{6}$

Simplification

Now, perform the addition and subtraction operations: $1-\frac{4}{6}+\frac{5}{6} = 1 + \frac{1}{6}$

Convert the mixed number

Convert $1 + \frac{1}{6}$ into an improper fraction. Multiply the denominator of the fraction by the whole number, add the numerator, and put over the original denominator. This gives $\frac{7}{6}$

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91影视

Simplify each series of additions and subtractions. $$1-\frac{2}{3}-\left(-\frac{5}{6}\right)$$

Short Answer

Step by step solution

Interpret the negative before the bracket

Finding a common denominator

Simplification

Convert the mixed number

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