Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 95

Chapter 1, Problem 95

Evaluate each expression. (-2/9 -1/4) - {-5/18 - (-1/2)}

Verified step by step guidance

First, simplify the expression inside the parentheses and the braces separately. Start with the first parentheses: $\left(-\frac{2}{9} - \frac{1}{4}\right)$.

Find a common denominator for the fractions inside the first parentheses. The denominators are 9 and 4, so the least common denominator (LCD) is 36. Rewrite each fraction with denominator 36: $-\frac{2}{9} = -\frac{8}{36}$ and $-\frac{1}{4} = -\frac{9}{36}$.

Add the fractions inside the first parentheses: $-\frac{8}{36} - \frac{9}{36} = -\frac{17}{36}$.

Next, simplify the expression inside the braces: $\left\{-\frac{5}{18} - \left(-\frac{1}{2}\right)\right\}$. Remember that subtracting a negative is the same as adding a positive.

Rewrite $-\frac{1}{2}$ as $+\frac{1}{2}$ and find a common denominator for $-\frac{5}{18}$ and $+\frac{1}{2}$. The denominators are 18 and 2, so the LCD is 18. Convert $\frac{1}{2}$ to $\frac{9}{18}$, then add: $-\frac{5}{18} + \frac{9}{18} = \frac{4}{18}$. Simplify if possible.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Operations with Fractions

Understanding how to add, subtract, multiply, and divide fractions is essential. This includes finding common denominators to combine fractions and correctly handling negative signs to ensure accurate calculations.

Order of Operations

Applying the correct order of operations (PEMDAS) is crucial when evaluating expressions. This means simplifying expressions inside parentheses or braces first, then performing addition or subtraction in the correct sequence.

Working with Negative Numbers

Handling negative numbers properly is important, especially when subtracting negative values, which involves changing signs. Recognizing that subtracting a negative is equivalent to adding a positive helps avoid common mistakes.

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Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. N ∪ ∅