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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 63
Chapter 1, Problem 63

Add or subtract as indicated. Write answers in lowest terms as needed. 318+2143\(\frac{1}{8}\) + 2\(\frac{1}{4}\)

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First, convert the mixed numbers to improper fractions. For 3(1/8), multiply the whole number 3 by the denominator 8 and add the numerator 1: \(3 \times 8 + 1 = 25\), so \(3(1/8) = \frac{25}{8}\). For 2(1/4), multiply 2 by 4 and add 1: \(2 \times 4 + 1 = 9\), so \(2(1/4) = \frac{9}{4}\).
Next, find a common denominator for the fractions \(\frac{25}{8}\) and \(\frac{9}{4}\). The denominators are 8 and 4, and the least common denominator (LCD) is 8.
Rewrite \(\frac{9}{4}\) with the denominator 8 by multiplying both numerator and denominator by 2: \(\frac{9 \times 2}{4 \times 2} = \frac{18}{8}\).
Now, add the two fractions with the common denominator: \(\frac{25}{8} + \frac{18}{8} = \frac{25 + 18}{8} = \frac{43}{8}\).
Finally, convert the improper fraction \(\frac{43}{8}\) back to a mixed number by dividing 43 by 8. The quotient is the whole number part, and the remainder over 8 is the fractional part.

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Key Concepts

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

Mixed Numbers

Mixed numbers combine a whole number and a fraction, such as 3(1/8). To perform operations, they are often converted to improper fractions by multiplying the whole number by the denominator and adding the numerator.
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Adding Fractions

To add fractions, they must have a common denominator. If denominators differ, find the least common denominator (LCD), convert each fraction, then add the numerators while keeping the denominator the same.
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Simplifying Fractions

After performing addition or subtraction, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD) to write the answer in lowest terms.
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