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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 71
Chapter 1, Problem 71

Add or subtract as indicated. Write answers in lowest terms as needed. 7/12-1/9

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Identify the problem as a subtraction of two fractions: \(\frac{7}{12} - \frac{1}{9}\).
Find the least common denominator (LCD) of the fractions. The denominators are 12 and 9. Determine the LCD by finding the least common multiple (LCM) of 12 and 9.
Rewrite each fraction with the LCD as the new denominator by multiplying numerator and denominator by the necessary factor.
Subtract the numerators of the rewritten fractions while keeping the common denominator the same: \(\frac{a}{LCD} - \frac{b}{LCD} = \frac{a - b}{LCD}\).
Simplify the resulting fraction by reducing it to lowest terms, if possible, by dividing numerator and denominator by their greatest common divisor (GCD).

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Key Concepts

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

Finding a Common Denominator

To add or subtract fractions, they must have the same denominator. This involves finding the least common denominator (LCD), which is the least common multiple of the denominators. For example, for 7/12 and 1/9, the LCD is 36.
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Rationalizing Denominators

Performing Fraction Addition and Subtraction

Once fractions have a common denominator, add or subtract their numerators while keeping the denominator the same. For instance, convert 7/12 to 21/36 and 1/9 to 4/36, then subtract the numerators: 21 - 4 = 17.
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Performing Row Operations on Matrices

Simplifying Fractions to Lowest Terms

After performing addition or subtraction, simplify the resulting fraction by dividing numerator and denominator by their greatest common divisor (GCD). This ensures the answer is in simplest form, making it easier to interpret.
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Radical Expressions with Fractions
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