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 67

Chapter 1, Problem 67

Add or subtract as indicated. Write answers in lowest terms as needed. 13/15 - 3/15

Verified step by step guidance

Identify the denominators of the fractions. Here, both fractions have the same denominator, which is 15.

Since the denominators are the same, subtract the numerators directly: $\frac{13}{15} - \frac{3}{15} = \frac{13 - 3}{15}$.

Perform the subtraction in the numerator: $\frac{10}{15}$.

Simplify the fraction by finding the greatest common divisor (GCD) of 10 and 15, which is 5.

Divide both numerator and denominator by the GCD to write the fraction in lowest terms: $\frac{10 \div 5}{15 \div 5} = \frac{2}{3}$.

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Key Concepts

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

Adding and Subtracting Fractions with Like Denominators

When fractions have the same denominator, you can add or subtract their numerators directly while keeping the denominator unchanged. For example, 13/15 - 3/15 equals (13 - 3)/15 = 10/15.

Simplifying Fractions to Lowest Terms

After performing addition or subtraction, simplify the fraction by dividing the numerator and denominator by their greatest common divisor (GCD). For instance, 10/15 simplifies to 2/3 by dividing both by 5.

Understanding the Denominator in Fraction Operations

The denominator represents the total number of equal parts in a whole. When denominators are the same, it ensures the fractions refer to parts of the same size, allowing direct addition or subtraction of numerators.

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