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 54

Chapter 1, Problem 54

Add or subtract as indicated. Write answers in lowest terms as needed.2/9 + 5/9

Verified step by step guidance

Identify the operation: Since the problem is \(\frac{2}{9} + \frac{5}{9}\), we are adding two fractions with the same denominator.

Because the denominators are the same, add the numerators directly: \(2 + 5\).

Write the sum over the common denominator: \(\frac{2 + 5}{9}\).

Simplify the numerator: \(\frac{7}{9}\).

Check if the fraction \(\frac{7}{9}\) can be simplified further by finding the greatest common divisor (GCD) of 7 and 9. Since 7 and 9 have no common factors other than 1, the fraction is already in lowest terms.

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Key Concepts

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

Adding Fractions with Like Denominators

When adding fractions that have the same denominator, you keep the denominator the same and add the numerators directly. For example, 2/9 + 5/9 equals (2 + 5)/9, which simplifies the addition process.

Simplifying Fractions

After performing addition or subtraction, fractions should be simplified to their lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD). This ensures the fraction is expressed in its simplest form.

Understanding Numerators and Denominators

The numerator represents how many parts are considered, while the denominator indicates the total number of equal parts in a whole. Recognizing their roles is essential for correctly performing operations like addition or subtraction on fractions.

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Find each product. [(3a+b)-1]²

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Textbook Question

Let A = {2, 4, 6, 8, 10, 12}, B = {2, 4, 8, 10}, C = {4, 10, 12}, D = {2, 10}, andU = {2, 4, 6, 8, 10, 12, 14}. Determine whether each statement is true or false. D ⊆ A

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

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Simplify each expression. Write answers without negative exponents. Assume all variables represent nonzero real numbers. 6⁴/6^-2

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