Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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2:04 minutes

Problem 33

Textbook Question

Find each sum or difference. -7/3 + 3/4

Verified step by step guidance

First, identify the fractions involved in the expression: \(-\frac{7}{3}\) and \(\frac{3}{4}\).

To add these fractions, find a common denominator. The denominators are 3 and 4, so the least common denominator (LCD) is 12.

Convert each fraction to an equivalent fraction with the common denominator of 12. Multiply the numerator and denominator of \(-\frac{7}{3}\) by 4 to get \(-\frac{28}{12}\). Multiply the numerator and denominator of \(\frac{3}{4}\) by 3 to get \(\frac{9}{12}\).

Now, add the two fractions: \(-\frac{28}{12} + \frac{9}{12}\). Since they have the same denominator, you can add the numerators directly.

Simplify the resulting fraction, if possible, by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by it.

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Key Concepts

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

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. In this problem, -7/3 and 3/4 are both rational numbers. Understanding how to work with rational numbers is essential for performing operations like addition and subtraction.

Common Denominator

To add or subtract fractions, it is necessary to have a common denominator. The common denominator is a shared multiple of the denominators of the fractions involved. In this case, the denominators are 3 and 4, and the least common denominator is 12, which allows for the fractions to be expressed in a compatible form for addition.

Fraction Addition and Subtraction

Adding or subtracting fractions involves converting them to a common denominator, adjusting the numerators accordingly, and then performing the operation. After finding the common denominator, the numerators are added or subtracted, and the result is simplified if possible. This process is crucial for accurately calculating the sum or difference of the given fractions.