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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1:48 minutes

Problem 139

Textbook Question

Use the distributive property to calculate each value mentally. 123 5/8 * 1 1/2 - 23 5/8 * 1 1/2

Verified step by step guidance

Identify the expression: \((123 \frac{5}{8} \times 1 \frac{1}{2}) - (23 \frac{5}{8} \times 1 \frac{1}{2})\).

Use the distributive property: \((a \times c) - (b \times c) = (a - b) \times c\).

Rewrite the expression using the distributive property: \((123 \frac{5}{8} - 23 \frac{5}{8}) \times 1 \frac{1}{2}\).

Subtract the mixed numbers: \(123 \frac{5}{8} - 23 \frac{5}{8}\).

Multiply the result by \(1 \frac{1}{2}\).

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Key Concepts

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

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by two or more terms inside a set of parentheses. In the context of the given question, it can be used to simplify calculations by distributing the multiplication across the addition or subtraction of mixed numbers.

Mixed Numbers

Mixed numbers are numbers that consist of a whole number and a proper fraction, such as 1 1/2 or 23 5/8. To perform operations with mixed numbers, it is often helpful to convert them into improper fractions, which can simplify multiplication and addition. Understanding how to manipulate mixed numbers is essential for solving the problem accurately.

Mental Math Techniques

Mental math techniques involve strategies that allow individuals to perform calculations in their heads without the use of paper or a calculator. Techniques such as breaking numbers into easier components, rounding, and using the distributive property can enhance efficiency and accuracy in solving arithmetic problems, especially when dealing with fractions and mixed numbers.