Problem 26 Multiply. \(\frac{5}{7} \cdot\... [FREE SOLUTION]

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Basic College Mathematics

Marvin L. Bittinger, Judith A. Beecher, Barbara L. Johnson

$Math Studyset 91影视 Explanations$ Math

13 Edition

Chapter 10: Problem 26

Multiply. $\frac{5}{7} \cdot\left(-\frac{2}{3}\right)$

Short Answer

Expert verified

-$ \frac{10}{21} $

Step by step solution

- Multiply the Numerators

To multiply the fractions, first multiply the numerators together. The numerators of the fractions given are 5 and -2. So, we calculate: \[ 5 \times -2 = -10 \]

- Multiply the Denominators

Next, multiply the denominators together. The denominators of the fractions given are 7 and 3. So, we calculate: \[ 7 \times 3 = 21 \]

- Form the Resulting Fraction

Combine the results from Step 1 and Step 2 to form the resulting fraction. From Step 1, we have -10 as the numerator, and from Step 2, we have 21 as the denominator. Thus, the resulting fraction is: \[ \frac{-10}{21} \]

- Simplify the Fraction

Check if the fraction can be simplified. In this case, -10 and 21 do not have any common factors other than 1, so the fraction $ \frac{-10}{21} $ is already in its simplest form.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Numerator Multiplication

When multiplying fractions, the first step is to multiply the numerators, the numbers on top. For the exercise $\frac{5}{7} \cdot(-\frac{2}{3}),$ you start by multiplying 5 and -2. The calculation is: \[ 5 \times -2 = -10. \] Remember, the result of numerator multiplication goes on top of the new fraction. Don't forget the negative sign; multiplication follows the rules for multiplying positive and negative numbers.

Denominator Multiplication

Next, you need to multiply the denominators, which are the numbers at the bottom of each fraction. For the given example, $\frac{5}{7} \cdot(-\frac{2}{3}), $ the denominators are 7 and 3. You calculate: \[ 7 \times 3 = 21. \] Just like with numerators, place the result on the bottom of the new fraction. This operation is straightforward multiplication. Each step directly influences the form of the resulting fraction, making it essential to handle these calculations carefully.

Simplifying Fractions

The last step in fraction multiplication is to check if the resulting fraction can be simplified. From the steps above, we have the fraction $\frac{-10}{21}\text{.} $ Simplification checks whether the numerator and denominator share any common factors other than 1. Since 10 and 21 don't have any common factors (other than 1), $\frac{-10}{21}$ is already in its simplest form. Simplifying fractions helps make values easier to understand and work with, so always check for possible simplification.

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91影视

Multiply. \(\frac{5}{7} \cdot\left(-\frac{2}{3}\right)\)

Short Answer

Step by step solution

- Multiply the Numerators

- Multiply the Denominators

- Form the Resulting Fraction

- Simplify the Fraction

Key Concepts

Numerator Multiplication

Denominator Multiplication

Simplifying Fractions

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