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Chapter 10: Problem 27

Multiply. \(-\frac{3}{8} \cdot\left(-\frac{2}{9}\right)\)

Short Answer

Expert verified
\(\frac{1}{12}\)

Step by step solution

01

- Identify the fractions

The fractions involved are \(-\frac{3}{8}\) and \(-\frac{2}{9}\).
02

- Multiply the numerators

Multiply the numerators of the fractions: \(-3\) and \(-2\). \(-3\times -2 = 6\).
03

- Multiply the denominators

Multiply the denominators of the fractions: \(8\) and \(9\). \(8\times 9 = 72\).
04

- Combine the results

Combine the results from Step 2 and Step 3 into a single fraction: \(\frac{6}{72}\).
05

- Simplify the fraction

Simplify the fraction \(\frac{6}{72}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 6: \(\frac{6 \div 6}{72 \div 6} = \frac{1}{12}\).

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Key Concepts

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

numerator and denominator
In fractions, the numerator and denominator are crucial components. The numerator is the number above the fraction line, and the denominator is the number below it. For example, in the fraction \(-\frac{3}{8}\), \(-3\) is the numerator and \[8\] is the denominator. When multiplying fractions, multiply the numerators together and the denominators together.
simplifying fractions
Simplifying fractions involves reducing a fraction to its simplest form. This is done by dividing both the numerator and the denominator by their Greatest Common Divisor (GCD). For instance, to simplify the fraction \(\frac{6}{72}\), find the GCD of 6 and 72, which is 6. Then, divide both the numerator and the denominator by this GCD: \(\frac{6 \div 6}{72 \div 6} = \frac{1}{12}\). This process makes the fraction easier to work with and understand.
negative fractions
Dealing with negative fractions means understanding how the negative sign affects multiplication. When multiplying two negative fractions, such as \(-\frac{3}{8} \cdot \left(-\frac{2}{9}\right)\), the negative signs cancel out. Multiply the absolute values of the fractions' numerators and denominators as usual. For example, \(-3\cdot -2 = 6\) (the negative signs cancel out), and \8\cdot 9 = 72\. The resultant fraction would be positive, \(\frac{6}{72}\).

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Most popular questions from this chapter

Solve. Population Decrease. The population of a rural town was \(12,500 .\) It decreased 380 each year for 4 years. What was the population of the town after 4 years?

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Multiply. \(\left(-\frac{5}{6}\right)\left(\frac{1}{8}\right)\left(-\frac{3}{7}\right)\left(-\frac{1}{7}\right)\)

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