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Chapter 0: Problem 54

Find each product or quotient, and write it in lowest terms as needed. $$ \frac{5}{9} \cdot \frac{2}{7} $$

Short Answer

Expert verified
\( \frac{10}{63} \)

Step by step solution

01

- Multiply the numerators

To find the product of two fractions, first multiply the numerators (the top numbers). In this case, multiply 5 by 2.\[5 \times 2 = 10\]
02

- Multiply the denominators

Next, multiply the denominators (the bottom numbers). In this problem, multiply 9 by 7.\[9 \times 7 = 63\]
03

- Write the product as a fraction

Combine the results of the first two steps to write the product as a fraction. So the result is:\[ \frac{10}{63} \]
04

- Simplify the fraction (if necessary)

Check if the fraction can be simplified. The fraction \( \frac{10}{63} \) is already in its simplest form; the greatest common divisor of 10 and 63 is 1.

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Key Concepts

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

Numerator
The numerator is the top part of a fraction. It represents how many parts of a whole are being considered. For example, in the fraction \(\frac{5}{9}\), the number 5 is the numerator. When multiplying fractions, you multiply the numerators from each fraction together. In our exercise, we calculated \(5 \times 2 = 10\), so the numerator of the product is 10.
Denominator
The denominator is the bottom part of a fraction. It indicates how many equal parts the whole is divided into. For instance, in the fraction \(\frac{5}{9}\), the number 9 is the denominator. When multiplying fractions, you multiply the denominators from each fraction together. In our example, we multiplied \(9 \times 7 = 63\), making the denominator of the product 63.
Simplifying Fractions
Simplifying fractions means reducing the fraction to its lowest terms, making it easier to understand or work with. To simplify a fraction, you find the greatest common divisor (GCD) of both the numerator and the denominator and divide both by that number. In our example, the fraction \(\frac{10}{63}\) is already in its simplest form because the GCD of 10 and 63 is 1.
Simplifying is a crucial step to ensure the fraction is as reduced as possible.

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Most popular questions from this chapter

Find each sum or difference, and write it in lowest terms as needed. $$ \frac{3}{8}+\frac{5}{6} $$

Find each product or quotient, and write it in lowest terms as needed. $$ \frac{1}{8} \cdot \frac{10}{7} $$

A laptop computer with a regular price of \(\$ 597\) is on sale at \(20 \%\) off. Find the amount of the discount and the sale price of the computer.

Find each product or quotient, and write it in lowest terms as needed. $$ \frac{15}{4} \cdot \frac{8}{25} $$

It takes \(2 \frac{3}{8}\) yd of fabric to make a costume for a school play. How much fabric would be needed for seven costumes?
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