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Chapter 4: Problem 115

Multiply, and write the answer in simplified form. \(\frac{3}{7} \cdot 21 n\)

Short Answer

Expert verified
9n

Step by step solution

01

Multiply the Fractions

To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number, and keep the denominator the same. Here, multiply the numerator of \(\frac{3}{7}\) by 21: \(\frac{3 \times 21n}{7}\).
02

Simplify the Numerator

Simplify the numerator by performing the multiplication: \(3 \times 21 = 63\). So the expression becomes \(\frac{63n}{7}\).
03

Divide to Simplify

Simplify the fraction by dividing the numerator by the denominator: \(\frac{63n}{7} = 9n\).

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Key Concepts

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

Simplifying Fractions
Simplifying a fraction means reducing it to its simplest form so that the numerator and denominator do not share any common factors other than 1. Start by identifying the greatest common divisor (GCD) of both the numerator and the denominator. Divide both by this GCD. In our example, once we have \(\frac{63n}{7}\), we divide 63 by 7 to get 9, which simplifies the fraction. Always check if further simplification is possible.
Numerator and Denominator
A fraction consists of two parts: the numerator and the denominator. The numerator is the top number that represents the number of parts we have. The denominator is the bottom number that shows the total number of equal parts the whole is divided into. In \(\frac{3}{7}\), 3 is the numerator and 7 is the denominator. When multiplying fractions, multiply the numerators together and the denominators together. In our case, we kept the denominator the same because we were multiplying by a whole number.
Whole Numbers
Whole numbers are positive numbers without fractions or decimals. They include 0, 1, 2, 3, etc. When multiplying a fraction by a whole number, treat the whole number as a fraction with a denominator of 1. For example, 21 becomes \(\frac{21}{1}\). When we multiply \(\frac{3}{7}\) by 21, we actually calculate \(\frac{3}{7} \cdot\ \frac{21n}{1}\), which simplifies to \(\frac{63n}{7}\). Then, divide the numerator by the denominator to get the final simplified form.

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Most popular questions from this chapter

In the following exercises, simplify. $$ \frac{\frac{5}{14}+\frac{1}{8}}{\frac{9}{56}} $$

In the following exercises, subtract. $$\frac{8}{11}-\frac{6}{11}$$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\frac{2}{3}\) when (a)\(x=-\frac{1}{6} \quad\) (b) \(x=-\frac{5}{3}\)

In the following exercises, simplify. $$ \frac{18 r}{27 s} $$

In the following exercises, determine whether the each number is a solution of the given equation. $$ y+\frac{3}{5}=\frac{5}{9} $$ $$ (a)y=\frac{1}{2} $$ $$ (b)y=\frac{52}{45} $$ $$ (c)y=-\frac{2}{45} $$
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