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Chapter 7: Problem 114

Divide: \(\frac{2}{3} \div 4 .\) (Section 1.2, Example 6)

Short Answer

Expert verified
\(\frac{2}{3} \div 4 = \frac{1}{6}\)

Step by step solution

01

Rewrite the division as multiplication

The division of a number can be rewritten as multiplication by its reciprocal. So, rewrite \(\frac{2}{3} \div 4\) as \(\frac{2}{3} \times \frac{1}{4}\)
02

Multiply the fractions

Now, multiply the two fractions. To do this, multiply the numerators together for the new numerator, and the denominators together for the new denominator. \( \frac{2}{3} \times \frac{1}{4} = \frac{2 \times 1}{3 \times 4} = \frac{2}{12} \)
03

Simplify the fraction

The fraction can be simplified by dividing the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{2}{12} = \frac{1}{6} \)

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Most popular questions from this chapter

Explain how to subtract rational expressions when denominators are the same. Give an example with your explanation.

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I can solve \(\frac{x}{9}=\frac{4}{6}\) by using the cross-products principle or by multiplying both sides by \(18,\) the least common denominator.

denominators are opposites, or additive inverses. Add or subtract as indicated. Simplify the result, if possible. $$\frac{2 x+3}{x^{2}-x-30}+\frac{x-2}{30+x-x^{2}}$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{x}{x+6}-1$$

Add or subtract as indicated. Simplify the result, if possible. $$\frac{2}{x-1}+\frac{3}{x+2}$$
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