Q8. - Algebra 1

Question

State whether each sentence is true or false. If false, replace the underlined word, phrase, expression, or number to make a true sentence.

 

The expression $\frac{\frac{1}{2}}{\frac{3}{4}}$ can be simplified to  $\underset{¯}{\frac{2}{3}}$.

Step-by-Step Solution

Answer

The given statement is True.

Step 1. State the concept of complex fractions.

A complex fraction has one or more fractions in the numerator or denominator, which can be simplified by using division.

Step 2. Explanation of the statement.

To simplify a complex fraction, write it as a division expression, then find the reciprocal of the second expression and multiply.

$$\begin{gathered} \frac{\frac{1}{2}}{\frac{3}{4}}=\frac{1}{2}÷\frac{3}{4} \\ =\frac{1}{2}\times \frac{4}{3} \\ =\frac{2}{3} \end{gathered}$$

Step 3. Write whether the statement is true or false.

Since the expression $\frac{\frac{1}{2}}{\frac{3}{4}}=\frac{2}{3}$, therefore, the given statement “The expression $\frac{\frac{1}{2}}{\frac{3}{4}}$ can be simplified to $\underset{¯}{\frac{2}{3}}$.” is true.