Question

Add or Subtract Fraction.

$$\begin{gathered} \overline{)a}\frac{2}{3}+\frac{1}{6} \\ \overline{)b}\frac{2}{3}÷\frac{1}{6} \end{gathered}$$

Short answer

Part (a) The value of$\frac{2}{3}+\frac{1}{6}$is $\frac{5}{6}$.

Part (b) The value of $\frac{2}{3}÷\frac{1}{6}$is 4.

Step-by-step solution

Part (a) Step 1. Given information.

Consider the expression.

$\overline{)a}\frac{2}{3}+\frac{1}{6}$

Part (a) Step 2. Determine the operation.

The operation is an addition.

Part (a) Step 3. Determine the whether the given fraction has the same denominator.

The given fraction does not have the same denominator.

So, find the least common denominator of 3 and 6.

$\begin{array}{rcl}3& =& 3·1\\ 6& =& 2·3\\ & \Rightarrow & LCM=3·2\\ & \Rightarrow & LCM=6\end{array}$

Part (a) Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 6.

$\begin{array}{rcl}\frac{2}{3}+\frac{1}{6}& =& \frac{2·2}{3·2}+\frac{1}{6}\\ & =& \frac{4}{6}+\frac{1}{6}\end{array}$

Part (a) Step 5. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

$\begin{array}{rcl}\frac{2}{3}+\frac{1}{6}& =& \frac{4+1}{6}\\ & =& \frac{5}{6}\end{array}$

Thus, the value is $\frac{5}{6}$.

Part (b) Step 1. Now, consider the fraction.b23÷16Determine the operation.

The operation is division.

Part (b) Step 2. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

$\begin{array}{rcl}\frac{2}{3}÷\frac{1}{6}& =& \frac{2}{3}·6\\ & =& \frac{2}{\cancel{3}}·\cancel{3}·2\\ & =& 4\end{array}$

Hence, the value is $4$.