Question

Simplify:

(a) $\frac{4k}{5}-\frac{1}{6}$

(b)$\frac{4k}{5}·\frac{1}{6}$

Short answer

Part (a) The obtained value is $\frac{24k-5}{30}$.

Part (b) The obtained value is $\begin{array}{rcl}& & \frac{2k}{15}\end{array}$.

Step-by-step solution

Part (a) Step 1. Find the LCD of the denominator.

Consider the given expression.

$\frac{4k}{5}-\frac{1}{6}$

Find the factor of 5 and 6.

localid="1644662914052" $$\begin{gathered} 5=1·5 \\ 6=2·3 \\ \overline{\mathrm{LCD}=2·3·5} \\ =30 \end{gathered}$$

Part (a) Step 2. Rewrite the expression.

Write the fraction as an equivalent fraction LCD.

$\begin{array}{rcl}\frac{4k}{5}-\frac{1}{6}& =& \frac{4k\cdot 6}{5\cdot 6}-\frac{1\cdot 5}{6\cdot 5}\\ & =& \frac{24k}{30}-\frac{5}{30}\end{array}$

Subtract the numerators and place the difference over the common denominators.

$\frac{24k}{30}-\frac{5}{30}=\frac{24k-5}{30}$

Part (b) Step 1. Multiply the fractions.

Since the given operation is multiplication. Thus,

$\frac{4k}{5}\cdot \frac{1}{6}=\frac{4k\cdot 1}{5\cdot 6}$

Part (b) Step 2. Cancel the common factors.

Factor the number and cancel the common factor from numerators and denominators.

$\begin{array}{rcl}\frac{4k\cdot 1}{5\cdot 6}& =& \frac{2\cdot 2k}{5\cdot 2\cdot 3}\\ & =& \frac{2k}{5\cdot 3}\\ & =& \frac{2k}{15}\end{array}$