Answer
$= \frac{1}{2}$
Work Step by Step
1. Follow the acronym PEDMAS:
P: arenthesis
E: ponents
D:ivision
M:ultiplication
A:ddition
S:ubtraction
$= $ P.E.D.M.A.S
This is used to determine which order of operations is completed first from top to bottom. For example, you would complete the division of two numbers before the addition of another two numbers. In this case, we multiply and divide before adding:
Note: We can never divide by a fraction, so we multiply by the reciprocal of the fraction:
$\frac{2}{3} \times \frac{1}{4} \div \frac{1}{2} + \frac{2}{3}\times \frac{1}{4}$
$= \frac{2}{3} \times \frac{1}{4} \times \frac{2}{1} + \frac{2}{3}\times \frac{1}{4}$
$= \frac{2}{12} \times \frac{2}{1} + \frac{2}{3}\times \frac{1}{4}$
$= \frac{4}{12} + \frac{2}{3}\times \frac{1}{4}$
$= \frac{4}{12} + \frac{2}{12}$
2. Find a common denominator when adding: No further multiplication of any fractions is needed as both fractions already have a common denominator of $12$.
$= \frac{6}{12}$
3. Finally we simplify the fraction:
$= \frac{1}{2}$
