Chapter SR4, Problem 69P

Solution

To simplify the expression $\frac{4}{9}+\frac{3}{4}-\frac{7}{12}$ .

  $\frac{11}{18}$

Given:

The expression, $\frac{4}{9}+\frac{3}{4}-\frac{7}{12}$.

Concept Used:

To add or subtract fractions with unlike denominators, follow the below steps:

Step 1: Find the least common multiple (LCM) for the denominators.

Step 2: Multiply the numerator and denominator to get like denominators.

Step 3: Turn the other fractions into equivalent fractions.

Step 4: Add the numerators over the common denominator.

Step 5: Simplify and reduce the answer if necessary.

Calculation:

In order to simplify the given expression, note that the least common multiple of 9, 4, and 12 is 36. So, make all denominators equal to the LCM and combine the numerators over the common LCM to simplify further as shown below

  $\begin{array}{c}\frac{4}{9}+\frac{3}{4}-\frac{7}{12}=\frac{4}{9}\cdot \frac{4}{4}+\frac{3}{4}\cdot \frac{9}{9}-\frac{7}{12}\cdot \frac{3}{3}\\ =\frac{16}{36}+\frac{27}{36}-\frac{21}{36}\\ =\frac{16+27-21}{36}\\ =\frac{22}{36}\\ =\frac{11}{18}\end{array}$

Thus, the simplified expression is $\frac{11}{18}$ .