Chapter 1.5, Problem 73PPSE

Solution

To simplify the expression $\frac{1}{3}\left(b+12\right)-\frac{1}{4}\left(b+12\right)$ .

  $\frac{1}{12}b+1$

Given:

The expression, $\frac{1}{3}\left(b+12\right)-\frac{1}{4}\left(b+12\right)$ .

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.
• In any expression, terms are separated by plus or minus signs.
• Coefficients are the constants in front of the variable terms.
• Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Calculation:

In order to simplify the expression $\frac{1}{3}\left(b+12\right)-\frac{1}{4}\left(b+12\right)$ , remove the parenthesis and combine the like terms to simplify further as shown below

  $\begin{array}{c}\frac{1}{3}\left(b+12\right)-\frac{1}{4}\left(b+12\right)=\frac{1}{3}\cdot b+\frac{1}{3}\cdot 12-\frac{1}{4}\cdot b-\frac{1}{4}\cdot 12\\ =\frac{1}{3}\cdot b+4-\frac{1}{4}\cdot b-3\\ =\left(\frac{1}{3}\cdot b-\frac{1}{4}\cdot b\right)+\left(4-3\right)\\ =\left(\frac{1}{3}-\frac{1}{4}\right)b+\left(1\right)\\ =\left(\frac{4-3}{12}\right)b+1\\ =\frac{1}{12}b+1\end{array}$

Therefore, the simplified expression is $\frac{1}{12}b+1$ .