Question

How do you simplify \[\dfrac{1}{4}(2s + 3t - 6)\] ?

Answer 1

Hint: This question can be solved by simply opening the brackets and expanding the simplified term. Multiply each term with the coefficient outside the bracket, and write the products together to obtain the answer. The sign of the obtained terms will be the same as that inside the bracket, since the coefficient outside the bracket is positive.

Complete step by step answer:
We have to simplify \[\dfrac{1}{4}(2s + 3t - 6)\] .
For this, we will expand the given expression.
First, we will begin with the term having \[s\] . We have \[2s\] inside the brackets, and \[\dfrac{1}{4}\] outside the bracket. Hence, we need to multiply both of them.
For the first term, we have
 \[\dfrac{1}{4} \times 2s = \dfrac{{2s}}{4} = \dfrac{s}{2}\]
Thus, the first term is obtained as \[\dfrac{s}{2}\] .
Next, we move on to the second term, i.e., the term having \[t\] . We have \[3t\] inside the brackets, and \[\dfrac{1}{4}\] outside the bracket. Hence, we need to multiply both of them.
 \[\dfrac{1}{4} \times 3t = \dfrac{3}{4}t\]
Notice that the last term inside the bracket is \[ - 6\] . We will preserve the minus sign while multiplying.
 \[\dfrac{1}{4} \times - 6 = \dfrac{{ - 6}}{4} = \dfrac{{ - 3}}{2}\]
We have obtained the products for all three terms inside the bracket. To form the final answer, we need to combine them into a single expression.
On combining these terms, we get
 \[\dfrac{s}{2} + \dfrac{3}{4}t + \left( {\dfrac{{ - 3}}{2}} \right)\]
After some simplification, we finally obtain \[\dfrac{s}{2} + \dfrac{3}{4}t - \dfrac{3}{2}\] .

Thus, the final answer obtained comes out to be \[\dfrac{s}{2} + \dfrac{3}{4}t - \dfrac{3}{2}\] .

Note: Simplifying an expression means writing the expression in simpler terms. The expression is manipulated to form simpler and easier-to-comprehend terms. While simplifying an expression, students need to be careful while performing the calculations after opening the brackets in the expression.