Question

Solve the following equation and check the answer.
 $ \dfrac{{8m + 4}}{{12m + 20}} = \dfrac{1}{2} $

Answer 1

Hint: First of all we will take the given expression, and will do cross-multiplication between the two fractions. Then will simplify the equations, making the pair of like terms and then will find the value of the variable “m”.
Always remember that when we expand the brackets or open the brackets, the sign outside the bracket is most important. If there is a positive sign outside the bracket then the values inside the bracket does not change and if there is a negative sign outside the bracket then all the terms inside the bracket changes. Positive terms change to negative and negative term changes to positive

Complete step-by-step answer:
Take the given expression –
 $ \dfrac{{8m + 4}}{{12m + 20}} = \dfrac{1}{2} $
Do cross multiplication where the denominator of the opposite is multiplied with the numerator on one side.
 $ \Rightarrow (8m + 4)(2) = 1(12m + 20) $
Open the brackets on both the sides of the equation.
 $ \Rightarrow 16m + 8 = 12m + 20 $
Make the group of like terms on one side of the equation. So, take the constant on the right hand side of the equation and the term with the variable on the left hand side of the equation. Remember when you move terms from one side to another, the sign also changes. Positive terms become negative and vice-versa.
 $ \Rightarrow \underline {16m - 12m} = \underline {20 - 8} $
Simplify the above equation –
 $ \Rightarrow 4m = 12 $
When the term is multiplicative at one side, moved to the other side then it goes to the denominator.
 $ \Rightarrow m = \dfrac{{12}}{4} $
Split the factors in the numerator.
 $ \Rightarrow m = \dfrac{{4 \times 3}}{4} $
Common multiples from the numerator and the denominator cancel each other. Therefore, remove from the numerator and the denominator.
 $ \Rightarrow m = 3 $ is the required answer.
So, the correct answer is “m = 3”.

Note: While doing simplification remember the golden rules-
Addition of two positive terms gives the positive term
Addition of one negative and positive term, you have to do subtraction and give signs of bigger numbers, whether positive or negative.
Addition of two negative numbers gives a negative number but in actual you have to add both the numbers and give a negative sign to the resultant answer.