Question

How do you solve $\dfrac{{5h}}{4} + \dfrac{1}{2} = \dfrac{{3h}}{8}$?

Answer 1

Hint: We are given an expression. We have to simplify the expression. First, simplify the terms at the left hand side of the equation by taking LCM of the denominator. Then, multiply and divide the fractional term by the constant value to convert the denominator same as another denominator. Then, add the numerator. Then, cross multiply the terms on both sides of the equation. Then, simplify the expression for the variable.

Complete step by step solution:
Given expression, $\dfrac{{5h}}{4} + \dfrac{1}{2} = \dfrac{{3h}}{8}$.

Now, we will determine the LCM of 4 and 2.

$ \Rightarrow LCM\left( {4,2} \right) = 4$

Now, rewrite the expression by multiplying and dividing the fraction $\dfrac{1}{2}$ by 2.

$ \Rightarrow \dfrac{{5h}}{4} + \dfrac{1}{2} \times \dfrac{2}{2} = \dfrac{{3h}}{8}$

On combining like terms, we get:

$ \Rightarrow \dfrac{{5h}}{4} + \dfrac{2}{4} = \dfrac{{3h}}{8}$

Now, the denominator of both the terms is the same. Then, add the numerators over the common denominator.

$ \Rightarrow \dfrac{{5h + 2}}{4} = \dfrac{{3h}}{8}$

Cross multiply the terms on both sides of the equation.

$ \Rightarrow 8\left( {5h + 2} \right) = 4\left( {3h} \right)$

Apply the distributive property on both sides of the equation. .

$ \Rightarrow 40h + 16 = 12h$

Subtract $12h$ from both sides of the equation.

$ \Rightarrow 40h + 16 - 12h = 12h - 12h$

On combining like terms, we get:

$ \Rightarrow 28h + 16 = 0$

Now, we will subtract 16 from both sides of the equation.

$ \Rightarrow 28h + 16 - 16 = 0 - 16$

On combining like terms, we get:

$ \Rightarrow 28h = - 16$

Divide both sides of the equation by 28.

$ \Rightarrow \dfrac{{28h}}{{28}} = - \dfrac{{16}}{{28}}$

On simplifying the expression further, we get:

$ \Rightarrow h = - \dfrac{4}{7}$

The solution of the equation $\dfrac{{5h}}{4} + \dfrac{1}{2} = \dfrac{{3h}}{8}$ is $ - \dfrac{4}{7}$.

Note: The students please note that while adding the fractions the denominator of both the fractions must be the same and then the numerators must be added over the common denominator. Please note that if the fractions have different denominators then we have to take the LCM of the denominators and then multiply and divide the fractional terms to convert the denominator as a common denominator and then the expression is simplified further.