Question

How do you solve \[m - 1\dfrac{1}{2} = - \dfrac{5}{4}\]?

Answer 1

Hint: We can first reorder the terms according to the question. After that we can solve the question for the variable ‘m’. We can group the like terms on one side so that it will be easier to solve. Then after forming the easier equation, we can simplify it, and we will get our answer.

Complete step-by-step solution:
The given equation is:
\[m - 1\dfrac{1}{2} = - \dfrac{5}{4}\]
First, we will convert the mixed fraction to an improper fraction. In this question, \[1\dfrac{1}{2}\]is a mixed fraction. We need to multiply the whole number here with the denominator of the fraction. Then, we will add the resulting answer with the numerator to get the final result. Here the whole number is \[1\]. So, we will multiply \[1\]with the fraction’s denominator that is \[2\], and we get the answer as \[2\]. Then we will add the answer with the fraction’s numerator that is \[1\] to get the final answer as \[3\].
Now, we will reform the mixed fraction into an improper fraction by changing the numerator with our final answer. Here, the denominator remains the same:
 \[ \Rightarrow 1\dfrac{1}{2} = \dfrac{3}{2}\]
Now when we put the value of \[1\dfrac{1}{2}\]in the equation, we get:
\[ \Rightarrow m - \dfrac{3}{2} = - \dfrac{5}{4}\]
Now, we will add \[\dfrac{3}{2}\]on both the sides to simplify the equation:
\[ \Rightarrow m - \dfrac{3}{2} + \dfrac{3}{2} = - \dfrac{5}{4} + \dfrac{3}{2}\]
\[ \Rightarrow m = \dfrac{{ - 5 + 6}}{4}\]
\[ \Rightarrow m = \dfrac{1}{4}\]
Therefore, our equation is solved, and we have got our final answer as:
\[m = \dfrac{1}{4}\]

Note: This method is very easy and the equation gets solved very quickly. But there is another way to solve this question. Instead of solving the equation in fraction, we can solve it by changing the fraction into decimal numbers. Once we convert them into decimal numbers, it becomes easy to add or subtract the numbers.