Question

How do you subtract two negative mixed numbers?

Answer 1

Hint: To solve this we need the definition of the mixed numbers. A mixed number is formed by a combining three parts, a whole number, a numerator and a denominator. For example \[2\dfrac{1}{5}\] . The numerator and the denominator are part of the proper fraction. We know that \[2\dfrac{1}{5}\] means \[2 + \dfrac{1}{5}\] we follow this concept to answer the above problem.

Complete step-by-step answer:
Let’s take examples to solve the given problem.
 \[ \Rightarrow 2\dfrac{1}{5} + 3\dfrac{1}{2} = ?\]
We add the whole numbers and fraction separately,
 \[ \Rightarrow 2\dfrac{1}{5} + 3\dfrac{1}{2} = 2 + 3 + \dfrac{1}{5} + \dfrac{1}{2}\]
 \[ = 5 + \dfrac{1}{5} + \dfrac{1}{2}\]
As we know if we need to add fraction we take LCM of 5 and 2,
 \[ = 5 + \dfrac{{2 + 5}}{{10}}\]
 \[ = 5 + \dfrac{7}{{10}}\]
 \[ = 5\dfrac{7}{{10}}\]
Thus we have,
 \[ \Rightarrow 2\dfrac{1}{5} + 3\dfrac{1}{2} = = 5\dfrac{7}{{10}}\] .
For subtractions let’s take the same mixed numbers,
 \[ \Rightarrow - 3\dfrac{1}{2} - [-2\dfrac{1}{5}] = ?\]
We subtract whole number and fractions separately,
 \[ \Rightarrow 2\dfrac{1}{5} - 3\dfrac{1}{2} = \left( {2 - 3} \right) + \dfrac{1}{5} - \dfrac{1}{2}\]
 \[ = - 1 + \dfrac{1}{5} - \dfrac{1}{2}\]
As we know if we need to add fraction we take LCM of 5 and 2,
 \[ = - 1 + \dfrac{{2 - 5}}{{10}}\]
 \[ = - 1 + \dfrac{{ - 3}}{{10}}\]
 \[ = - \left( {1 + \dfrac{3}{{10}}} \right)\]
 \[ = - 1\dfrac{3}{{10}}\]
Thus we have,
 \[ \Rightarrow 2\dfrac{1}{5} - 3\dfrac{1}{2} = - 1\dfrac{3}{{10}}\]

Note: We follow the same procedure for the addition and subtraction of mixed numbers. We can also solve this by converting the mixed numbers to improper fraction and taking LCM and simplifying we will have a required result, but it will have more calculation when compared to the above method.