Question

How do you simplify $-7\dfrac{1}{2}+5\dfrac{1}{3}$ ?

Answer 1

Hint: To simplify addition of two fractions we should first convert them to simple fraction and then make the denominator the same in two fractions then we just can subtract the numerator of 2 fraction. We can take the LCM between 2 denominators and then change each denominator to LCM.

Complete step-by-step answer:
Let’s convert the 2 mixed fraction to simple fraction
We can write $-7\dfrac{1}{2}$ as $\dfrac{-15}{2}$ and $5\dfrac{1}{3}$ as $\dfrac{16}{3}$
To add 2 fractions we have made their denominator the same for that we will take L.C.M of 2 denominators.
The LCM of 2 and 3 is equal to 6
We have to change the denominator to 10 for that we have to change the numerator also so that the value of the function does not change. We can see that the denominator of the first fraction is already 10, so we don’t have to change that; we only have to change the denominator of the second fraction.
So we can write $\dfrac{-15}{2}=\dfrac{-45}{6}$ and $\dfrac{16}{3}=\dfrac{32}{6}$
Now $-7\dfrac{1}{2}+5\dfrac{1}{3}$ can be written as $\dfrac{-45}{6}+\dfrac{32}{6}$
Now we can see the denominator in both fraction are same both are 6
Now we can simply add the numerator of 2 fractions.
By adding the 2 fractions we get $\dfrac{-45}{6}+\dfrac{32}{6}=\dfrac{-13}{6}$
So the answer is $\dfrac{-13}{6}$
if we convert $\dfrac{-13}{6}$ to mixed fraction the answer would be $-2\dfrac{1}{6}$

Note: While subtracting or adding 2 fractions if one of the denominators is irrational then we can convert the 2 denominators into products of denominators. We should make the denominator the same in both fractions not necessarily it must convert into LCM. But keep in mind that while changing the denominator don’t forget to change the numerator so that the value of fraction does not change.