Question

How do you simplify $\dfrac{7}{12}+\dfrac{4}{5}$ ?

Answer 1

Hint: To simplify addition of two fractions we should first make the denominator the same in two fraction then we just can add the numerator of 2 fraction. To make the denominator same we can take L.C.M of 2 denominators and change the denominator.

Complete step by step answer:
To add 2 fractions we have made their denominator the same for that we will take L.C.M of 2 denominators.
In the given question $\dfrac{7}{12}+\dfrac{4}{5}$ the denominators are 12 and 5.LCM of 12 and 5
To calculate LCM we can write 12 and 5 in the product of prime numbers.
$12=2\times 2\times 3$
$5=5$
From above representation the LCM of 12 and 5 is $2\times 2\times 3\times 5=60$
We have to change the denominator to 60 for that we have to change the numerator also so that the value of the function does not change. We have to multiply the same number with the numerator which we will multiply with the denominator to convert to LCM.
We can write $\dfrac{7}{12}=\dfrac{7\times 5}{12\times 5}$
So we can write $\dfrac{7}{12}=\dfrac{35}{60}$
And $\dfrac{4}{5}=\dfrac{4\times 12}{5\times 12}$
$\dfrac{4}{5}$ can be written as $\dfrac{48}{60}$
Now $\dfrac{7}{12}+\dfrac{4}{5}$ can be written as $\dfrac{35}{60}+\dfrac{48}{60}$
Now we can see the denominators in both fractions are the same, both are 60.
Now we can simply add the numerator of 2 fractions.
By adding the 2 fractions we get $\dfrac{35}{60}+\dfrac{48}{60}=\dfrac{83}{60}$
Now if we want we can convert $\dfrac{83}{60}$ into a mixed fraction for that we can divide 83 by 60 and the quotient will be the whole number, remainder will be numerator and the denominator will remain unchanged.
So $\dfrac{83}{60}=1\dfrac{23}{60}$
The answer is $1\dfrac{23}{60}$ or $\dfrac{83}{60}$ .

Note:
While adding 2 fractions if one of the denominators is irrational then we can convert the 2 denominators into products of denominators. The main thing is we should make the denominator the same in both fractions that does not mean that 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.