Question

Solve the fraction: \[\dfrac{9}{11}-\dfrac{4}{15}\].

Answer 1

Hint: Find the common denominator of the two fractions. Then subtract the two numerators (top numbers). Put the answer over the denominator and simplify the fraction formed.

Complete step-by-step answer:
Give us two fractions \[\dfrac{9}{11}\]and \[\dfrac{4}{15}\]where we need to subtract the second from the first.

The first step towards subtraction is to ensure that the bottom numbers (the denominators) are the same.

Here the denominators are different \[\dfrac{9}{11}\]and \[\dfrac{4}{15}\]. Let’s make the denominators the same.

We know the denominators are 11 and 15. They both don’t have any numbers in common. So let’s multiply 11 and 15.

\[11\times 15=165\]

Now we got the denominator as 165.

First let us take the fraction \[\dfrac{9}{11}\]. We need to make the denominator of the fraction as 165. So multiply by 15 in the numerator and denominator.

\[\dfrac{9\times 15}{11\times 15}=\dfrac{135}{165}-(1)\]

Now let us take the fraction \[\dfrac{4}{15}\]. We need to make the denominator 165.

So let’s multiply by 11 in the numerator and denominator.

\[\dfrac{4\times 11}{15\times 11}=\dfrac{44}{165}-(2)\]

Now let us subtract (2) from (1).

\[\therefore \dfrac{135}{165}-\dfrac{44}{165}=\dfrac{135-44}{165}\]

Now let’s subtract the top numbers (the numerators). Put the answer over the same denominator.

\[\dfrac{135-44}{165}=\dfrac{91}{165}\]

We cannot further simplify the fraction, as they don’t have any common factors.

\[\therefore \dfrac{9}{11}-\dfrac{4}{15}=\dfrac{91}{165}\]

Note: It can be solved by cross multiplying the numerator and denominator divided by the multiplication of both denominators.

\[\dfrac{9}{11}-\dfrac{4}{15}=\dfrac{\left( 9\times 15 \right)-\left( 4\times 11 \right)}{11\times 15}=\dfrac{135-44}{165}=\dfrac{91}{165}\]
We get the same answer as we have got in the first method. This is a shortcut for the same.