Question

Multiply the following fractions and reduce to a lowest form and convert into a mixed fraction:
$\dfrac{2}{3}\times 4$

Answer 1

Hint: At first multiply the numerator with the numerator and the denominator with the denominator. Then cancel out the common factors from the numerator and the denominator if possible. If it is an improper fraction then convert it into a mixed fraction.

Complete step-by-step solution:
In the question we have the following multiplication:
$\dfrac{2}{3}\times 4$
We know that we can always write a whole number as a fraction by dividing that whole number by 1. If we divide any number by 1 the number remains the same.
Therefore we can write 4 as $\dfrac{4}{1}$.
Now our multiplication becomes,
$\dfrac{2}{3}\times \dfrac{4}{1}$
To multiply two fractions we need to multiply the numerator by the numerator and the denominator by the denominator. Therefore,
$=\dfrac{2\times 4}{3\times 1}$
Now we can see that there is no common factor in the numerator and the denominator. Therefore,
$=\dfrac{8}{3}$
If we look at the above fraction very carefully, we can see that the numerator is bigger than the denominator. Therefore the result is an improper fraction. We can always convert an improper fraction into a mixed fraction.
A mixed fraction is a combination of a whole part and a proper fraction part. Proper fraction means the numerator is smaller than the denominator.
So, from the above improper fraction we need to separate the whole part and the proper fraction part.
To find out the whole part we will divide the numerator by the denominator. That means we will divide 8 by 3.
If we divide 8 by 3, our quotient will be 2 and also the remainder will be 2.
We know that the quotient is our whole part of the mixed fraction. The numerator of the proper fraction part is our remainder of the division, which is 2, and the denominator is the divisor, which is 3.
Therefore,
$\dfrac{8}{3}=2\dfrac{2}{3}$
Hence, the result of the multiplication is $2\dfrac{2}{3}$.

Note: When we multiply fractions to get the required result we should always cancel out the common factors from the numerator and the denominator. Otherwise the result will not be in the simplest form.