# What is the set of numbers to which 56/7 belong?

Nov 15, 2016

It is a natural number, but it also belongs to whole number, integers fractions, rational numbers and real numbers.

#### Explanation:

Although $\frac{56}{7}$ is expressed as fraction, as numerator is completely divisible by denominator, the number can be reduced a follows

$\frac{56}{7} = \frac{8 \times 7}{1 \times 7} = \frac{8 \times \cancel{7}}{1 \times \cancel{7}} = \frac{8}{1} = 8$

Hence, one can say that

the number can be said to belong to Natural numbers , the set of numbers naturally occurring i.e. $\left\{1 , 2 , 3 , 4 , 5 , 6 , \ldots \ldots \ldots \ldots \ldots\right\}$

the number can also be said to belong to set of Whole numbers, which is actually $0$ added to natural numbers i.e. $\left\{0 , 1 , 2 , 3 , 4 , 5 , 6 , \ldots \ldots \ldots \ldots \ldots\right\}$.

We can also say it belongs to set of integers $\left\{0 , \pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 5 , \pm 6 , \ldots \ldots \ldots \ldots \ldots\right\}$

As it is written (or can be written as a fraction say $\frac{56}{7}$ or $\frac{24}{3}$ etc., we can also say that it belongs to set of fractions and set of rational numbers .

It can be represented on real number line too, $8$ units to the right of $0$ and hence it is a real number too.