# How do you name two monomials with the quotient of 24a^2b^3?

May 16, 2017

Choose any monomial and multiply it by $24 {a}^{2} {b}^{3}$ to find the other monomial.

#### Explanation:

A quotient is the answer to a division.

For example,

Which 2 numbers have a quotient of $4$?

$\frac{100}{25} = \frac{72}{18} = \frac{60}{15} = \frac{48}{12} = \frac{32}{8} = \frac{\frac{3}{2}}{\frac{3}{8}} = 4$

To find another two, choose one and multiply it by $4$.

$23 \times 4 = 92 \text{ } \therefore \frac{92}{23} = 4$

In this case it is the same with algebra:

Choose any monomial (one term) and multiply it by $24 {a}^{2} {b}^{3}$ to find the other monomial.

For example:

$5 {a}^{3} {b}^{5} \times 24 {a}^{2} {b}^{3} = 120 {a}^{5} {b}^{8}$

$\therefore \frac{120 {a}^{5} {b}^{8}}{5 {a}^{3} {b}^{5}} = 24 {a}^{2} {b}^{3}$