Question

Please help

Answer 1

Answer:

The pairs are:

$\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}$ =>  $\frac{p^2}{9q^2}$

$\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}$ => $6pq^3$

$\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}$ => $6p^2q^2$

$\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}$ => $\frac{q}{3}$

Step-by-step explanation:

We are going to solve the questions one by one and then write the quotients with every question.

In order to calculate the division, the terms are multiplied then exponents are added or subtracted between numerator and denominator to get the simplest form of answer.

First Expression:

$\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}$

When two fractions have to be divided the second fraction is reversed i.e. numerator becomes denominator and vice versa.

$= \frac{4p^3q}{6p^2q^2} * \frac{2p^2q^2}{12pq^3}\\=\frac{p^5q^3}{9p^3q^5}\\=\frac{p^2}{9q^2}$

Second Expression:

$\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}$

Removing the division symbol

$=\frac{10p^3q^3}{2p^2q} * \frac{6pq^2}{5pq}\\=\frac{6p^4q^5}{p^3q^2}\\=6pq^3$

Third Expression:

$\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}$

Removing the division symbol

$=\frac{14p^2q^3}{2pq} * \frac{6p^3q^2}{7p^2q^2}\\= \frac{6p^5q^5}{p^3q^3}\\= 6p^2q^2$

Fourth Expression:

$\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}$

Removing the division symbol

$=\frac{16pq^3}{24p^2q^3} * \frac{p^3q^3}{2p^2q^2}\\=\frac{p^4q^6}{3p^4q^5}\\=\frac{q}{3}$

Hence,

The pairs are:

$\frac{4p^3q}{6p^2q^2}\div \frac{12pq^3}{2p^2q^2}$ =>  $\frac{p^2}{9q^2}$

$\frac{10p^3q^3}{2p^2q}\div \frac{5pq}{6pq^2}$ => $6pq^3$

$\frac{14p^2q^3}{2pq}\div \frac{7p^2q^2}{6p^3q^2}$ => $6p^2q^2$

$\frac{16pq^3}{24p^2q^3}\div \frac{2p^2q^2}{p^3q^3}$ => $\frac{q}{3}$