Question

What is the quotient? StartFraction a minus 3 Over 7 EndFraction divided by StartFraction 3 minus a Over 21 EndFraction StartFraction negative (a minus 3) squared Over 147 EndFraction StartFraction (a minus 3) squared Over 147 EndFraction 3 –3

Answer 1

Answer:

Correct answer is

$\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3$

Step-by-step explanation:

Let us rephrase the given statement mathematically.

We are given the fractions as:

$\dfrac{a-3}{7}$

to be divided by:

$\dfrac{3-a}{21}$

To find:

$\dfrac{a-3}{7}\div\dfrac{3-a}{21}$

Now, let us have a look at the division rule in fractions:

$\dfrac{a}{b} \div \dfrac{c}{d}$

is equivalent to

$\dfrac{a}{b} \times \dfrac{d}{c}$

In other words, we say that the second fraction $\frac{c}{d}$ is changed to $\frac{d}{c}$ and $\div$ is changed to $\times.$

Now solving the given fraction by applying above rules:

$\dfrac{a-3}{3}\div\dfrac{3-a}{21}$

$\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{3-a}\\\Rightarrow \dfrac{a-3}{7}\times \dfrac{21}{-(a-3)}\\\Rightarrow \dfrac{1}{1}\times \dfrac{3}{-1}\\\Rightarrow -3$

So, correct answer is:

$\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3$