Answer:
Correct answer is
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
Step-by-step explanation:
Let us rephrase the given statement mathematically.
We are given the fractions as:
[tex]\dfrac{a-3}{7}[/tex]
to be divided by:
[tex]\dfrac{3-a}{21}[/tex]
To find:
[tex]\dfrac{a-3}{7}\div\dfrac{3-a}{21}[/tex]
Now, let us have a look at the division rule in fractions:
[tex]\dfrac{a}{b} \div \dfrac{c}{d}[/tex]
is equivalent to
[tex]\dfrac{a}{b} \times \dfrac{d}{c}[/tex]
In other words, we say that the second fraction [tex]\frac{c}{d}[/tex] is changed to [tex]\frac{d}{c}[/tex] and [tex]\div[/tex] is changed to [tex]\times.[/tex]
Now solving the given fraction by applying above rules:
[tex]\dfrac{a-3}{3}\div\dfrac{3-a}{21}[/tex]
[tex]\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[/tex]
So, correct answer is:
[tex]\text{Quotient of }\dfrac{a-3}{7}\div\dfrac{3-a}{21} = -3[/tex]
