Answer:
"The expression will always equal m" is true about the quotient of [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex]
Step-by-step explanation:
Let us solve the question
∵ The expression is [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex]
→ In the division of fractions, we change the division to multiplication
and reciprocal the fraction after the division sign
∵ The reciprocal of [tex]\frac{1}{n}[/tex] is [tex]\frac{n}{1}[/tex]
∴ [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex] = [tex]\frac{m}{n}[/tex] × [tex]\frac{n}{1}[/tex]
→ In the multiplication of fractions, we can simplify the terms in
the numerators by the terms in the denominators
∵ There is n in the numerator and denominator
∴ Cancel n up and down
∴ [tex]\frac{m}{n}[/tex] × [tex]\frac{n}{1}[/tex] = [tex]\frac{m}{1}[/tex]
∴ [tex]\frac{m}{n}[/tex] × [tex]\frac{n}{1}[/tex] = m
∴ [tex]\frac{m}{n}[/tex] ÷ [tex]\frac{1}{n}[/tex] = m
∴ The quotient is m
∴ The expression will always equal m
