To compare whether or not two fractions are equivalent, they must have the same denominator.
What is a common denominator you can make between [tex] \frac{4m}{5n} [/tex] and [tex] \frac{8m}{10n} [/tex]? Some possible options are 5n or 10n.
I'll make both denominators 5n:
1) [tex] \frac{4m}{5n} [/tex] already has 5n in the denominator.
2) To get 5n in the denominator for [tex] \frac{8m}{10n} [/tex], you want to divide both the numerator and denominator by 2 (same as multiplying top and bottom by [tex] \frac{1}{2} [/tex]). Since you're doing the same thing to the numerator and denominator, you are not changing the value of the fraction:
[tex] \frac{8m}{10n} \times \frac{ \frac{1}{2}}{\frac{1}{2}} \\
= \frac{ \frac{8m}{2}}{\frac{10n}{2}}\\
= \frac{4m}{5n} [/tex]
Now compare the two fractions. Since [tex]\frac{4m}{5n} = \frac{4m}{5n}[/tex], your fractions are equivalent!
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Answer: They are equivalent
