Visualize Fractions: example 4.13

ⓐ It takes four $\frac{1}{8}$ tiles to exactly cover the $\frac{1}{2}$ tile, so $\frac{4}{8}=\frac{1}{2}.$

ⓑ It takes five $\frac{1}{10}$ tiles to exactly cover the $\frac{1}{2}$ tile, so $\frac{5}{10}=\frac{1}{2}.$

ⓒ It takes six $\frac{1}{12}$ tiles to exactly cover the $\frac{1}{2}$ tile, so $\frac{6}{12}=\frac{1}{2}.$

Suppose you had tiles marked $\frac{1}{20}.$ How many of them would it take to equal $\frac{1}{2}?$ Are you thinking ten tiles? If you are, you’re right, because $\frac{10}{20}=\frac{1}{2}.$

We have shown that $\frac{1}{2},\frac{2}{4},\frac{3}{6},\frac{4}{8},\frac{5}{10},\frac{6}{12},$ and $\frac{10}{20}$ are all equivalent fractions.