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Modeling Equivalent Fractions

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Modeling Equivalent Fractions

Let’s think about Andy and Bobby and their favorite food again. If Andy eats \(\frac{1}{2}\) of a pizza and Bobby eats \(\frac{2}{4}\) of the pizza, have they eaten the same amount of pizza? In other words, does \(\frac{1}{2}=\frac{2}{4}?\) We can use fraction tiles to find out whether Andy and Bobby have eaten equivalent parts of the pizza.

Equivalent Fractions

Equivalent fractions are fractions that have the same value.

Modeling Equivalent Fractions

Fraction tiles serve as a useful model of equivalent fractions. You may want to use fraction tiles to do the following activity. Or you might make a copy of the figure above and extend it to include eighths, tenths, and twelfths.

Start with a \(\frac{1}{2}\) tile. How many fourths equal one-half? How many of the \(\frac{1}{4}\) tiles exactly cover the \(\frac{1}{2}\) tile?

Modeling Equivalent Fractions

Since two \(\frac{1}{4}\) tiles cover the \(\frac{1}{2}\) tile, we see that \(\frac{2}{4}\) is the same as \(\frac{1}{2},\) or \(\frac{2}{4}=\frac{1}{2}.\)

How many of the \(\frac{1}{6}\) tiles cover the \(\frac{1}{2}\) tile?

Modeling Equivalent Fractions

Since three \(\frac{1}{6}\) tiles cover the \(\frac{1}{2}\) tile, we see that \(\frac{3}{6}\) is the same as \(\frac{1}{2}.\)

So, \(\frac{3}{6}=\frac{1}{2}.\) The fractions are equivalent fractions.

Example

Use fraction tiles to find equivalent fractions. Show your result with a figure.

  1. How many eighths equal one-half?
  2. How many tenths equal one-half?
  3. How many twelfths equal one-half?

Solution

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

Modeling Equivalent Fractions

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

Modeling Equivalent Fractions

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

Modeling Equivalent Fractions

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.

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