Lesson 26: Using Manipulatives to Reduce Fractions

New Concept

We can use our fraction manipulatives to reduce a given fraction by making an equivalent model that uses fewer pieces.

What’s next

This lesson starts with a visual, hands-on approach to reducing. Next, you'll apply this skill to adding and subtracting mixed numbers with various examples.

Property

We can use fraction manipulatives to reduce a given fraction by making an equivalent model that uses the fewest pieces. For example, the fractions $\frac{4}{8}$, $\frac{3}{6}$, and $\frac{2}{4}$ all reduce to $\frac{1}{2}$.

Examples

Using manipulatives shows that $\frac{2}{6}$ is equivalent to one $\frac{1}{3}$ piece.
Using manipulatives shows that $\frac{4}{8}$ is equivalent to one $\frac{1}{2}$ piece.
Using manipulatives shows that $\frac{6}{8}$ is equivalent to three $\frac{1}{4}$ pieces, so it reduces to $\frac{3}{4}$.

Explanation

Think of reducing fractions like swapping your piggy bank change for bigger bills. Four quarters and a one dollar bill are worth the same, but the bill is simpler! Reducing fractions is about finding the simplest name for that amount by using the biggest, fewest pieces possible. This makes fractions much easier to work with and compare.

Property

When adding mixed numbers, we first add the fraction parts, and then we add the whole-number parts. Likewise, when subtracting mixed numbers, we first subtract the fraction parts, and then we subtract the whole-number parts.

Examples

$2\frac{3}{4} + 2\frac{3}{4} = 4\frac{6}{4} = 4 + 1\frac{2}{4} = 5\frac{1}{2}$
$5\frac{3}{8} - 1\frac{1}{8} = 4\frac{2}{8} = 4\frac{1}{4}$
$1\frac{1}{8} + 2\frac{7}{8} = 3\frac{8}{8} = 3 + 1 = 4$

Explanation

Adding mixed numbers is like sorting snacks. First, combine all the loose cracker bits (the fractions). Then, combine all the whole sandwich packs (the whole numbers). If your cracker bits overflow and make a whole new sandwich (an improper fraction), you just add it to the sandwich pile! This final step makes sure your answer is neat and tidy.