Equivalent Fractions

Equivalent Fractions #

The same amount under a new name.

Cutting every piece in two gives the same amount a new name

Half of this bar is colored in.

Now cut every piece in 2.

$\frac{1}{2}=\frac{2}{4}$1/2 = 2/4 — equivalent fractions: one amount, two names.

Simplest Form #

Undo the cuts until the pieces are biggest.

Simplifying is undoing the cuts until the pieces are as big as they can be

6 of the 8 pieces are colored in here.

$\frac{6}{8}=\frac{3}{4}$6/8 = 3/4. Same amount, bigger pieces — that is simplest form.

A Common Denominator #

Pieces must match before you combine them.

You cannot combine pieces until they are all the same size

The bottom number is the denominator. Halves and thirds differ, so they will not add.

6 is the first number in both the 2 and 3 times tables: $\frac{1}{2}=\frac{3}{6}$1/2 = 3/6 and $\frac{1}{3}=\frac{2}{6}$1/3 = 2/6.

Adding Fractions with the Same Denominator #

When the pieces match, just count them.

When the pieces already match you only have to count them

$\frac{3}{8}$3/8 and $\frac{2}{8}$2/8. The pieces already match, so nothing has to be rewritten.

Count them: 3 + 2 = 5, so $\frac{3}{8}+\frac{2}{8}=\frac{5}{8}$3/8 + 2/8 = 5/8. The denominator stays 8.

Adding Fractions with Unlike Denominators #

Match the pieces first, then add.

Make the pieces the same size first, then add as usual

A half and a third will not count — rewrite both in sixths: $\frac{3}{6}$3/6 and $\frac{2}{6}$2/6.

Now count the colored pieces: $\frac{3}{6}+\frac{2}{6}=\frac{5}{6}$3/6 + 2/6 = 5/6.

Subtracting Fractions #

Counting the pieces back down.

Subtracting fractions is counting matching pieces down instead of up

$\frac{5}{6}$5/6 take away $\frac{1}{6}$1/6. The pieces already match, so this is counting down.

Count down: 5 − 1 = 4, so $\frac{5}{6}-\frac{1}{6}=\frac{4}{6}$5/6 − 1/6 = 4/6. The denominator stays 6.

Unlike bottoms need a common denominator first: $\frac{1}{2}=\frac{2}{4}$1/2 = 2/4, then 3 − 2 = 1 quarter.