Equivalent Fractions

Equivalent Fractions #

The same amount under a new name.

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

Read the full lesson →

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

Read the full lesson →

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

Read the full lesson →

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

Read the full lesson →

$\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

Read the full lesson →

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

Read the full lesson →

$\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.