Adding and Subtracting Fractions

Numbers such as 1/2, 1/4 and 1/3 are fractions.
When dealing with fractions, the top number is called the numerator and the bottom number is
called the denominator.
1 numerator
2 denominator
When solving fractions, the numerator is being divided by the denominator.

There are a few different types of fractions including proper fractions, improper fractions and
mixed numbers.
When the denominator is greater than the numerator, it is considered a proper fraction.
Proper fractions are numbers like

Fractions can also be negative numbers like

When the denominator is smaller than the numerator, it is considered an improper fraction.
Improper Fractions are numbers like

When there is a whole number and a fraction, it is considered a mixed number.
Mixed numbers are numbers like

To convert a mixed number to an improper fraction, multiply the whole number by the
denominator and add the result to the numerator. The denominator will stay the same.

To convert an improper fraction to a mixed number, divide the numerator by the denominator.
The remainder will be the numerator of the fraction and the denominator will stay the same.

Adding and Subtracting Fractions

If fractions have the same denominator, the numerators can be added together. The
denominators remain the same.
An Example:

If fractions do not have the same denominator, a common multiple of the denominators must be
found before the fractions can be added together.
A common multiple can be defined as any number that is divisible by two different values. In
this case, a common multiple is needed for the two different denominator values.
An Example:

The multiples of 5 are 1 x 5 = 5, 2 x 5 = 10, 3 x 5 = 15, 4 x 5 = 20, 5 x 5 = 25 …
The multiples of 3 are 1 x 3 = 3, 2 x 3 = 6, 3 x 3 = 9, 3 x 4 = 12, 3 x 5 = 15, 3 x 6 = 18 …
A common multiple of 3 and 5 is 15.
The numerator and the denominator of each fraction must be multiplied by the same number in
order for the fractions to be added.

1) Try this example:

Subtracting Fractions:

Subtracting fractions is very similar to adding fractions. When subtracting fractions with
equivalent denominators, subtract the numerators and use the same denominator.
An Example:

If fractions do not have the same denominator, a common multiple of the denominators must be
found before the fractions can be subtracted.
An Example:

The multiples of 4 are: 1 x 4 = 4, 2 x 4 = 8, 3 x 4 = 12, 4 x 4 = 16, 5 x 4 = 20, 6 x 4 = 24,
7 x 4 = 28, 8 x 4 = 32 …
The multiples of 7 are: 1 x 7 = 7, 2 x 7 = 14, 3 x 7 = 21, 4 x 7 = 28, 5 x 7 = 35 …
A common multiple of 4 and 7 is 28.
The numerator and the denominator of each fraction must be multiplied by the same number in
order for the fractions to be subtracted.

2) Try this example:

Adding and Subtracting Mixed Numbers

To add and subtract mixed numbers, the first step is to convert the mixed numbers to improper
fractions. Then add or subtract them as fractions.
An Example:

The multiples of 8 are: 1x 8 = 8, 2 x 8 = 16, 3 x 8 = 24…
The multiples of 2 are: 1 x 2 = 2, 2 x 2 = 4, 3 x 2 = 6, 4 x 2 = 8, 5 x 2 = 10…
The common multiple of 8 and 2 is 8. The fraction 29/8 has an 8 in the denominator; therefore a
1 is used in the multiplication for a common denominator.

An Example:

The multiples of 5 are 1 x 5 = 5, 2 x 5 = 10, 3 x 5 = 15, 4 x 5 = 20, 5 x 5 = 25, 6 x 5 = 30,
7 x 5 = 35, 8 x 5 = 40…
The multiples of 7 are: 1 x 7 = 7, 2 x 7 = 14, 3 x 7 = 21, 4 x 7 = 28, 5 x 7 = 35, 6 x 7 = 42…
The common multiple of 5 and 7 is 35.

3) Try this example: