Lesson 8: Put It All Together: Add and Subtract Fractions

Property

To add numbers, they must represent the same kind of unit.
For fractions, this means they must have a common denominator.
We can only add fractions once they are in the form $\frac{a}{c} + \frac{b}{c} = \frac{a+b}{c}$.
If denominators are different, we must first find equivalent fractions that share a common denominator.

Examples

Property

To find an equivalent fraction, multiply the numerator and the denominator by the same whole number, $n$, where $n > 1$.
This process corresponds to visually decomposing each part of an area model into $n$ smaller, equal parts.

Examples

Property

If one denominator, $d_2$, is a multiple of another denominator, $d_1$, then the larger denominator, $d_2$, can be used as a common denominator.

Examples

Property

The lowest common denominator (LCD) for two fractions is the smallest number that both denominators divide into evenly.
Finding the LCD is the same as finding the lowest common multiple (LCM) of their denominators.

To find the LCD, you can list multiples of the larger number until you find one that is also a multiple of the smaller number.

Examples

• For $\frac{1}{6}$ and $\frac{3}{8}$, we list multiples of 8: 8, 16, 24. Since 6 divides into 24, the LCD is 24.