Adding and subtracting fractions and mixed numbers
How to add and subtract fractions with like and unlike denominators using the least common denominator, how to work with mixed numbers including regrouping, and negative fractions.
Like denominators
Two eighths plus three eighths is five eighths, the same way two apples plus three apples is five apples. The denominator names the size of the pieces, and it doesn't change.
Always check whether the answer can be simplified.
Unlike denominators
You can't add thirds and fourths directly, because the pieces are different sizes. First cut everything into pieces of the same size.
Mixed numbers
One way to add or subtract mixed numbers is to handle the whole numbers and the fractions separately.
Subtraction sometimes needs regrouping (borrowing), just like subtracting whole numbers.
If regrouping feels awkward, you can always convert to improper fractions first: \(\frac{21}{4} - \frac{8}{3} = \frac{63}{12} - \frac{32}{12} = \frac{31}{12} = 2\frac{7}{12}\).
Negative fractions
A negative fraction can be written three ways: \(-\frac{2}{5} = \frac{-2}{5} = \frac{2}{-5}\). When adding and subtracting, it's easiest to put the sign in the numerator and use the integer rules.
Practice
Quick check
What is \(\frac{1}{2} + \frac{1}{3}\)?
With the LCD \(6\):\(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\). Adding tops and bottoms separately gives \(\frac{2}{5}\), which is wrong.
Quick check
What is the least common denominator of \(\frac{3}{4}\) and \(\frac{1}{10}\)?
The LCD is \(\text{LCM}(4, 10) = 20\).\(40\) also works as a common denominator but isn't the least.
Finished this lesson?
Mark it as completed and it's saved on this device. Sign up to see it everywhere.