Addition and subtraction of fractions
Instructions
Move the numerator and denominator sliders to change the pie charts representing fractions, check or uncheck the substration box to modify the operation. Move the "up/down" slider to overlap the pie charts. Check the Lowest Common Denominator (LCD) to transform the graphs to the necessary LCD with their respective calculations. Move the "answer" slider to make the answer chart appear with its calculations.
Explanation
To add or subtract fractions with different denominators, follow these steps:
- Find the least common denominator (LCD) of both fractions. The LCD is the smallest number that both denominators can divide into without leaving a remainder. For example, if you have fractions like \(\frac{3}{4}\) and \(\frac{5}{6}\), the LCD between \\(4\\) and \\(6\\) is \\(12\\).
-
Convert the fractions so that they have the same denominator
using the LCD. Multiply both the numerator and the denominator of
each fraction by the necessary number to make the denominators equal
to the LCD.
- For \( \frac{3}{4} \), multiply both the numerator and the denominator by \(3\): $$\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$$
- For \( \frac{5}{6} \), multiply both the numerator and the denominator by \(2\): $$\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}$$
- Add or subtract the numerators and keep the common denominator. Continuing with the example: $$\frac{9}{12} + \frac{10}{12} = \frac{19}{12}$$ If it were a subtraction, you would simply subtract the numerators: $$\frac{9}{12} - \frac{10}{12} = \frac{-1}{12}$$
- Simplify the fraction, if possible, by dividing the numerator and the denominator by their greatest common divisor (GCD).