Are you struggling with adding and subtracting equivalent fractions?
Don’t worry, you’re not alone. Many people find working with fractions challenging, but with a little practice, you can master this essential skill.
To start, let’s review some basic terminology.
A fraction is a number that represents a part of a whole. It is made up of two parts: the numerator and the denominator.
$$ \frac{\text{numerator}}{\text{denominator}} $$
The numerator represents the number of parts you have, while the denominator represents the total number of parts in the whole.
Equivalent fractions are fractions that have the same value but are written differently.
Example: $\frac{1}{2}$ and $\frac{2}{4}$
Understanding Equivalent Fractions
Equivalent fractions simplify to the same value.
Example: $\frac{1}{2} = \frac{2}{4} = \frac{4}{8}$
Adding Equivalent Fractions: Example
To add: $\frac{1}{2} + \frac{1}{5}$
Step 1: Find the LCD of 2 and 5 → 10
Multiples:
${2, 4, 6, 8, \fcolorbox{red}{yellow}{10}, 12, …}$
${5, \fcolorbox{red}{yellow}{10}, 15, …}$
Convert each fraction:
$$ \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \ \frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10} $$
Add:
$$ \frac{5}{10} + \frac{2}{10} = \frac{7}{10} $$
Therefore, $\frac{1}{2} + \frac{1}{5} = \frac{7}{10}$
Subtracting Equivalent Fractions: Example
To subtract: $\frac{3}{5} - \frac{1}{3}$
Step 1: Find the LCD of 5 and 3 → 15
Multiples:
${5, 10, \fcolorbox{red}{yellow}{15}, 20, …}$
${3, 6, 9, 12, \fcolorbox{red}{yellow}{15}, 18, …}$
Convert:
$$ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \ \frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15} $$
Subtract:
$$ \frac{9}{15} - \frac{5}{15} = \frac{4}{15} $$
Summary
To add or subtract equivalent fractions:
- Find the lowest common denominator (LCD)
- Convert each fraction to an equivalent with the LCD
- Add or subtract the numerators
- Simplify if necessary
Practice often, and you’ll master adding and subtracting equivalent fractions with ease.