Solve: Adding and Subtracting 3/5 + 1/2 - 1/3 Step by Step

Fractions represent parts of wholes, and you can only add parts when they're from the same-sized whole! $\frac{3}{5}$ means 3 parts of 5, while $\frac{1}{2}$ means 1 part of 2 - these are different sized pieces.

List multiples of each number: 5: 5, 10, 15, 20, 25, 30... 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30... 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30... The first number that appears in all lists is 30.

To convert $\frac{3}{5}$ to denominator 30, multiply both top and bottom by 6: $\frac{3 \times 6}{5 \times 6} = \frac{18}{30}$. This creates an equivalent fraction with the same value!

Check if 23 and 30 share any common factors. Since 23 is prime and doesn't divide 30, $\frac{23}{30}$ is already in simplest form!

Remember: $\frac{18}{30} + \frac{15}{30} - \frac{10}{30} = \frac{18 + 15 - 10}{30} = \frac{23}{30}$. Work left to right with the numerators: 18 + 15 = 33, then 33 - 10 = 23.