Calculate the following fractions: a) 2/3 + 1/3, b) 3/5 + 1/5, c) 4/5 + 5/10, d) 3/8 + 1/4, e) 5/6 - 4/6

Here are the calculations for the fractions:

1. Calculate.

• a)

  Step 1: Add the numerators since the denominators are the same.

  $$\frac{2}{3} + \frac{1}{3} = \frac{2+1}{3} = \frac{3}{3}$$

  Step 2: Simplify the fraction.

  $$\frac{3}{3} = 1$$

  The answer is $\boxed{\text{1}}$

• b)

  Step 1: Add the numerators since the denominators are the same.

  $$\frac{3}{5} + \frac{1}{5} = \frac{3+1}{5} = \frac{4}{5}$$

  The answer is $\boxed{\frac{4}{5}}$

• c)

  Step 1: Find the least common denominator (LCD) for 5 and 10, which is 10. Convert $\frac{4}{5}$ to an equivalent fraction with a denominator of 10.

  $$\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}$$

  Step 2: Add the fractions.

  $$\frac{8}{10} + \frac{5}{10} = \frac{8+5}{10} = \frac{13}{10}$$

  The answer is $\boxed{\frac{13}{10}}$

• d)

  Step 1: Find the LCD for 8 and 4, which is 8. Convert $\frac{1}{4}$ to an equivalent fraction with a denominator of 8.

  $$\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8}$$

  Step 2: Add the fractions.

  $$\frac{3}{8} + \frac{2}{8} = \frac{3+2}{8} = \frac{5}{8}$$

  The answer is $\boxed{\frac{5}{8}}$

• e)

  Step 1: Subtract the numerators since the denominators are the same.

  $$\frac{5}{6} - \frac{4}{6} = \frac{5-4}{6} = \frac{1}{6}$$

  The answer is $\boxed{\frac{1}{6}}$

• f)

  Step 1: Find the LCD for 10 and 5, which is 10. Convert $\frac{2}{5}$ to an equivalent fraction with a denominator of 10.

  $$\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$$

  Step 2: Subtract the fractions.

  $$$$