**Multiplication:** Multiplying two fractions together is quite simple. Given that multiplication is commutative (we can do it in any order), we simply perform the fractional operations of multiplication and division in sequence.

\[ \frac{2}{3} \times \frac{4}{5} = 1 \times 2 \div 3 \times 4 \div 5 = \frac{2 \times 4}{3 \times 5} = \frac{8}{15} \]

**Division:** Since division is simply the inverse of multiplication, we can divide one fraction by another be inverting the division and multiplication operations (that is, we mulitply by the reciprocal):

\[ \frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3\times 4} = \frac{10}{12} = \frac{5}{6}.\]

**Addition:** Adding fractions is slightly harder, because we can only add like items together. Thus, to add two fractions together, we must ensure that the denominators are equal.

\[ \frac{2}{3} + \frac{4}{5} = \frac{2 \times 5}{3 \times 5} + \frac{4 \times 3}{5 \times 3} = \frac{10}{15} + \frac{12}{15} = \frac{10+12}{15} = \frac{22}{15}. \]

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