Dividing is Multiplying

Property Dividing by a number is the same as multiplying by its reciprocal. For any numbers $a$ and $b$ (where $b \ne 0$), $a \div b = a \times \frac{1}{b}$.

Examples Shawna dividing $2\frac{2}{3}$ cups for 4 plants ($2\frac{2}{3} \div 4$) is the same as finding $\frac{1}{4}$ of the food ($2\frac{2}{3} \times \frac{1}{4}$). To solve $1\frac{3}{5} \div 4$, you can instead calculate $1\frac{3}{5} \times \frac{1}{4} = \frac{8}{5} \times \frac{1}{4} = \frac{2}{5}$. Compare: $4\frac{1}{2} \div 3$ is equal to $\frac{1}{3} \times 4\frac{1}{2}$, since dividing by 3 is the same as multiplying by $\frac{1}{3}$.

Explanation Why is dividing by 4 the same as multiplying by $\frac{1}{4}$? It’s two ways of asking the same thing! Dividing asks 'how many groups of 4 can I make?' while multiplying by $\frac{1}{4}$ asks 'what is one fourth of my stuff?' Both questions split your total into four equal shares, leading to the exact same answer.