Number - Fractions as Division and Fractions of Quantities

Four friends want to share $3$ identical pizzas equally. How much pizza does each friend get?

$3 \div 4 = \frac{3}{4}$

Since $3$ pizzas are being divided among $4$ people, the division is $3 \div 4$. This is represented as the fraction $\frac{3}{4}$. Each friend receives $\frac{3}{4}$ of a pizza.

Calculate $\frac{3}{5}$ of $45$ liters.

$(45 \div 5) \times 3 = 9 \times 3 = 27 \text{ liters}$

First, find $\frac{1}{5}$ of $45$ by dividing $45$ by $5$, which equals $9$. Then, multiply by $3$ to find the value of three parts.

Express the improper fraction $\frac{17}{3}$ as a mixed number using division.

$17 \div 3 = 5 \text{ remainder } 2$, so $\frac{17}{3} = 5\frac{2}{3}$

Divide the numerator by the denominator. The quotient ($5$) becomes the whole number, and the remainder ($2$) becomes the new numerator over the original denominator ($3$).

A bag contains $60$ marbles. $\frac{2}{3}$ of them are blue. How many marbles are blue?

$\frac{2}{3} \times 60 = (60 \div 3) \times 2 = 20 \times 2 = 40$

To find $\frac{2}{3}$ of $60$, we divide the total number of marbles by $3$ to find one part ($20$ marbles), and then multiply by $2$ to find two parts ($40$ marbles).