Number and Operations—Fractions: Interpreting Fractions as Division (CCSS.5.NF.3)

This is $5 \div 2 = \frac{5}{2} = 2\frac{1}{2}$. Fractions as division tell how much in each share. Draw 5 bars and split each into 2 equal parts; each kid gets 2 whole bars and one half of another.

Think of this as $3 \div 4 = \frac{3}{4}$. Each friend gets one of 4 equal shares of 3 pizzas. Picture 3 pizzas cut into 4 equal slices each; one friend's share is 3 slices total, which is $\frac{3}{4}$ of a pizza. Check: $\frac{3}{4} \times 4 = 3$.

This is $7 \div 3 = \frac{7}{3} = 2\frac{1}{3}$. The fraction shows how much each class receives. Using fraction bars: represent 7 meters as 7 equal bars, partition each into 3 equal parts, and group one part from each bar; each class gets 2 whole meters and one third of another.

Compute $50 \div 9 = \frac{50}{9} = 5\frac{5}{9}$. Fractions as division tell the amount in each share. A fraction-bar model would show 50 units split into 9 equal shares; each share is 5 whole pounds and $\tfrac{5}{9}$ of a pound (between 5 and 6).