Question

name: ____________________ date: _______ dividing fractions using models practice b i can use visual fraction models to represent and solve division of fractions. draw a model to find each quotient. 1.) $\frac{2}{3} div \frac{1}{2} =$ __ 2.) $\frac{3}{8} div \frac{1}{4} =$ 3.) $\frac{5}{6} div \frac{1}{3} =$ 4.) $\frac{4}{10} div \frac{2}{5} =$ 5.) $\frac{1}{2} div \frac{2}{6} =$ 6.) $\frac{2}{3} div \frac{2}{9} =$ challenge: 7.) $\frac{3}{10} div \frac{2}{5} =$ 8.) $\frac{1}{2} div \frac{2}{3} =$

Explanation:

Step1: Apply reciprocal rule

For fraction division, $\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Step2: Calculate 1: $\frac{2}{3} \div \frac{1}{2}$

$\frac{2}{3} \times \frac{2}{1} = \frac{4}{3} = 1\frac{1}{3}$

Step3: Calculate 2: $\frac{3}{8} \div \frac{1}{4}$

$\frac{3}{8} \times \frac{4}{1} = \frac{12}{8} = \frac{3}{2} = 1\frac{1}{2}$

Step4: Calculate 3: $\frac{5}{6} \div \frac{1}{3}$

$\frac{5}{6} \times \frac{3}{1} = \frac{15}{6} = \frac{5}{2} = 2\frac{1}{2}$

Step5: Calculate 4: $\frac{4}{10} \div \frac{2}{5}$

$\frac{4}{10} \times \frac{5}{2} = \frac{20}{20} = 1$

Step6: Calculate 5: $\frac{1}{2} \div \frac{2}{6}$

Simplify $\frac{2}{6}=\frac{1}{3}$, then $\frac{1}{2} \times \frac{3}{1} = \frac{3}{2} = 1\frac{1}{2}$

Step7: Calculate 6: $\frac{2}{3} \div \frac{2}{9}$

$\frac{2}{3} \times \frac{9}{2} = \frac{18}{6} = 3$

Step8: Calculate 7: $\frac{3}{10} \div \frac{2}{5}$

$\frac{3}{10} \times \frac{5}{2} = \frac{15}{20} = \frac{3}{4}$

Step9: Calculate 8: $\frac{1}{2} \div \frac{2}{3}$

$\frac{1}{2} \times \frac{3}{2} = \frac{3}{4}$

Answer:

1.) $\frac{4}{3}$ or $1\frac{1}{3}$
2.) $\frac{3}{2}$ or $1\frac{1}{2}$
3.) $\frac{5}{2}$ or $2\frac{1}{2}$
4.) $1$
5.) $\frac{3}{2}$ or $1\frac{1}{2}$
6.) $3$
7.) $\frac{3}{4}$
8.) $\frac{3}{4}$

Model Guidance (for drawing):

For each problem:

1. Draw a rectangle to represent the first fraction (e.g., for $\frac{2}{3}$, divide the rectangle into 3 equal parts, shade 2).
2. Divide the same rectangle into sections matching the denominator of the second fraction, then count how many of the second fraction's fit into the shaded area of the first. This will match the calculated quotient.