Question

center activity 5.25 * recording sheet
partner a
partner b
fractions as quotients
number bank
2 3 4 5 3/2 1/3 2/3 5/3 5/4 1/4 1/5 3/5 4/5
a
three circle graphs divided into five parts, one part shaded each
____ ÷ __ = __ __ × __ = ____
b
two circle graphs divided into three parts, one part shaded each
____ ÷ __ = __ __ × __ = ____
c
five circle graphs divided into four parts, one part shaded each
____ ÷ __ = __ __ × __ = ____

Explanation:

Step1: Analyze Part A

Each circle in Part A is divided into 5 parts, with 1 part shaded, so each shaded fraction is $\frac{1}{5}$. There are 3 circles.
For division: Total shaded (3 times $\frac{1}{5}$ is $\frac{3}{5}$) divided by number of circles (3) should give $\frac{1}{5}$. So $\frac{3}{5} \div 3 = \frac{1}{5}$.
For multiplication: Number of circles (3) times fraction per circle ($\frac{1}{5}$) gives total shaded: $3 \times \frac{1}{5} = \frac{3}{5}$.

Step2: Analyze Part B

Each circle in Part B is divided into 3 parts, with 1 part shaded, so each shaded fraction is $\frac{1}{3}$. There are 2 circles.
For division: Total shaded ($\frac{2}{3}$) divided by number of circles (2) gives $\frac{1}{3}$. So $\frac{2}{3} \div 2 = \frac{1}{3}$.
For multiplication: Number of circles (2) times fraction per circle ($\frac{1}{3}$) gives total shaded: $2 \times \frac{1}{3} = \frac{2}{3}$.

Step3: Analyze Part C

Each circle in Part C is divided into 4 parts, with 1 part shaded, so each shaded fraction is $\frac{1}{4}$. There are 5 circles.
For division: Total shaded ($\frac{5}{4}$) divided by number of circles (5) gives $\frac{1}{4}$. So $\frac{5}{4} \div 5 = \frac{1}{4}$.
For multiplication: Number of circles (5) times fraction per circle ($\frac{1}{4}$) gives total shaded: $5 \times \frac{1}{4} = \frac{5}{4}$.

Answer:

Part A:

$\boldsymbol{\frac{3}{5} \div 3 = \frac{1}{5}}$; $\boldsymbol{3 \times \frac{1}{5} = \frac{3}{5}}$

Part B:

$\boldsymbol{\frac{2}{3} \div 2 = \frac{1}{3}}$; $\boldsymbol{2 \times \frac{1}{3} = \frac{2}{3}}$

Part C:

$\boldsymbol{\frac{5}{4} \div 5 = \frac{1}{4}}$; $\boldsymbol{5 \times \frac{1}{4} = \frac{5}{4}}$