Question

name:
today we divided a unit fraction by a whole number
\\( \frac { 1 } { 2 } \div 4 = \frac { 1 } { 8 } \\)
(think...we started with a whole piece, cut it in half, and divided the half into 4 smaller
pieces. one of these smaller pieces is equal to \\( \frac { 1 } { 8 } \\) of the whole
use todays work to help you complete the following problems.

1. a pan of macaroni and cheese is \\( \frac { 1 } { 3 } \\) full. three friends equally split this

remaining macaroni and cheese.
a. draw a model that represents the situation.

Explanation:

Step1: Understand the problem

We have a pan that is $\frac{1}{3}$ full. We need to divide this $\frac{1}{3}$ among 3 friends. So we need to calculate $\frac{1}{3}\div3$.

Step2: Use the rule for dividing fractions

The rule for dividing a fraction $\frac{a}{b}$ by a whole number $c$ is $\frac{a}{b}\div c=\frac{a}{b\times c}$. Here $a = 1$, $b=3$ and $c = 3$. So $\frac{1}{3}\div3=\frac{1}{3\times3}$.

Step3: Calculate the result

$3\times3=9$, so $\frac{1}{3\times3}=\frac{1}{9}$.

Answer:

Each friend gets $\frac{1}{9}$ of the full - pan of macaroni and cheese.

For drawing the model:

• Draw a rectangle to represent the full pan.
• Divide the rectangle into 3 equal parts (since the pan is $\frac{1}{3}$ full). Shade 1 of these 3 parts to represent the $\frac{1}{3}$ full pan.
• Now, to divide this $\frac{1}{3}$ among 3 friends, divide the shaded part into 3 equal smaller parts. Each of these smaller parts represents $\frac{1}{9}$ of the full pan.