Lesson 9: How Much in Each Group? (Part 2)

Let’s practice dividing fractions in different situations.

9.1: Number Talk: Greater Than 1 or Less Than 1?

Decide whether each of the following is greater than 1 or less than 1.

  1. $\frac12\div\frac14$
  2. $1\div\frac34$
  3. $\frac23\div\frac78$
  4. $2\frac78\div2\frac35$

9.2: Two Water Containers

  1. After looking at these pictures, Lin says, “I see the fraction $\frac 25$.” Jada says, “I see the fraction $\frac 34$.” What quantities are Lin and Jada referring to?

  2. How many liters of water fit in the water dispenser?

    Write a multiplication equation and a division equation for the question, then find the answer. Draw a diagram, if needed. Check your answer using the multiplication equation.

9.3: Amount in One Group

Write a multiplication equation and a division equation and draw a diagram to represent each situation and question. Then find the answer. Explain your reasoning.

  1. Jada bought $3\frac12$ yards of fabric for \$21. How much did each yard cost?
  2. $\frac 49$ kilogram of baking soda costs \$2. How much does 1 kilogram of baking soda cost?
  3. Diego can fill $1\frac15$ bottles with 3 liters of water. How many liters of water fill 1 bottle?
  4. $\frac54$ gallons of water fill $\frac56$ of a bucket. How many gallons of water fill the entire bucket?

9.4: Inventing a Situation

  1. Think of a situation that involves a question that can be represented by $\frac{1}{3}\div\frac14 = {?}$ Write a description of that situation and the question.

  2. Trade descriptions with a member of your group.

    • Review each other’s description and discuss whether each invented question is an appropriate match for the equation.
    • Revise your description or question based on feedback from your partner.
  3. Find the answer to your question. Explain or show your reasoning. If you get stuck, draw a diagram.

Summary

Sometimes we have to think carefully about how to solve a problem that involves multiplication and division. Diagrams and equations can help us. 

Let’s take this example: $\frac34$ of a pound of rice fills $\frac25$ of a container. 

There are two whole amounts to keep track of: 1 whole pound, and 1 whole container. The equations we write and the diagram we draw depend on what question we are trying to answer. Here are two questions that could be asked:

  • How many pounds fill 1 container?
  • What fraction of a container does 1 pound fill?

We can represent and answer the first question (how many pounds fill a whole container) with:

$$\frac 25 \boldcdot {?} = \frac 34$$

$$\frac 34 \div \frac 25 = {?}$$

 

If $\frac25$ of a container is filled with $\frac 34$ pound, then $\frac 15$ of a container is filled with half of $\frac34$, or $\frac38$, pound. One whole container then has $5 \boldcdot \frac38$ (or $\frac {15}{8}$) pounds.

We can represent and answer the second question (what fraction of the container 1 pound fills) with:

$$\frac34 \boldcdot {?} = \frac25$$

$$\frac25 \div \frac34 ={?}$$

 

If $\frac 34$ pound fills $\frac25$ of a container, then $\frac14$ pound fills a third of $\frac25$, or $\frac {2}{15}$, of a container. One whole pound then fills $4 \boldcdot \frac{2}{15}$ (or $\frac {8}{15}$) of a container.

Practice Problems ▶