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

Learning Goal

Let’s practice dividing fractions in different situations.

Learning Targets

I can find the amount in one group in different real-world situations.

Warm Up: Number Talk: Greater Than 1 or Less Than 1?

Decide whether each quotient is greater than 1 or less than 1.

$\frac{1}{2} \div \frac{1}{4}$
$1 \div \frac{3}{4}$
$\frac{2}{3} \div \frac{7}{8}$
$2 \frac{7}{8} \div 2 \frac{3}{5}$

Activity 1: Two Water Containers

A photo of a measuring cup with water in it. The water is being poured into a container with five marks. All the water goes up to the second mark on the jar.

Problem 1

After looking at these pictures, Lin says, “I see the fraction $\frac{2}{5}$ .” Jada says, “I see the fraction $\frac{3}{4}$ .” What quantities are Lin and Jada referring to?

Problem 2

Consider the problem: How many liters of water fit in the water dispenser?

Write a multiplication equation and a division equation for the question.
Find the answer and explain your reasoning. If you get stuck, consider drawing a diagram.
Check your answer using the multiplication equation.

Activity 2: 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.

Jada bought $3 \frac{1}{2}$ yards of fabric for $21. How much did each yard cost?
$\frac{4}{9}$ kilogram of baking soda costs $2. How much does 1 kilogram of baking soda cost?
Diego can fill $1 \frac{1}{5}$ bottles with 3 liters of water. How many liters of water fill 1 bottle?
$\frac{5}{4}$ gallons of water fill $\frac{5}{6}$ of a bucket. How many gallons of water fill the entire bucket?

Are you ready for more?

The largest sandwich ever made weighed 5,440 pounds. If everyone on Earth shares the sandwich equally, how much would you get? What fraction of a regular sandwich does this represent?

Activity 3: Inventing a Situation

Problem 1

Think of a situation that involves a question that can be represented by $\frac{1}{3} \div \frac{1}{4} = ?$ Write a description of that situation and the question.

Problem 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.

Problem 3

Find the answer to your question. Explain or show your reasoning. If you get stuck, draw a diagram.

Lesson Summary

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

For example, $\frac{3}{4}$ of a pound of rice fills $\frac{2}{5}$ of a container. There are two whole amounts to keep track of here: 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.

How many pounds fill 1 container?

$\frac{2}{5} \cdot ? = \frac{3}{4}$

$\frac{3}{4} \div \frac{2}{5} = ?$

A tape diagram with 5 segments and labeled as "1 container" and "? pounds". The first two segments are blue and labeled "three-fourths pound" and "two-fifths container".

If $\frac{2}{5}$ of a container is filled with $\frac{3}{4}$ pound, then $\frac{1}{5}$ of a container is filled with half of $\frac{3}{4}$ , or $\frac{3}{8}$ , pound. One whole container then has $5 \cdot \frac{3}{8}$ (or $\frac{15}{8}$ ) pounds.

What fraction of a container does 1 pound fill?

$\frac{3}{4} \cdot ? = \frac{2}{5}$

$\frac{2}{5} \div \frac{3}{4} = ?$

A tape diagram with 4 segments and labeled as "1 pound" and "? container". The first three segments are yellow and labeled "three-fourths pound" and "two-fifths container".

If $\frac{3}{4}$ pound fills $\frac{2}{5}$ of a container, then $\frac{1}{4}$ pound fills a third of $\frac{2}{5}$ , or $\frac{2}{15}$ , of a container. One whole pound then fills $4 \cdot \frac{2}{15}$ (or $\frac{8}{15}$ ) of a container.