Lesson 6 Problems with Equal Groups of Fractions

- Let’s solve problems with fractions.

Warm-up True or False: Two and Three Factors

Decide whether each statement is true or false. Be prepared to explain your reasoning.

$\frac{10}{12} = 5 \times \frac{2}{12}$
$1 \times \frac{10}{12} = 5 \times \frac{2}{12}$
$\frac{24}{4} = 6 \times 3 \times \frac{1}{4}$
$12 \times 2 \times \frac{1}{4} = 8 \times 3 \times \frac{1}{4}$

Activity 1 Banana Bread Recipe

A bakery is making banana bread. Here is the recipe for 1 batch.

Recipe:

1 banana
$\frac{2}{3}$ cup butter
$\frac{3}{2}$ teaspoons baking soda
$\frac{5}{8}$ cup sugar
2 large eggs
$\frac{5}{2}$ cups of all-purpose flour

The bakery makes 2 batches of banana bread on Monday. Complete the table to show how much of each ingredient is used.
Monday’s banana bread
ingredient
expression
amount of ingredient
bananas
butter
cup(s)
baking soda
teaspoon(s)
sugar
cup(s)
eggs
flour
cup(s)
On Tuesday, the bakery needs $\frac{8}{3}$ cups of butter to make enough banana bread for the day. How many batches were made? Explain or show your reasoning.
Recipe:

1 banana

$\frac{2}{3}$ cup butter

$\frac{3}{2}$ teaspoons baking soda

$\frac{5}{8}$ cup sugar

2 large eggs

$\frac{5}{2}$ cups of all-purpose flour
Based on the number of the batches made on Tuesday, complete the table for each ingredient.
Tuesday’s banana bread
ingredient
expression
amount of ingredient
bananas
butter
$\frac{8}{3}$ cups
baking soda
teaspoon(s)
sugar
cup(s)
eggs
flour
cup(s)

ingredient	expression	amount of ingredient
bananas
butter		cup(s)
baking soda		teaspoon(s)
sugar		cup(s)
eggs
flour		cup(s)

ingredient	expression	amount of ingredient
bananas
butter		$\frac{8}{3}$ cups
baking soda		teaspoon(s)
sugar		cup(s)
eggs
flour		cup(s)

Activity 2 How Much Milk Was Used?

The bakery that sells banana bread also sells fresh milkshakes. Each serving uses $\frac{1}{10}$ liters of milk.
Here are five descriptions of the milkshakes sold in a week and five expressions that represent the liters of milk used.

Match each description to an expression that represents it.

On Monday, the bakery sold 8 servings of milkshake. How much milk was used?
On Tuesday, two customers bought 4 servings of milkshake each. How much milk was used?
On Wednesday, four customers bought 2 servings of milkshake each. How much milk was used?
On Thursday, two customers each bought a serving of milkshake. They placed the same order three more times for their friends that day. How much milk was used?
On Saturday, four friends each purchased a serving of milkshake for breakfast. They came back for the same after dinner. How much milk was used?

$4 \times (2 \times \frac{1}{10})$

$4 \times \frac{2}{10}$

$8 \times \frac{1}{10}$

$2 \times (4 \times \frac{1}{10})$

$2 \times \frac{4}{10}$

Practice Problem

Problem 1

Each bead weighs $\frac{5}{8}$ gram. How much do 7 beads weigh? Explain or show your reasoning.