Unit 3, Lesson 6
Problems with Equal Groups of Fractions
Grade 4
Activity 1
A bakery makes banana bread. Here is the list of ingredients for 1 batch:
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Ingredients:
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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 cups of butter to make enough banana bread for the day. How many batches are made on Tuesday? Explain or show your reasoning.
Recipe:
- 1 banana
- cup butter
- teaspoons baking soda
- cup sugar
- 2 large eggs
- cups all-purpose flour
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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 cups baking soda _______ teaspoon(s) sugar _______ cup(s) eggs _______ flour _______ cup(s)
Activity 2
The bakery that sells banana bread also sells fresh milkshakes. Each milkshake uses gallon of milk.
Here are 5 descriptions of the milkshakes sold in a week and 5 expressions that represent the gallons of milk used.
Match each description to an expression that represents it.
- On Monday, the bakery sold 8 milkshakes. How much milk was used?
- On Tuesday, 2 customers bought 4 milkshakes each. How much milk was used?
- On Wednesday, 4 customers bought 2 milkshakes each. How much milk was used?
- On Thursday, 2 customers each bought a milkshake. They placed the same order 3 more times for their friends that day. How much milk was used?
- On Saturday, 4 friends each bought a milkshake for breakfast. They placed the same order after dinner. How much milk was used?
Student Section Summary
We learned to multiply a whole number and a fraction by thinking about equal-size groups, just as we did when multiplying two whole numbers.
We can think of as 6 groups of 4. A diagram like this can help to show that the product is 24:
We also can think of as 6 groups of . Diagrams can help us see that the product is :
After looking at patterns closely, we noticed that when we multiply a whole number and a fraction, the whole number is multiplied only by the numerator of the fraction and the denominator stays the same.
Example:
We also learned that:
- Every fraction can be written as the multiplication of a whole number and a unit fraction. For example, can be written as .
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We can write different multiplication expressions for the same fraction. For example, can be written as: