Fractions give us a way to talk about the amounts that are in between whole numbers (whole number are numbers like 0, 1, 8, 12). To understand fractions, think of a circle (like a pizza) broken into some number of equal sections. A fraction compares two amounts: the number of equal pieces within the whole, and some number of pieces within that whole.

The top number in a fraction, the numerator, tells you how many sections have been chosen. The denominator, which is on the bottom of the fraction, tells you how many equal parts the whole has been divided into.

Fractions are common in recipes—the instructions for how to cook or bake something. Bakers need to know enough about fractions to make sure their measurements are correct.

Now meet two girls who want to use a recipe to bake cupcakes. Click "View" on the left to watch as they decide how to make more cupcakes than the recipe describes.

As you can see, sometimes you need to double or triple a recipe in order to make a larger batch of cupcakes or a bigger cake. But how can you double or triple a fractional ingredient? In this lesson, you will learn how to do just that.

As you work on this lesson, you will solve some math problems. You should have paper and a pencil ready.

Goals
Here are the big ideas you will learn about in this lesson:

• A math model can be used to understand math problems.
• Multiplication of a whole number and a fraction follows certain rules.

Strategies
You will be using many reading and writing strategies to complete this lesson. The key strategies that you will focus on are:

• Determining important information
• Making inferences
• Categorizing basic facts and ideas
• Identifying and using text features

• numerator
• product
• triple

Imagine following the recipe on the left to make 12 cupcakes. But if you needed more than 12, how would you know how much of each ingredient to use?

One way to increase the number of cupcakes (and keep them tasting the same!) is to double the recipe. Doubling just means to "take two" of something.

Here's how doubling works in math: you either add a number to itself or multiply it by 2. (For example, to double the number 3, you either add 3 + 3 or multiply 3 x 2.)

If you want to double the number of cupcakes, then you have to double the ingredients too to make sure the cupcakes taste the same. Doubling 1 egg means you need 2 eggs in the larger recipe. And since the recipe calls for 2 cups of flour, you will need 4 cups of flour if you double it.

Either way you choose to double—adding a number to itself or multiplying it by 2—you will get the same result in the end.

How many teaspoons of salt will you need if you double the recipe? What math did you use to arrive at that answer? Write your answer in two to three sentences.

The cupcakes recipe calls for 1/3 cup of butter or margarine. If you are doubling the recipe, then you need to find a way to double 1/3 as well. An area model can help you. The rectangle on the left has been divided into 3 equal sections, or thirds. Each section is 1/3 of the whole rectangle.

The shaded section is double the size of each 1/3 section. Using addition, you can see 1/3 + 1/3 = 2/3. You also can use multiplication: there are 2 equal sections, each is 1/3, so 2 x 1/3 = 2/3.

Want to see this in action? Click "View" on the left to watch a cartoon of two kids talking about how to double 1/3 in a recipe.

As you go through this lesson, remember that 1/3 + 1/3 and 2 x 1/3 both equal 2/3. Notice that when you add fractions with a common denominator, you add the numerators. What steps do you think you have to take to turn 2 x 1/3 into 2/3? Thinking about the connection between addition and multiplication can help you when you multiply a fraction by a whole number.

How do you double a fraction that has a numerator other than 1, such as 2/3?

You can still use unit fractions to think about how to double 2/3. Consider this: if 1 whole is divided into 3 sections, each section is 1/3. And 2/3 is the same as 2 sections of 1/3. You know that 2 doubled is 4. So 2/3 doubled is the same as 4 sections of 1/3, or 4/3.

Click "View" on the left to watch a video of the two girls doing this problem, then continue reading below.

You can also use a model to understand how to double 2/3. Click "View" on the bottom left to see how the area model works. Picture A shows a candy bar broken into 3 equal sections, or thirds. Each part is 1/3. Picture B shows 2 sections, or 2/3, of the bar. Picture C shows that 2/3 has been doubled—now there are 4 total sections of 1/3 instead of 2. Picture D shows that 4/3 is more than the whole chocolate bar that you started with! It is 1 bar and 1/3 of another bar, or 1 1/3.

In the video, the two girls doubled 2/3 to make it 4/3, or 1 1/3. In one to two sentences, explain how you would double the fraction 2/7.

Let's try the idea of doubling with another fraction. Imagine you want to double a recipe that calls for 3/4 of a stick of butter. How many sticks of butter will you need?

The model on the left shows a rectangle broken into 4 sections, or fourths. 3 of these sections together is 3/4. Doubling that amount gives you a total of 6 sections of 1/4. Notice:

Click "View" on the bottom left to see an area model that shows how 1 2/4 is another name for 6/4.

When you double a fraction, you just double the numerator. The denominator does not change, because you are not changing the number of pieces that make up the whole. This method will work anytime you multiply a fraction by a whole number.

Now think about this. A friend is learning about fractions and tells you that 1/4 + 1/4 + 1/4 = 3/12. Explain why this is not correct. Write your answer in two to three sentences.

Imagine your cupcakes were popular—and you had to triple the recipe to make enough to go around! You can use a multiplication rule, or set of instructions, to quickly figure out how much flour, sugar, and chocolate you will need.

To multiply a fraction and a whole number, multiply the numerator of the fraction by the whole number. The denominator stays the same.

For example:

This rule will work anytime you multiply a fraction by a whole number.

Using this rule, answer the following question. A recipe calls for 2/3 cup of sugar, but you want to make 3 times the recipe. Describe in two to three sentences how you would figure out how much sugar you would need.

You have been looking at some of the connections between addition and multiplication in this lesson. Knowing how to add fractions can help you think about how to multiply a fraction by a whole number. Now read this story about two students who are baking three batches of oatmeal raisin cookies for a bake sale. They need to use what they know about addition and multiplication to make sense of all the fractions that they see.

Click "View" on the left to begin the reading.

Devon and Jake guess that they can feed 100 people with all the cookies they baked. They want to give each person 1/2 cup of milk to enjoy with their cookies. How much milk do they need? In two or three sentences, write about how you can figure this problem out using multiplication or addition.

In this lesson you have seen how to multiply a whole number by a fraction. Now let's check your understanding of how to do this.

You will now check your understanding of the vocabulary words for this lesson by placing them in sentences. Click "View" on the left to begin the activity.

Before moving to the next screen, choose two words from the vocabulary list and write a new sentence for each word.

Vocabulary words: denominator, double, fraction, model, numerator, product, triple

Bakers and chefs need to know how to follow recipes that include fractions. They also need to know how to adjust the recipes for bigger parties. As you have seen in this lesson, doubling and tripling fractions does not have to be a confusing process.

In this activity, you will drag the cards on the left into triangles on the right so that each triangle contains three cards that are equal to one another. For example, the cards "1/3 + 1/3," "1/3 x 2," and "2/3" would all be placed on the same triangle.

Click "View" on the left to begin the activity. Your teacher will review the answers with you.

Then, before moving on to the final assignment, you may want to watch this lesson's videos again or reread the passage.

Fractions in the Kitchen

Video: 0m 27s

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Doubling with Fractions

Video: 0m 53s

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Chocolate and More Chocolate

Video: 1m 02s

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Oatmeal, Raisins, and Fractions

Document

View

In this lesson, you have learned how to multiply a fraction by a whole number. You will now write an essay that shares what you have learned and what you think about it.

Begin by reviewing your notes. Click "review my work" above and view or print out the screen that pops up.

Final Assignment Instructions

• Click Multiplying Fractions by Whole Numbers: Recipes–Final Assignment (PDF).
• Choose one of the topics in the PDF and write an essay.
• Organize your response so that it includes at least three supporting details that you have learned from the reading passage, video(s), and other materials in this lesson.
• Use at least three vocabulary words (or a form of the words) as part of your supporting details. For example, for the word jump, you could use jumps, jumped, or jumping.