Core Focus on Decimals & Fractions Multiplying Fractions With Models Lesson 5.1

Warm-Up 1.6 × × ×

Multiplying Fractions with Models Use models to multiply fractions. Lesson 5.1

Find the value of (which is read ) by completing the following steps. Step 1Divide a piece of paper horizontally into as many sections as are shown in the denominator of one of the factors. For, divide the paper into 4 horizontal sections. Step 2Use blue to color in as many horizontal sections as are shown in the numerator. For, color in 3 of the 4 sections. Step 3Divide the piece of paper vertically into as many sections as are shown in the denominator of the factor. For, divide the paper into 6 vertical sections.

Find the value of (which is read ) by completing the following steps. Step 4Use yellow to color in as many vertical sections as are shown in the numerator. For, color in one of the vertical sections. Step 5The answer to your product is Blue and yellow make green Simplify if necessary

Find the value of (which is read ) by completing the following steps. Step 6Repeat Steps 1-5 by finding the product of at least four different pairs of fractions from the purple box. Step 7Does it matter which fraction in the equation is shaded first? Explain your reasoning.

Example 1 Rafael’s mom had cup of blueberries. She split the blueberries among her three children. Each received of the blueberries. What fraction of a cup of blueberries did each child receive? Write the problem. Draw a rectangle and divide it into fourths horizontally. Shade of the rectangle, or three of the four sections, with blue.

Example 1 Continued… Rafael’s mom had cup of blueberries. She split the blueberries among her three children. Each received of the blueberries. What fraction of a cup of blueberries did each child receive? Divide the rectangle vertically into thirds. Shade of the rectangle, or one of the vertical sections, with yellow. There are now 12 sections on the rectangle. This is the value of the denominator.

Example 1 Continued… Rafael’s mom had cup of blueberries. She split the blueberries among her three children. Each received of the blueberries. What fraction of a cup of blueberries did each child receive? There are 3 sections that were shaded twice. This is the value of the numerator. Simplify. Each child received cup of the blueberries.

Example 2 Find the value of using models. Draw a rectangle and divide it into thirds horizontally. Shade two of the three sections with blue. Divide the rectangle vertically into fifths. Shade four of the five vertical sections with yellow.

Example 2 Continued… Find the value of using models. There are 15 sections on the rectangle. This is the value of the denominator. There are 8 sections shaded twice. This is the value of the numerator. The fraction is in simplest form, so

Communication Prompt Why might knowing how to use models to multiply fractions be helpful to you?

Exit Problems 1.Draw a model to represent. Find the product. 2.Draw a model to represent. Find the product. 3.Write the equation to match the model. 4.Write the equation to match the model.