Multiplying+fractions

Multiplying Fractions
An instructional sequence for learning how to multiply with fractions generally takes students through three steps:

4 · 1/2 means 4 groups of 1/2, or 1/2 + 1/2 + 1/2 + 1/2, which equals 4 halves, or 4/2.
 * 1. Multiplying a fraction by a whole number - repeated addition of the fraction:**

1/2 of 4, or 4 divided equally into 2 parts, which is 4/2, or just 2. (What would 2/3 of 9 equal?)
 * 2. Multiplying a whole number by a fraction - taking a part of a whole number:**

1/2 · 6/7 means 1/2 of 6/7, or 1/2 of 6 sevenths, which is 3 sevenths - most easily seen as a drawing. 1/2 · 6/7 can also be represented like this, which by counting, shows 6/14, which is equivalent to 3/7.
 * 3. Multiplying a fraction by a fraction - taking a part of a fraction:**

**What real-world problems can be solved using each of these ways to multiply fractions?**
Match each problem below to a type of multiplication above.

1. A bakery has planned to make cakes today. They need the following ingredients for each cake. They want to bake 12 cakes. How much of each ingredient do they need for all 12 cakes? 3/4 cup of sugar 2 1/3 cups of flour 1/4 teaspoon of salt 2/3 tablespoon of baking powder

2. You have 6 donuts and you want to give 2/3 of them to a friend and keep 1/3 for yourself. How many donuts would your friend get? That is, how much is 2/3 of 6? 3. A pan of brownies was left out on the counter and 1/4 of the brownies were eaten. Then you came along and ate 2/3 of the brownies that were left. How much of the whole pan of brownies was eaten?

**How can you calculate answers to multiplications involving fractions**?
1. When you multiply a fraction by a whole number, it looks like you multiply the whole number times the numerator, and leave the denominator as it is. This is how you calculated 4 halves.

Watch the video: [] or this one: []

2. When you multiply a whole number by a fraction, you divide the whole number by the denominator. If the numerator is more than 1, you then multiply the answer by the numerator. (This is how you found 2/3 of 9.)

3. What can you do to calculate a fraction times a fraction? Is it different for 1/2 · 6/7 if the answer is 3/7 or 6/14?

**Assignment:** Have your students work through the section of the Student Packet on Multiplying Fractions. As you plan the lessons, decide which tasks should be done in groups of 2, which should be done individually, and where you should have whole class discussions. Allow students to work at the tasks without giving them answers. Let them use fraction manipulatives, or encourage them to make drawings. Don't just tell them the procedure (algorithm) - let them get to the point where it is obvious, by the work they've done with drawings. Then record your observations, suggestions for improvements, interesting comments or solutions by students, etc. in the discussion tab for this page.