Multiplying Fractions: Visual Fraction Models

GOAL: You will learn how to multiply fractions by a whole number.

GOAL: You will learn how to multiply fractions by a whole number. HOW: You will look at visual fraction models.

1 2 - You know that fractions can be shown as part of a whole or part of a set and represent a value between zero and one.  

1 2  - You know that the top number in a fraction is called a numerator and stands for the part of the whole.  

1 2 - You also know that the number down below the line is the denominator and that represents all the parts that make up the whole.

- You know how to multiply whole numbers, like in the problem 3 x 4 - You know how to multiply whole numbers, like in the problem 3 x 4. You can say you have 3 groups of 4 or 4 plus 4 plus 4, which is twelve. That is repeated addition. - When you multiply a fraction by a whole number, you are doing repeated addition with the fraction. When multiplying fractions, you can also look at visual models. Let’s see what that would look like.

Here we have the fraction ¼ Here we have the fraction ¼. This is what it looks like as a visual model. If we want to multiply ¼ times five, we could multiply this visual model five times.

- Our numerator has stayed the same because the parts that the wholes are divided into has stayed the same. We can count out for our numerator. We have five 1/4 pieces, so 5 is our numerator, and 4 is our denominator. That’s an improper fraction! Remember, improper fractions can be shown as mixed numbers. If we combined the individual ¼ pieces together, our visual model would look like this.

- If we combined the individual ¼ pieces together, our visual model would look like this. We have one whole and ¼ left over, or 1 ¼ (write). Let’s see how this works in another problem.

4 x 2/3. Here is our fraction 2/3 4 x 2/3. Here is our fraction 2/3. We are multiplying it by 4, so we would have 4 visual models like this.

Here is are our fraction of 2/3 multiplied four times Here is are our fraction of 2/3 multiplied four times. Remember, our denominator stays the same (write 3), but we can count up to find our numerator. Eight! 8/3. What would this look like as a visual model? Let’s see. Remember, another way to write an improper fraction would be as a mixed number, just like our model shows us – see how there are still 8 thirds shaded in for this model? The answer 8/3 is equivalent or equal to 2 1/3.

Remember, another way to write an improper fraction would be as a mixed number, just like our model shows us – see how there are still 8 thirds shaded in for this model? This model shows us 2 2/3 (write 2 2/3 by model). The answer 8/3 is equivalent or equal to 2 2/3 (write = 2 2/3 up at the top)

In this lesson, you learned how to multiply a fraction by a whole number by using visual models.