Multiplying Mixed Numbers

Contributor: Erika Wargo. Lesson ID: 12892

Take a bite out of fractions and learn how to multiply fractions and mixed numbers. Learn the song, roll the dice, interact with interactives, and plan a meal as you learn to mix it up with fractions!

categories

Middle School

subject
Math
learning style
Kinesthetic, Visual
personality style
Otter
Grade Level
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

The new puppy walks 1½ miles a day. If he walks 5 days a week, how far does the puppy walk in 5 days?

Fractions are part of a whole and can be used to name a part of another part.

When you want to find the part of another part, you multiply. The word "of" is a key word used to identify when multiplication should be used. When a whole number and a fraction are used to name an amount, such as 1½, it is called a "mixed number" or "mixed fraction." Multiplying mixed numbers and fractions is a little different from multiplying fractions less than one, such as ½ x ½. However, some of the steps are the same.

Watch two videos on multiplying mixed numbers and fractions and whole numbers. Respond to the following questions in your math journal:

  1. What are the two steps shown to multiply a fraction by a whole number, such as 4 x ½?
  2. How do you multiply a mixed number by another mixed number? What steps are involved?
  3. What should you not do when multiplying a fraction and a mixed number, as shown in the video?

After you watch the first video, Multiplying Fractions with Whole Numbers Song by NUMBEROCK, respond to question #1.

 

Now, watch Real Math Solutions' Multiplying Fractions - Multiplying Mixed Numbers by a Fraction and respond to questions #2-3:

 

As you saw in the videos above, multiplying mixed numbers and fractions follows these steps:

  1. Convert all mixed numbers or whole numbers to improper fractions.
  2. Multiply the numerators.
  3. Multiply the denominators.
  4. Reduce your answer and convert back to a mixed number, if necessary.

When you have a whole number, and want to change it to a fraction, write the whole number as the numerator and a 1 as the denominator. For example, 5 as an improper fraction is written as 51. All whole numbers have 1 as a denominator when changed into a fraction.

Example: At the beginning of the lesson, you were presented with this word problem:

The new puppy walks 1½ miles a day. If he walks 5 days a week, how far does the puppy walk in 5 days?

Use the diagram below to help you visualize what the question is asking. If the puppy walks 1½ miles each day and repeats that for 5 days, we have 5 equal groups of 1½.

 

Since multiplication is repeated addition, instead of adding the mixed numbers, you want to multiply them.

  1 1 x 5 =            
  2          

 

Step 1: Convert all mixed numbers or whole numbers to improper fractions.

  1 1 x 5 = 3 x 5 =  
  2 2 1  

 

Step 2: Multiply the numerators.

              3 x 5 = 15
    2 1 ?

 

Step 3: Multiply the denominators.

              3 x 5 = 15
    2 1 2

 

Step 4: Reduce your answer and convert back to a mixed number, if necessary.

Divide 15 by 2 and you get 7½. The puppy walked a total of 7½ miles in 5 days.


In your math journal, write a response to the following questions:

  • How do you write a whole number as an improper fraction?
  • Describe how to multiply two mixed numbers.
  • Where else might you run into problems like these in everyday life?

Now, move on to the Got It? section to complete interactive practice with multiplying mixed numbers.

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