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
Middle School (6-8)
Lesson Type
Quick Query

Lesson Plan - Get It!

Audio:

The new puppy walks 1-½ 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 1-½, 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 1-½ 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 1-½ miles each day and repeats that for 5 days, we have 5 equal groups of 1-½.

$1\:&space;\frac{1}{2}\:&space;\times&space;\:&space;5\:&space;=&space;\:$

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

$1\:&space;\frac{1}{2}\:&space;\times&space;\:&space;5\:&space;=&space;\:\;&space;\rightarrow&space;\;&space;\frac{3}{2}\:&space;\times&space;\:&space;\frac{5}{1}\:&space;=$

Step 2: Multiply the numerators.

$\frac{3}{2}\:&space;\times&space;\:&space;\frac{5}{1}\:&space;=&space;\:&space;\frac{15}{?}$

Step 3: Multiply the denominators.

$\frac{3}{2}\:&space;\times&space;\:&space;\frac{5}{1}\:&space;=&space;\:&space;\frac{15}{2}$

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

Divide 15 by 2 and you get 7-½. The puppy walked a total of 7-½ 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.

Elephango's Philosophy

We help prepare learners for a future that cannot yet be defined. They must be ready for change, willing to learn and able to think critically. Elephango is designed to create lifelong learners who are ready for that rapidly changing future.