Multiplying Mixed Numbers

Multiplying Mixed Numbers

Learning Goal: Use models, equations, and previously learned strategies to multiply mixed numbers.

What is a Mixed Number?

A number that is greater than one whole and is made of a whole number plus a fraction

Multiple Choice

Select the example of a mixed number below:

• $$\frac{1}{2}$$

  
  

• $$\frac{10}{3}$$
  

• $$2\ \frac{1}{3}$$
  

Reminder on Converting Mixed Numbers

• Multiply the denominator and whole number

• Add that product to the numerator

• Put your answer over the denominator

Multiple Choice

Change this Mixed Number into an Improper Fraction.

• 50/8

• 20/8

• 16/8

• 12/8

Multiple Choice

Convert to a mixed number: 

• 4 2/5
• 3 9/5
• 4 4/5
• 4/5

Multiple Choice

Change the mixed number below to an improper fraction.

$$2\ \frac{4}{5}$$  

• $$\frac{14}{2}$$  

• $$\frac{11}{5}$$  

• $$\frac{14}{5}$$  

Multiple Choice

Change the mixed number to an improper fraction.

• 8/3

• 15/3

• 16/1

• 16/3

Multiple Choice

• 1/10

• 1/20

• 2/20

• 2/5

Multiple Choice

• 1/42

• 3/42

• 1/14

• 2/14

Multiple Choice

• 240/4

• 60

• 30

• 80/4

Multiple Choice

• 14/24

• 7/12

• 7/24

• 2/3

​First step....

​Change all mixed numbers and whole numbers to improper fractions.

​

​For whole numbers put a 1 under the whole number.

​

​For mixed

​numbers -->

Multiple Choice

How would you rewrite this to solve it?

Multiple Choice

How could you rewrite the problem to solve it?

​Then...

​Once you convert then numbers to improper fractions you multiply.

​

​

​numerator x numerator

​--------------------------------

​denominator x denominator

​

​If the fraction is improper...

​You will need to divide like this.

​

​

​Improper means that the top number is larger than the bottom number.

Multiple Choice

Convert the improper fraction to a mixed number

Multiple Choice

Convert to a mixed number: 

• 4 2/5
• 3 9/5
• 4 4/5
• 4/5

Multiple Choice

Change this Improper Fraction to a Mixed Number.

• 5 1/3

• 4 2/3

• 6

• 5 2/3

​If the fraction is not improper...

​you simplify by dividing like this...

​Vocabulary

​Simplified Fraction: an equivalent form of the fraction where the numerator and denominator are integers and have a greatest common factor of 1.

​Simple Steps to Simplify a Fraction: divide the top and bottom numbers by their greatest common factor.

Multiple Choice

Simplify the fraction 2/9

• Already Simplified

• 2/4

• 1/4

Multiple Choice

$$\frac{10}{12}\ =$$  

• $$\frac{2}{3}$$  

• $$\frac{3}{4}$$  

• $$\frac{5}{6}$$  

• $$\frac{6}{7}$$  

Multiple Choice

$$\frac{3}{21}\ =$$  

• $$\frac{1}{7}$$  

• $$\frac{2}{7}$$  

• $$\frac{3}{7}$$  

• $$\frac{4}{7}$$  

Multiple Choice

Multiply.  Be sure to simplify your answer when possible.

• 11 3/4

• 10 2/36

• 47/4

• 423/36

Multiple Choice

$$1\frac{2}{5}\ \times\ 2\frac{1}{3}$$  

• $$3\frac{2}{15}$$  

• $$3\frac{3}{15}$$  

• $$3\frac{4}{15}$$  

• $$3\frac{5}{15}$$  

Multiple Choice

$$2\ \frac{3}{4}\ \ \times\ \ 8$$  

Solve this problem

• 22

• $$\frac{11}{4}$$  

• $$\frac{8}{1}$$  

Multiple Choice

A batch of oatmeal muffins calls for $$\frac{2}{3}$$ cups of oats. How many cups of oats do you need to make four batches of muffins?

• $$2$$  cups
  

• $$\frac{2}{12}\$$ cup
  

• $$4\frac{2}{3}$$ cups

• $$2\frac{2}{3}$$ cups