Adding Mixed Numbers with Like and Unlike Denominators

Adding Mixed Numbers with

Like and Unlike Denominators

Multiple Choice

Before adding Mixed Numbers, 

what is the first thing you need to ask yourself?

 $1\frac{1}{4}\ +\ 2\frac{2}{5}\ =$  

• Are the denominators Like or Unlike?

• Are there whole numbers?

• Are there fractions?

Multiple Choice

The denominators are UNlike, what do we do before adding?

 $1\frac{1}{4}\ +\ 2\frac{2}{5}\ =$  

• Change both denominators to be 5.

• Find a Common Denominator for both fractions

• Start adding the mixed numbers

• Change both denominators to be 4.

Multiple Choice

Since the denominators are UNlike, we need to find a Common Denominator.

 $1\frac{1}{4}\ +\ 2\frac{2}{5}\ =$  
What is the Least Common Multiple of 4 and 5?

• 8

• 10

• 5

• 20

Multiple Choice

4: 4, 8, 12, 16, 20
5: 5, 10, 15, 20
The Least Common Multiple of 4 and 5 is 20.

 $1\frac{1}{4}\ +\ 2\frac{2}{5}\ =$  
To find equivalent fractions that both have 20 as the common denominator we:

• multiply  $\frac{3}{4}\ \times\ \frac{4}{4}$  
  
  multiply   $\frac{2}{5}\ \times\ \frac{5}{5}$  

• multiply  $\frac{3}{4}\ \times\ \frac{1}{5}$  
  
  multiply   $\frac{2}{5}\ \times\ \frac{1}{4}$  

• multiply  $\frac{3}{4}\ \times\ \frac{5}{5}$ 
  
  multiply  $\frac{2}{5}\ \times\ \frac{4}{4}$  

Multiple Choice

 $1\frac{1}{4}\ +\ 2\frac{2}{5}\ =$  

After finding the equivalent fractions, what is the new equation?

•  $1\frac{1}{20}\ +\ 2\frac{2}{20}\ =$  

•  $1\frac{5}{20}\ +\ 2\frac{8}{20}\ =$  
  

•  $\frac{5}{20}\ +\ \frac{8}{20}\ =$  
  

•  $1\frac{6}{20}\ +\ 2\frac{10}{20}\ =$  
  

Multiple Choice

 $1\frac{5}{20}\ +\ 2\frac{8}{20}\ =$  
How do we add these mixed numbers?

• Add the whole numbers.
  Add the fractions.

• Add the whole numbers to the numerators. 

• Add the whole numbers to the denominators. 

Multiple Choice

 $1\frac{5}{20}\ +\ 2\frac{8}{20}\ =$  

•  $3\frac{13}{40}$  

•  $\frac{16}{20}$  

•  $1\frac{13}{20}$  

•  $3\frac{13}{20}$  

Remember:
If the fraction in your mixed number
sum (answer to addition) is IMPROPER
you will need to convert it into a
mixed number.
Example:

 $4\frac{5}{4}$   =  $4\ +\ \frac{4}{4}\ +\ \frac{1}{4}$   $=\ 5\ \frac{1}{4}$  

Multiple Choice

Ask: Can I add these?

 $2\ \frac{7}{8}+5\ \frac{3}{4}\ =$  

Don't forget: 
"It's improper to leave a mixed number with an IMPROPER fraction!"
You have to convert it.

•  $7\ \frac{10}{8}$  

•  $8\ \frac{5}{8}\$  

•  $7\ \frac{13}{8}$  

Multiple Choice

Ask: Can I add these?

 $4\ \frac{2}{3}\ +\ 7\ \frac{7}{9}=$  

Don't forget: "It's improper to leave a mixed number with an IMPROPER fraction!"You have to convert it.

•  $12\ \frac{4}{9}$  

•  $11\ \frac{9}{12}$  

•  $12\frac{9}{9}$   

Multiple Choice

Ask: Can I add these?

 $3\ \frac{6}{10\ }+2\ \frac{3}{10}=$  

•  $5\ \frac{19}{20}$  

•  $\frac{14}{10}$  

•  $5\ \frac{9}{10}$  

Multiple Choice

Ask: Can I add these?

 $10\ \frac{3}{5}\ +\ 1\ \frac{4}{20}=$  

•  $11\ \frac{16}{20}$  Simplified:  $11\ \frac{4}{5}$  

•  $11\ \frac{7}{20}$  

•  $11\frac{7}{25}$  

Multiple Choice

Ask: Can I add these?

 $6\ \frac{3}{4}\ +\ 2\ \frac{1}{7}=$  

•  $8\ \frac{4}{28}$  

•  $8\ \frac{4}{7}$  

•  $8\frac{25}{28}$   

Multiple Choice

Ask: Can I add these?

 $3\ \frac{2}{5}\ +\ 4\ \frac{3}{7}=$  

•  $7\ \frac{5}{12}$  

•  $7\ \frac{29}{35}$  

•  $7\frac{5}{35}$  Simplified:  $7\ \frac{1}{7}$  

Multiple Choice

Ask: Can I add these?

 $5\ \frac{1}{4}+12\ \frac{3}{4}=$  

•  $18$  

•  $17\ \frac{4}{4}$  

•  $17\ \frac{12}{12}$