Subtracting Mixed Numbers

Subtracting Mixed Numbers

Mini-Lessons and Practice

Format

• Mini-Lesson

• Practice Problem

• Solution

Mini-Lesson

• When two things are being taken away from something, add the two things together before you subtract.

• Example: I have $20. I buy a shirt for $7 and some socks for $2. How much money do I have left?

• Add what was spent - $7 + $2 = $9

• Then subtract the $9 from the $20.

• $20 - $9 = $11

Work Out the Problem on the Next Slide, then continue to see if you got it correct.

Open Ended

A baker made 10  $\frac{3}{4}$   dozen cookies before he opened his store in the morning.
​He sold 2  $\frac{3}{4}$  ​ dozen of his cookies in the morning. He sold 3  $\frac{1}{2}$  ​ dozen of his cookies in the afternoon. 

How many dozen cookies did he sell that day?
and
How many dozen cookies does he have left at the end of the day?

Just put the number in the answer box. You do not need to label it.

Solution to How Many Dozen He Sold

 $2\ \frac{3}{4}+3\ \frac{1}{2}$  

We need to add the amount he sold in the morning to the amount he sold in the afternoon.

Add the whole numbers 2 + 3 = 5
Add the fractions 3/4 + 1/2
Use a common denominator of 4.
1/2 = 2/4 So, 3/4 + 2/4 = 5/4
Now change the 5/4 to a mixed number = 1 1/4
Add the whole number to 1 1/4 + 5 =  $6\ \frac{1}{4}$  

Solution to How Many Dozen He Has Left

He started with 10 3/4 dozen. We now know he sold 6 1/4 dozen. To find what's left, we subtract.

10 3/4 - 6 1/4

Subtract the whole numbers 10-6 = 4

Subtract the fractions 3/4 - 1/4 = 2/4

Simplify the fraction. 2/4 = 1/2

Put the whole number and fraction back together.

4 1/2

Mini-Lesson - Renaming

• When subtracting the fractions part of the mixed number, the first fraction may be smaller than the second number.

• You can't take away more than you have.

• There are two ways to rename the mixed numbers to get what you need.

Mini-Lesson continued

One Way...

Change both mixed numbers into improper fractions, then subtract.

Example: 5 1/4 - 2 3/4

5 1/4 = 21/4

2 3/4 = 11/4

Now I can subtract the numerators.

21/4 - 11/4 = 10/4

This improper fraction can be divided out to get the mixed number.

10/4 = 2 2/4 which is 2 1/2 when simplified

Mini-Lesson continued

Another Way...

5 1/4 - 2 3/4

Rename the 5 1/4 by breaking apart one of the whole numbers into 4 pieces. You now have 4 wholes and 4/4. Add the 1/4 to the 4/4 and you get 5/4.

5 1/4 = 4 5/4

4 5/4 - 2 3/4 Subtract the whole numbers, then subtract the fractions.

4 - 2 = 2 and 5/4 - 3/4 = 2/4 which simplifies to 1/2

Put them together for 2 1/2

Multiple Choice

David biked 8  $\frac{3}{8}$   miles on Tuesday and 5  $\frac{7}{8}$   miles on Wednesday.
How much farther did he bike on Tuesday than he did on Wednesday?

• 3 $\frac{4}{8}$  

• 2 $\frac{1}{2}$  

• 3 $\frac{1}{2}$  

Solution

 $\frac{3}{8}$  is smaller than  $\frac{7}{8}$  
So we have to rename our mixed numbers. 
8 $\frac{3}{8}$  = 7 $\frac{11}{8}$  

 7 $\frac{11}{8}$   $-$   5 $\frac{7}{8}$  = 2 $\frac{4}{8}$  which simplifies to 2 $\frac{1}{2}$  
or using the improper fraction method

 $\frac{67}{8}-\frac{47}{8}\ =\ \frac{20}{8}\ =2\ \frac{4}{8}\ =\ 2\ \frac{1}{2}$  

Your time to shine! You've got this!

Multiple Choice

 $5\ \frac{1}{4}\ -\ 1\ \frac{1}{2}\ =$  

•  $\frac{18}{2}\ or\ 9$  

•  $\frac{17}{4}\ or\ 4\ \frac{1}{4}$  

•  $3\ \frac{2}{4}\ or\ 3\ \frac{1}{2}$  

•  $\frac{15}{4}\ or\ \ 3\ \frac{3}{4}$  

Now complete the "Assignment" section of the slides

Solution

 $5\ \frac{1}{4}\ -1\ \frac{1}{2}\$  
One way...
Change  $5\ \frac{1}{4}$  to  $4+\frac{4}{4}+\frac{1}{4}=4\ \frac{5}{4}$ 

Change  $1\ \frac{1}{2}\ to\ 1\ \frac{2}{4}$   
Now...
 $4\ \frac{5}{4}-1\ \ \frac{2}{4}\ =3\ \frac{3}{4}$  

Alternate Solution

 $Change\ 5\ \frac{1}{4}\ to\ an\ improper\ fraction\ -\ \frac{21}{4}$ 

 $Change\ 1\ \frac{1}{4}$  to have a common denominator:  $1\ \frac{2}{4}$  

Then change to an improper fraction:  $\frac{6}{4}$  

Subtract the numerators:  $\frac{21}{4}-\frac{6}{4}=\frac{15}{4}\ or\ 3\ \frac{2}{4}or\ 3\ \frac{1}{2}$  

Now complete the assignment section

of the slides