Chapter 3.1 Dividing Fractions
Goal: Divide a fraction, whole number or mixed number by a fraction or mixed number
Example 1: Divide a whole number by a unit fraction
Cut two pizzas into pieces that are each ¼ of a whole. How
people can you serve if every person eats 1 piece or ¼ of a
pizza?
The first number
ALWAYS represents the
Express the situation using a number sentence & a model.
TOTAL AMOUNT of any
quantity
A bottle contains 2 quarts of cooking oil. A chef uses !! of a quart of cooking oil each day.
!
How many days will the cooking oil last?
When dividing, there are two situations that can be represented:
Total Amount ÷ Number of Groups = Size of ONE group
Total Amount ÷ Size of ONE group = Number of Groups
Rewrite the examples above to represent the other type of division problem.
Pizza: ________________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Cooking Oil: _____________________________________________________
_____________________________________________________________
_____________________________________________________________
_____________________________________________________________
Example 2: Divide a whole number by a proper fraction
5÷!=
!
Model:
12 ÷ !" =
!
Model:
7÷!=
!
Model:
Procedure:
Steps:
1.
5÷!=
!
Keep the first number.
NEVER CHANGE THE
TOTAL AMOUNT!
2. Change division to
multiplication
3. Flip the second number
12 ÷ !" =
!
TAKE THE
RECIPROCAL
4. Multiply & Simplify
5. LABEL YOUR
ANSWER
7÷!=
!
Write a story problem for the problem 12 ÷ !" =
!
Example 3: Divide a fraction by a fraction
!
!
÷ =
!
!
Model:
A plank is ! meters in length. A construction worker cuts the plank into pieces of size !"
!
meters. How many pieces were cut from the plank?
Write a number sentence:
Model:
Solve using the procedure:
Check your answer:
!
Example 4: Divide a fraction by an improper fraction or a mixed number.
!
!
!
!
÷
!
!
÷1
!
!