Dividing fractions by whole numbers
This lesson teaches how to divide fractions by whole numbers (sharing divisions) using mental math. We use the analogy of dividing pie pieces evenly among a certain number of people.
In the video, I explain two different division situations where we don't have to use the "rule" or shortcut for fraction division, but instead can use mental math. The first is when a fraction is divided by a whole number. The second is when the answer to a fraction division is a whole number.
First, let’s divide pieces of pie evenly
among
a certain number of people. This means that we divide a fraction by a whole number. 




Note how we can check each division by multiplication! 
1. Color each person’s share with a different color, and write a division sentence.








2. Write a division sentence for each problem and solve it.
a. There is 6/9 of a pizza left
over,

b. A cake was cut into 20 pieces,
and now there are 12 pieces left. Four people share those equally. What fraction of the original cake does each person get?

Next, we divide unit fractions—fractions like 1/2, 1/3, 1/5, 1/8, 1/12, and so on (of the form 1/n).  
Onehalf is divided
equally among four people. Each person gets 1/8 of it.

Onefifth is divided among three people. Each person gets 1/15. To see that,

3. Split the unit fraction equally
among the people. Write a division sentence. Write a multiplication
sentence to check your division.
a. Divide between two people.

b. Divide between two people.

c. Divide between two people.


d. Divide between two people.

e. Divide among five people.

f. Divide among four people.


g. Divide among four people.

h. Divide among three people.

i. Divide among three people.



4. Solve.









5. Three children share 1/4 lb of chocolate equally.
a. How much does each one get, in pounds?
b. In ounces?
6. A half a liter of juice is poured evenly into five glasses.
a. How much juice is in each glass, measured in liters?
b. How many milliliters of juice is in each glass?
7. There are 12 beakers with various amounts of oil in them. The line plot
shows how much oil
each beaker has, in cups.
If all the oil in the beakers was poured together, and then distributed evenly
into the 12 beakers,
how much oil would be in each beaker?
8. Solve.









9. Solve the opposite problem: if each person got this much pie, how much was there originally?




10. Write a story problem to match each division, and solve.





11. One morning, Joshua's gasoline container was only 1/8 full.
He poured
half of it into his lawnmower.
a. How full is the gasoline container now?
b. If the container holds 3 gallons, what is the amount of gasoline left, in gallons?
(Challenge)
In quarts?
Lastly, we will divide multiple leftover pie pieces among
a certain number of people. This is a bit trickier, but I think you can do it! 




12. The leftover pie is divided equally. How much does each person get? Write a division sentence.
a. Divide 5/6 between two people. 
b. Divide 2/3 among three people. 

c. Divide 2/3 among four people.

d. Divide 3/4 among four people.


e. Divide 2/5 among three people.

f. Divide 4/5 among three people. 
This lesson is taken from Maria Miller's book Math Mammoth Fractions 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Fractions 2
A selfteaching worktext that teaches fractions using visual models, a sequel to Math Mammoth Fractions 1. The book covers simplifying fractions, multiplication and division of fractions and mixed numbers, converting fractions to decimals, and ratios.
Download ($5.75). Also available as a printed copy.