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The Division Principle
8 ÷ 4 = 2Dividen
d
Divisor
Quotient
Dividend
: The amount you want to divide up: The number you divide by
Quotient : The answer after you divide one number by another
The Division Principle
8 ÷ 4 = 2Dividen
d
Divisor
Quotient
21 3 4 5 6 7 8
Total number to be divided
Number of groups is the quotient.
1 2
Num
ber i
n ea
ch
grou
p is th
e
divi
sor.
The Division of Fractions Principle
• IT IS THE SAME !! 2 ÷ 1/2 = 4
2
1
Tota
l num
ber t
o be
divi
ded
The number in each group is ½ so each group needs to be cut in half.
The number of groups is the quotient.
1 2
3 4
Another problem Dividing Fractions
2 ÷ 1/3 =
2
1
Tota
l num
ber t
o be
divi
ded
Need to cut each group into thirds.
Number of total groups
6?
Is there anything you notice about dividing by a fraction that is different from dividing with whole numbers?
1/31/3
1/3
1/31/3
1/3
1 2
3
4 5
6
You already know this…If it takes 2 cups of cheese for half a pizza,
How much cheese will it take for a whole pizza?
Think about it……
Cups of cheese 2 ?
pizza ½ 1
x 2
x 2
Cups of cheese 2 4
pizza ½ 1
2 1
24
Look for a pattern in the following problems.
Divide this
2 1
36
Cups of cheese 2 ?
pizza 1/3 1
x 3
x 3
Cups of cheese 2 6
pizza 1/3 1
Look for the pattern.
Divide this
1 1
55
Cups of cheese 1 ?
pizza 1/5 1
x 5
x 5
Cups of cheese 1 5
pizza 1/5 1
Do you see a pattern?
The pattern lies with what we multiply by to get the solutions.
x 3
x 3
Cups of cheese 2 6pizza 1/3 1
x 2
x 2
Cups of cheese 2 4pizza ½ 1
x 5
x 5
Cups of cheese 1 5pizza 1/5 1
How is the number we multiply by related to the fraction we are dividing by?
The number we multiply by is the RECIPROCAL of the fraction we are dividing by.
Reciprocal
a number that you multiply by so the result equals 1.
The easiest way to find the reciprocal of a fraction is to just flip the fraction over.
1/2 X 2 = 1
1/4 X 4 = 11/3 X 3 = 12/5 X 5/2 = 1
Determine the algorithm
• What are the “rules” for dividing fractions?
– Take the reciprocal of the fraction you are dividing by
– And multiply
A look at some simple problems
2 1
2
2 1
3
11
5
2 2
5
2 1
5
Complete the problems on your whiteboard.Show your work
Step Up a Notch w/ more problemsComplete the problems on your whiteboard.
Show your work
2 2
3
6 3
4
3 3
4
1 1/4 1
2
Stumper Problems
2
3
1
3
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