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Today we will compute simple division of
fractions.
Compute= calculate or work out
But First let’s review what we’ve already learned!
• When multiplying fractions, they do NOT need to have a common denominator.
• To multiply two (or more) fractions, multiply across, numerator by numerator and denominator by denominator.
• If the answer can be simplified, then simplify it.
• Example:
• Example:
Remember that when multiplying Remember that when multiplying fractionsfractions
2
5
9
2
2 9
5 2
18
10
3
4
5
2
35
4 2
15
8
2
2
9
5
Equivalent Fractions
• Name the same amount but have different numerators and denominators.
12
= 24
12
1414
Equivalent Fractions
• Are sometimes called equal fractions: two or more fractions that name the same number.
12
= 24
12
4
4
1
1
Equivalent Fraction Models
12
24
36
= =
Simplifying 10
40
=104
101
104
101 =
4
14=
10 = Greatest Common Factor
Write the numerator and denominator as a product of factors, then cancel common factors and obtain the result.
Reduce
Simplifying 72
16
=44
184 =
418
=
Write the numerator and denominator as a product of common factors then cancel the common factors and obtain the result.
44
184
22
92 =
22
92 29
Repeat the simplification process until all common factors are removed.
Converting Mixed Numbers153
+= 16
3
15333
Multiply the whole number by the denominator
Add the numerator to the result
Compute the final result
Place over the initial denominator
Converting Mixed Numbers269
+= 56
9
26999
Multiply the whole number by the denominator
Add the numerator to the result
Compute the final result
Place over the initial denominator
In this expression it means
“How many one eighths are in three fourths?”
Let’s think about what dividing fractions means.
3 1 ?
4 8 : =
For example, how many one eighth slices of pizza are in three fourths of a pizza?
How many one eighths are in three fourths?To find this we
must first find 3/4 of the pizza.
We then cut each fourth into halves to make
eighths.
3 1
4 8 : = 6
3 1
4 8 : = ?
We can see there are 6 eighths in three
fourths.
How many one eighths are in one half?
Using a fraction manipulative, we show one half of a
circle.To find how many one eighths are in one half, we cover the one half with eighths
and count how many we use.
EXAMPLE 1:
1 1 ?
2 8 : =
We find there are 4. There are four one eighths in one half.
1 1
2 8 : = 4
• When dividing fractions, they do NOT need to have a common denominator.
• To divide two fractions, change the operation to multiply and take the reciprocal of the second fraction (flip the second fraction). Keep-Change-Change.
Dividing FractionsDividing Fractions
2
5
9
2
2
5
2
9
Change Operation.
Flip 2nd Fraction.
• Finish the problem by following the rules for multiplying fractions.
Dividing FractionsDividing Fractions
2
5
9
2
2
52
9
4
45
Dividing FractionsEx) Divide.
6
5
22
15
Dividing FractionsEx) Divide.
6
5
22
15
5
6
22
15
Dividing FractionsEx) Divide.
Invert and Multiply !
6
5
22
15
5
6
22
15
Dividing FractionsEx) Divide.
15 and 5 have a common factor.
6
5
22
15
5
6
22
15
Dividing FractionsEx) Divide.
Divide them both by 5.
6
5
22
15
5
6
22
15
Dividing FractionsEx) Divide.
6
5
22
15
1
6
22
35
6
22
15
Dividing FractionsEx) Divide.
22 and 6 have a common factor.
6
5
22
15
1
6
22
35
6
22
15
Dividing FractionsEx) Divide.
Divide them both by 2.
6
5
22
15
1
6
22
35
6
22
15
Dividing FractionsEx) Divide.
Divide them both by 2.
6
5
22
15
1
3
11
31
6
22
35
6
22
15
Dividing FractionsEx) Divide.
6
5
22
15
1
3
11
31
6
22
35
6
22
15
Dividing FractionsEx) Divide.
6
5
22
15
11
9
1
3
11
31
6
22
35
6
22
15
It is important to know how to compute simple division of
fractions because...
• You will need to know it for 7th grade math!
• You will need it for the CST’s!
• Why else is it important?
What we’ve learned!
• How do you reduced fractions? Do you use the LCM or the GCF?
• What does compute mean?
• What happens if you need to multiply or divide fractions and the number is mixed?
