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Adding Mixed Numbers
1) I can make equivalent fractions.
2) I can turn improper fractions into mixed numbers.
3) I can add mixed numbers with unlike denominators.
Lesson objectives
Teachers' notes
Fraction Vocabulary
Drag the math term to the correct box.
numerator
whole number
2
3
4
denominator
Pull
Finding Common Denominators
In order to add fractions, they have to have a common denominator. Otherwise
it's like comparing...
and
Adding Fractions with Unlike Denominators
3
+
2
5
3
4
10
+
10
Click here to see them with
common denominators.
Pull
10
Adding Fractions with Unlike Denominators
3
+
6
8
Pull
4
5
8
+
5
8
Click here to see them with
common denominators.
Method 1: Use Improper Fractions
What size parts are the circles cut into?
How many yellow parts are on each side of the + ?
4
How many
4ths in all? >>
4
4
4
<< How many wholes and
remaining parts?
Method 2: Use Mixed Numbers
What size parts are the circles cut into?
How many whole circles and how many parts are yellow on each side of the + ?
Put it all back
together as a
mixed number.
Add whole numbers 1st
than fractions.
4
4 2/10
2 3/10
Let's try Method 1 again! Use Improper Fractions without models...
THE PROBLEM>>>
Step A: Convert to
improper fractions
Step B: Add numerators & keep
denominator.
4
10
10
2
2 10
10
42
10
23
10
42
23
3
10
Step C: Convert to mixed number.
65
10
6
5
10
2/10
2 3/10
Let's try Method 2 again! Use Mixed4Numbers
without models...
THE PROBLEM>>>
Step A: Add the whole
numbers first
Step B: Add the
fractions next.
Step C: Add everything
together.
4
2
6
2/10
5/10
3/10
6
5
10
Adding Fractions with Unlike Denominators
1
+
1
12
3
5
4
+
12
Click here to see them with
common denominators.
12
Pull
1
5
Adding Mixed Numbers with Unlike Denominators
1
1
+
9
9
+
1
1
2
3
6
9
Click here to see them with
common denominators.
Pull
1
1
Adding Mixed Numbers with Unlike Denominators
1
8
+
7
8
+
3
1
3
4
2
8
Click here to see them with
common denominators.
Pull
1
7
So...what do we do if we don't have fraction strips?
With your group, solve the following problem. Keep track of what steps you
are taking to figure out the answer.
3
11
12
+
5
7
9
How to Add Mixed Numbers
Find a common denominator and make equivalent fractions.
Add the fractional parts.
If it is an improper fraction, turn it into a mixed number.
Add the whole numbers together.
Method 1:
Use Improper Fractions
Method 2:
Use Mixed Numbers
A. Convert to
improper fractions.
B. Add numerators &
keep denominators.
C. Convert to
mixed number.
A. Add the whole
numbers first.
B. Add fraction numerators
& keep denominator.
C. Combine everything
together.
Method 1: Use Improper Fractions to subtract
What fraction parts are the bars cut into?
How many parts are blue on each side of the - ?
Take away the parts
of the 2nd fraction.
<<Convert back to
mixed number.
Method 1: Subtract using Improper fractions
4
5/6
-
Step A: Convert to
improper fractions.
2 1/6 =
4x6+5
6
-
2x6+1
6
=296
Step B: Subtract numerators.
29 - 13
6
Step C: Convert back to a
mixed number.
16
6
16
=6
= 2 4/6 = 2 2/3
-
13
6
Method 2: Subtract using Mixed Numbers
What fraction parts are the bars cut into?
How many whole bars and how many parts are blue on each side of the
1st Whole # take
away
2nd whole #
-?
1st Numerator
take away 2nd
numerator
Method 2: Subtract using Mixed Numbers
4
5/6
Step A: Subtract whole numbers
and subtract fractions
-
2 1/6 =
5
6
4-2 +
- 16
Step B: Combine results to a
mixed number.
Step C: Simplify if needed.
2 +
4
6
= 2 4/6
2 4/6 = 2 2/3
Method 1:
Use Improper Fractions
Convert to
improper fractions.
B. Subtract numerators &
keep denominators.
C. Convert to
mixed number.
A.
Method 2:
Use Mixed Numbers
Subtract the whole
numbers first.
B. Subtract fraction numerators
& keep denominator.
C. Keep as mixed number.
A.
All of these problems had like denominators.
What if the denominators are unlike???
How many pieces are the pies cut into?
Name each set of pies two ways:
AS a Mixed Number
&
&
an Improper Fraction
&
22
6
Look underneath!
or
3
4
6
Great
Job!
How can you add or subtract
when pieces are different sizes
34
12
Look underneath!
or
2
10
12
You can cut the pies...
and make the pieces the same size!!!
Method 1: Use improper fractions.
THE PROBLEM>>>
1
4/5
+
2
2/3
2
3+2
3
Follow these steps:
A. Convert to
improper fractions.
B. Find least common
denominator.
. Add numerators &
keep denominators.
1 5+4
5
9 x 3 = 27
5 x 3 = 15
9
5
8 x 5 = 40
3 x 5 = 15
C
D. Convert to
mixed number.
27 + 40
15
67 / 15
15
4 r 7
=15
67
=
15
7
=
15
4
8
3
PRACTICE Method 1: Use improper fractions to add.
4
1/4 +
3
1/5
STEPS:
A. Convert to
improper fractions.
B. Find least common
denominator.
. Add numerators &
keep denominators.
C
D. Convert to
mixed number.
PRACTICE Method 1: Use improper fractions to subtract.
4
2/3 -
3
1/5
STEPS:
A. Convert to
improper fractions.
B. Find least common
denominator.
. Subtract numerators
& keep denominators.
C
D. Convert to
mixed number.
Method 2: Use Mixed Numbers.
THE PROBLEM>>>
3
1/2
- 2
1/3
Follow these steps:
A. Subtract whole
numbers first.
B. Find least common
denominator of fractions.
. Subtract numerators &
keep denominators.
C
D. Put whole number and
fraction back together.
3-2 =1
1 x 3=3
2 x 3=6
3 - 2
6
-
1 x 2= 2
3 x 2= 6
=1
6
= 1 1/6
PRACTICE Method 2: Use mixed numbers to subtract.
5
3/4 -
2
1/3
STEPS:
A. Subtract whole
numbers first.
B. Find least common
denominator of fractions.
. Subtract numerators &
keep denominators.
C
D. Keep answer as a
mixed number.
PRACTICE Method 2: Use mixed numbers to add.
2
1/3 +
5 3/8
STEPS:
A. Add whole
numbers first.
B. Find least common
denominator of fractions.
. Add numerators &
keep denominators.
C
D. Keep answer as a
mixed number.
What do you have to remember to do when adding or
subtracting mixed numbers with unlike
denominators???
Does it matter which method you use for adding or
subtracting? Explain.
PRACTICE PROBLEMS
USE METHOD 1 OR 2
(Remember to find a common denominator and be sure to watch the signs!)
1
1
2/3 +
3
5
1/3 -
3 1/9 =
3 1/4 =
2
4
3/4 -
2 3/8 =
4
6
2/5 +
3 1/2 =
practice 5-5
Grade: «grade»
Subject: «subject»
Date: «date»
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05-05.ppt
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Problems to solve:
2
Things you learned.
1
Question you still have.
Attachments
05-05.ppt