5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
HOW TO ADD AND SUBTRACT
MIXED NUMBERS
WHAT'S THAT MEAN...?
TWO METHODS
THAT WORK !!
5
2
1/4
8 /31
1
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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?
2
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
Let's try Method 1 again! Use Improper Fractions without models...
THE PROBLEM>>>
4
2
2/10
3/10
Step A: Convert to
improper fractions
4 10 2 2 10 3
10 10
42 23
10 10
Step B: Add numerators &
42 23
keep denominator.
10
Step C: Convert to mixed
number.
65
10
6
5 10
3
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
Let's try Method 2 again! Use Mixed Numbers without models...
THE PROBLEM>>>
Step A: Add the whole
numbers first
Step B: Add the
fractions next.
Step C: Add everything
together.
4
2
2/10
3/10
2/10 3/10 4 2 6 5/10
5
10
6 5
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
OR
T
NA
MI N
O
N
IO
DE IT
D
KE AD
LI
Method 1:
Use Improper Fractions
A. Convert to improper fractions.
B. Add numerators & keep denominators.
C. Convert to mixed number.
C
E
R
!
P
A
Method 2:
Use Mixed Numbers
A. Add the whole numbers first.
B. Add fraction numerators
& keep denominator.
C. Combine everything
together.
6
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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.
7
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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
8
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
Method 1: Subtract using Improper fractions
4 5/6 ­ 2 1/6 =
Step A: Convert to
improper fractions.
­ = ­
4 x 6 + 5 2 x 6 + 1 29 13
6 6 6 6
Step B: Subtract numerators.
29 ­ 13 16 =
6 6
Step C: Convert back to a
16 4/6 mixed number.
6
= 2 = 2 2/3 9
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
Method 2: Subtract using Mixed Numbers
4 5/6 ­ 2 1/6 =
Step A: Subtract whole numbers
and subtract fractions
4 ­ 2 +
5 ­ 1 6 6
Step B: Combine results to a
mixed number.
4 = 2 4/6 2 + 6
Step C: Simplify if needed.
2 4/6 = 2 2/3 10
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
OR
T
A
Method 1: N
MI ION
Use Improper Fractions
O
T
N
DE RAC
KE BT
A. Convert to LI SU
C
!
P
A
E
R
improper fractions.
B. Subtract numerators & keep denominators.
C. Convert to mixed number.
All of these problems had like
Method 2:
Use Mixed Numbers
A. Subtract the whole numbers first.
B. Subtract fraction numerators
& keep denominator.
C. Keep as mixed number.
denominators.
What if the denominators are unlike???
11
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
22 6
or
4 6
3 34
12
or
10
12
2 How can you add or subtract when pieces are different sizes
12
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
Method 1: Use improper fractions.
THE PROBLEM>>> 1 4/5 + 2 2/3 Follow these steps:
9 8 5 3
B. Find least common 9 x 3 = 27 8 x 5 = 40 denominator.
5 x 3 = 15 3 x 5 = 15
A. Convert to 1 5 + 4 2 3 + 2 improper fractions. 5 3
C. Add numerators & keep denominators.
D. Convert to mixed number.
67 27 + 40 =
15 15
67 / 15 4 r 7 7 = 4
= 15 15 15 13
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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.
C. Add numerators & keep denominators.
D. Convert to mixed number.
14
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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.
C. Subtract numerators & keep denominators.
D. Convert to mixed number.
15
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
Method 2: Use Mixed Numbers.
THE PROBLEM>>> 3 1/2 ­ 2 1/3 Follow these steps:
A. Subtract whole numbers first.
3 ­ 2 = 1
­ 1 x 3 = 3 1 x 2 = 2 B. Find least common denominator of fractions. 2 x 3 = 6 3 x 2 = 6
C. Subtract numerators & keep denominators.
3 ­ 2 1 =
6 6
D. Put whole number and fraction back together.
= 1 1/6
16
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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.
C. Subtract numerators & keep denominators.
D. Keep answer as a mixed number.
17
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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.
C. Add numerators & keep denominators.
D. Keep answer as a mixed number.
18
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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.
19
5­ Adding and Subtracting Mixed Numbers and Improper Fractions.notebook March 04, 2013
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
1/9 =
2
4
3/4 -
3
5
1/3 -
3
1/4 =
4
6
2/5 +
2 3/8 =
3
1/2 =
20