Transcript Fractions V Mixed Numbers

Fractions V
Mixed Numbers
Mixed Number
A
mixed number has a part that
is a whole number and a part
that is a fraction.
3
= 1 4
Improper Fraction
A
fraction in which the
numerator is greater than the
denominator.
=
8
4
What is the improper fraction?
=
15
4
How to change a mixed number to
an improper fraction
 Multiply
the whole
number times the
denominator.
 Add your answer to the
numerator.
 Put your new number
over the denominator.
+1
4x =
2
7
2
Change this mixed number to an
improper fraction
 Multiply
the whole
number times the
denominator.
 Add your answer to the
numerator.
 Put your new number
over the denominator.
+2 20
6x =
3 3
Change this mixed number to an
improper fraction
 Multiply
the whole
number times the
denominator.
 Add your answer to the
numerator.
 Put your new number
over the denominator.
+ 2 17
3x =
5 5
Change this mixed number to an
improper fraction
 Multiply
the whole
number times the
denominator.
 Add your answer to the
numerator.
 Put your new number
over the denominator.
+ 3 19
4x =
4 4
Change this mixed number to an
improper fraction
 Multiply
the whole
number times the
denominator.
 Add your answer to the
numerator.
 Put your new number
over the denominator.
+ 2 20
6x =
3 3
Change this mixed number to an
improper fraction
 Multiply
the whole
number times the
denominator.
 Add your answer to the
numerator.
 Put your new number
over the denominator.
+ 3 43
8x =
5 5
Fraction Multiplication


Here are some fraction
multiplication problems
Can you tell how to multiply
fraction from these
examples?
2 5 10
 
3 7 21
4 1
4
 
5 7 35
2 5 10
 
3 1
3
3 5 15


4 12 48
6 4 24


5 10 50
1 1 1
 
3 3 9
Multiplication
Multiply numerator by numerator
 And denominator by denominator

2 5 10
 
3 1
3
N1 N 2 N1  N 2


D1 D2 D1  D2
Try some.
• Multiply the following:
1 5
 
3 8
2 4
 
3 5
5 5
 
8 8
4 2
 
9 3
Answers
• Multiply the following:
1 5
5
 
3 8 24
2 4
8
 
3 5 15
5 5 25
 
8 8 64
4 2
8
 
9 3 27
Mixed Numbers
•
•
•
Because of the order of operations,
Mixed numbers cannot be multiplied as is
Change mixed numbers to improper fractions, then
multiply.
2 5
3 1 
5 8
17 13


5 8
•
17 13 221


5 8
40
Believe it or Not, 221/40 is our best and final
answer. In Algebra, we leave our answers
SIMPLIFIED and IMPERFECT!
Try some
•
•
•
Change any whole or mixed numbers to
improper.
Multiply straight across.
Simplify answers
2
1 7 
5
1
8 
5
Answers
•
•
•
Change any whole or mixed numbers to
improper.
Multiply straight across.
Simplify answers
2
7 7 49
4
1 7   
9
5
5 1
5
5
1
1 8 8
3
8    1
5
5 1 5
5
Canceling
Reduce before you multiply
Canceling on paper
•
Rules: One factor from
any numerator cancels
with like factor from the
denominator.
4
1
16

21 7
3
16 9 15
 
21 20 12
3
9
15

12 3
4 1 20
1
1
3

7
Try one
•
•
Say “--- goes into ____ this many times.”
As you cross each number out and write what is
left after canceling above the number.
5 1

3 10
Answer
•
•
Say “--- goes into ____ this many times.”
As you cross each number out and write what is
left after canceling above the number.
1
5
1
5


3
10 2 6
Try one more
•
•
•
•
Make whole and mixed numbers improper
Cancel if you can
Multiply Numerators and denominators straight
across.
Simplify
10
1 14
4  4
21 2 15
Answer
•
•
•
•
Make whole and mixed numbers improper
Cancel if you can
Multiply Numerators and denominators straight
across.
Simplify
10
1 14
4 
4
21
2 15
10 9 14 4
 
 8
21 2 15 1