Download Fractions

Fractions
Definitions
• Fraction: a quotient of
two numbers
• Numerator: the top
number of a fraction
• Denominator: the
bottom number of a
fraction
• Example: ⅝
– 5 is the numerator
– 8 is the denominator
• Prime number: A whole • Examples of Prime
number, other than
numbers
one, whose factors are
• 2,3,5,7,11,13,17,19,23,
one and itself
29,31……
– Two numbers multiplied
together are factors
• (5)(3) = 15
– 5 and 3 are factors
– 2 is the only even prime
number
• Why?
– Every other Even
number has a
factor(can be divided)
by 2!
• Composite Numbers: Integers that can be written
as a product of 2 prime numbers, other than one
and itself
• Example:
10 = (5)(2)
• Other composite numbers: 12, 8, 4, 15, 21, 24, 33,
81……
• How to write a
composite number as a
product of primes
– First write the number as
a product. (think of two
numbers that multiply to
that number)
– If both numbers are
prime then you are
done, if not you need to
break down each
composite number.
Factor Tree:
30
^
5∙6
^
2∙3
So 30 = 5 ∙ 2 ∙ 3
• Write each composite
number as a product of
primes!
1. 40
2. 63
3. 81
• Answers
1. 40 = (2)(2)(2)(5)
2. 63 = (7)(3)(3)
3. 81 = (3)(3)(3)(3)
Writing Fractions in Lowest Terms
Using Product of Prime Numbers
1. Write the numerator
and the denominator
as a product of prime
24 = (2)(2)(2)(3)
72 (3)(2)(2)(2)(3)
2. Cancel out any
number that is in the
numerator and the
denominator
3. Multiply the remaining
numbers in the
numerator together. If
there is no numbers
left, then use 1
4. Multiply the remaining
numbers in the
denominator together.
If there is no numbers
left, then use 1
ANSWER
1
3
Examples:
20
35
24
70
20 = (2)(2)(5)
35 (5)(7)
20 = (2)(2)(5)
35
(5)(7)
20 = 4
35 7
24 = (4)(3)(2)
70 (7)(2)(5)
24 = (4)(3)(2)
70 (7)(2)(5)
24 = 12
70 35
Writing Fractions in Lowest Terms
by writing it as a Product
First, think of a common factor
that the numerator and
denominator both have.
Example:
24
108
Second, write the numerator
and the denominator as a
product using that common
factor.
Third, Cancel out the common
factor.
Check to see if the new
numerator and
denominator have any
common factors. If not,
then it is in lowest terms. If
not repeat the first and
second steps.
Writing Fractions in
Lowest Terms as a Product
• First write you numerator
and denominator as a
product using a common
factor
• Second cancel out any
common factors
• Repeat for the remaining
factors
• If you cannot repeat then
your fraction is in lowest
terms
Example: 16
18
Operations with Fractions
• Multiplying
Fractions
A ∙ C = A∙C
B D B∙D
B and D cannot equal
zero.
• Multiply the numerators
together and the
denominators together
• Then write your answer in
lowest terms
• Example:
2 ∙ 3 =6
7 10 70
Example: Page 21 # 19-22
19).
20).
½∙¼
10 · 3
6
21).
2· 3
3
22).
5
4
7 ∙ 3
8
21
Answers:
19).
20).
21).
22).
1/8
1/1 = 1
½
1/8
Dividing Fractions
Keep
Flip
Change
Keep the first fraction the
same
Flip the second fraction
Change the sign of division to a
multiplication sign
A÷C= A ∙ D
B D B ∙ C
B and C cannot equal zero.
Multiply the numerators
together and the
denominators together
Then write your answer in
lowest terms
• Example: Page 21 #2326
23). 1 ÷ 7 =
2 12
24). 7 ÷ 1
12 2
25). 3 ÷ 1
4 20
26). 3 ÷ 9
5 10
Answers:
23). 6/7
24). 7/6
25). 15
26). 2/3
Add/Subtract with the Same
Denominator
A + C = A+C
B B
B
A - C = A-C
B B
B
Add/Subtract the
numerators only
Leave the denominator
alone
Write your answer in
lowest terms
6+ 10 = 6 + 10 = 16
7 7
7
7
15 - 11 = 15-11= 4 = 1
16 16
16 16 4
• Example
4– 1
5 5
17 + 18
40 40
Answers
3
5
35 = 7
40
8
Equivalent Fractions
• Fractions with different
numerators and
denominators, but are
equal in value.
• Example:
1 = 2 = 3 = 4 = 18
2
4
6 8 36
• First think what number
multiplied to the
denominator will give
you your new
denominator
• Second multiply the
numerator and
denominator by that
same number.
• Do not write in lowest
terms
5
with a denominator of 21
7
Think : 7 times what number is 21?
3
Multiply the numerator and denominator by 3
5 ∙ 3 =
7 3
3
Does not change the value of the fraction! Why?
3
3 Is the same as one!
3
Write Each fraction as an
equivalent fraction
1). 7
8
1).
56/64
2). 16
11 with a denominator of 33
2).
48/33
3).
3). 40/72
with a denominator of 64
5
9 with a denominator of 72
Add/Subtract with the
Different Denominators
• Decide what is the common
denominator between the
two denominators
• Write each one as an
equivalent fraction using
the common denominator
• Add or subtract the
numerators
• Leave the denominator
alone
• Write your answer in lowest
terms
5 + 1
12 8
Common Denominator: 24
5 ∙ 2 = 10
12 2 24
1 ∙ 3= 3
8 3 24
10 + 3 = 13
24 24 24
Examples:
3 + 1
5
6
Answers:
23
30
1 + 2
3
9
5
9
7 - 8
10
15
1
6
Mixed Numbers to Improper
Fractions
• To write a Mixed
number into an
improper fraction
– Multiply the Whole
number by the
denominator
– Add the numerator to
your product
– Write your answer over
the denominator
– Simplify if possible
Example: 5 ⅞
(5)(8) = 40
40 + 7 = 47
Answer: 47
8
Whole Numbers to Fractions
• When you write a
whole number as a
fraction, you put your
whole number over
one.
• Example: 16 = 16
1