1. Fractions

2. 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

3. Examples of Prime numbers 2,3,5,7,11,13,17,19,23,29,31……
Prime number: A whole number, other than one, whose factors are one and itself
Two numbers multiplied together are factors
(5)(3) = 15
5 and 3 are factors
Examples of Prime numbers
2,3,5,7,11,13,17,19,23,29,31……
2 is the only even prime number
Why?
Every other Even number has a factor(can be divided) by 2!

4. Other composite numbers: 12, 8, 4, 15, 21, 24, 33, 81……
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……

5. 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

6. Write each composite number as a product of primes!40 63 81
Answers
40 = (2)(2)(2)(5)
63 = (7)(3)(3)
81 = (3)(3)(3)(3)

7. Writing Fractions in Lowest Terms Using Product of Prime Numbers
Write the numerator and the denominator as a product of prime
2. Cancel out any number that is in the numerator and the denominator
24 = (2)(2)(2)(3)
72 (3)(2)(2)(2)(3)

8. Multiply the remaining numbers in the numerator together
Multiply the remaining numbers in the numerator together. If there is no numbers left, then use 1
Multiply the remaining numbers in the denominator together. If there is no numbers left, then use 1
ANSWER 1 3

9. Examples: 20 35 24 70 20 = (2)(2)(5) (5)(7) 35 (5)(7) 20 = 4 35 7
(5)(7)
20 = 4
24 = (4)(3)(2)
70 (7)(2)(5)
(7)(2)(5)
24 = 12
Examples:

10. 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.

11. 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

12. 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

13. Example: Page 21 # 19-22 19). ½∙¼ 20). 10 · 3 21). 2 · 3 22). 7 ∙ 3
19). ½∙¼
20) · 3
6 5
21) · 3
3 4
22) ∙ 3
Answers: 19). 1/8 20). 1/1 = 1 21). ½ 22). 1/8

14. Keep Flip Change Dividing Fractions
Keep the first fraction the same Flip the second fraction Change the sign of division to a multiplication sign
Keep Flip Change
Multiply the numerators together and the denominators together
Then write your answer in lowest terms
A ÷ C = A ∙ D
B D B ∙ C
B and C cannot equal zero.

15. Answers: 23). 6/7 24). 7/6 25) ). 2/3
Example: Page 21 #23-26
23). 1 ÷ 7 =
24) ÷ 1
25) ÷ 1
26) ÷ 9

16. Add/Subtract with the Same Denominator
A + C = A+C
B B B
A - C = A-C
Add/Subtract the numerators only
Leave the denominator alone
Write your answer in lowest terms
6+ 10 = = = 15-11= 4 =

17. Example
4 – 1
Answers =

18. Equivalent Fractions
Fractions with different numerators and denominators, but are equal in value.
Example:
1 = 2 = 3 = 4 = 18
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

19. 5 with a denominator of 21 7
Think : 7 times what number is 21? 3
Multiply the numerator and denominator by 3
5 ∙ 3 =
3 Does not change the value of the fraction! Why?
3 Is the same as one!

20. Write Each fraction as an equivalent fraction
1). 7
with a denominator of 64
2). 16
11 with a denominator of 33 3)
9 with a denominator of 72
1). 56/64 2). 48/33 3). 40/72

21. 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
Common Denominator: 24 5 ∙ 2 = ∙ 3 = =

22. Examples: 6 9
Answers:

23. 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) = = 47 Answer: 47 8

24. Whole Numbers to Fractions
When you write a whole number as a fraction, you put your whole number over one.
Example: = 16 1