Download Worksheet 3.2: Prime Factorization and Fractions

Math 088
Fall, 2016
Worksheet 3.2: Prime Factorization and Fractions
1. Warm-up: Solve the following inequalities. Give your answer in interval notation, and use a test
value to check your answer.
3x + 5 < -4
Check:
6 − 2x ≥ 2
Check:
2. Divisibility rules
Any even number is divisible by 2
Example:
146 = 73 · 2
Any number ending in 0 or 5 is divisible by 5
365 = 73 · 5
Any number ending in 0 is divisible by 10
5670 = 567 · 10
If the sum of the digits is divisible by 3,
then the number is divisible by 3
132 = 44 · 3, because 1 + 3 + 2 = 6
If the sum of the digits is divisible by 9,
then the number is divisible by 9
504 = 56 · 9, because 5 + 0 + 4 = 9
Prime Factorization refers to factoring a number completely into prime numbers.
Use the Divisibility Rules above to find the prime factorization of each of the following:
112 =
99 =
280 =
108 =
130 =
125 =
105 =
220 =
204 =
3. Multiplying Fractions
When multiplying fractions, it’s always best to simplify first.
Factor the numerators and denominators, cancel what you can, and then multiply the remaining
terms.
25
9
100
9
12 · 10 =
99 · 10 =
21
75
·
45
14
=
39
20
·
4
9
6
7
·
=
2
25
·
9
10
22
21
·
9
121
·
125
6
=
70
9
=
·
4. Adding and Subtracting Fractions Use factoring to find the Least Common Denominator,
then add or subtract as indicated.
3
20
+
5
12
7
44
+
3
8
=
8
15
+
4
9
−
7
9
=
−
11
125
1
6
=
4
21
−
4
- 21
+
=
7
100
5
8
−
=
5
12
=