Section 4.3 And 4.4 Plus Warm Ups

Warm Ups: Write in Exponential Notation
c • b • 4 • b • b =
-5 • x • x • 3 • y • y =
d cubed =

Warm Ups: Simplify or Evaluate
15 + (4+6) 2  5 =
(4 + 8) 2  4 2 =
-3 2 + 5  2 3 =

Section 4.3: Prime Factorization and Greatest Common Factor By Ms. Dewey-Hoffman October 14 th , (Tuesday)

Finding Prime Factorizations
A PRIME NUMBER is a positive integer, greater than 1, with exactly two factors. 1 and itself.
3, 5, 7, and 9 are examples of prime numbers.
A COMPOSITE NUMBER is a positive integer greater than 1 with more than two factors.
4, 6, 8, 9, and 10 are composite numbers.
The number 1 is neither PRIME or COMPOSITE.

Tell whether each number is Prime or Composite.
23?
Prime: it only has two factors, 1 and 23.
129?
Composite: it has more than two factors: 1, 3, 43, and 129.
54?
Composite: 1, 2, 27, 6, 9, etc.

Prime Factorization
Writing a COMPOSITE NUMBER as a PRODUCT of its PRIME FACTORS shows the PRIME FACTORIZATION of the number.
OR…
Breaking a composite number into prime factors is Prime Factorization.
Remember Factor Trees?

Factor Trees
Use a factor tree to write the prime factorization of 825.
825 5 165 5 33 3 11
825 = 5 • 5 • 3 • 11
825 = 5 2  3  11 with Prime Factorization.

Greatest Common Factor (GCF)
You can use PRIME FACTORIZATION to find the Greatest Common Factor .
Any factors that are the same for two or more numbers are COMMON FACTORS.
A Common Factor for 12 and 10 is 2.
Common Factors for 12 and 24
are:
2, 3, 4, 6, and 12.
12 is the GREATEST COMMON FACTOR.

Find the GCF for 40 and 60: 40 60 2 20 2 10 2 5 2 30 2 15 3 5 40 = 2  2  2  5 or 40 = 2 3  5 60 = 2  2  3  5 or 60 = 2 2  3  5 So, 2  2  5 = 2 2  5 = 20, The GCF of 40 and 60 is 20.

Find the GCF for 6a 3 b and 4a 2 b
Write the Prime Factorization.
6a 3 b = 2•3•a•a•a•b
4a 2 b = 2 •2•a•a • b
What are the GCF?
GCF = 2 • a 2 • b
The GCF of 6a 3 b and 4a 2 b = 2 a 2 b

Example Problems:
Use Prime Factorization to find the GCF:
12 and 87
15m 2 n and 45m
12: 3 • 4 87: 3 • 29 3 is the only Common Factor so it is the GCF 15m 2 n: 3 • 5 • m • m • n 45m : 3 • 3 • 5 • m 3, 5, m are the common factors, so 15m is the GCF.

Section 4.4: Simplifying Fractions October 14 th Notes Continued

Finding Equivalent Fractions
Hopefully this is Review!
Find equivalent fractions by multiplying or dividing the numerator and denominator by the same nonzero factor.
4/12 = (Multiply)
4/12 = (Divide)

Example Problems:
Find two fractions equivalent to each fraction.
5/15 =
10/12 =
14/20 =

Fractions in Simplest Form
A fraction is in simplest form when the numerator and the denominator have no factors in common other than 1 .
Use GCF to write a fraction in simplest form.

Try these:
6/8
9/12
28/35

Word Problem…
You survey your friends about their favorite sandwich and find that 8 out of 12, or 8/12, prefer peanut butter. Write this fraction in simplest form.

Simplest form of Variable Fractions
You can simplify fractions that contain variables.
Assume that no expression has a denominator that equals zero.

Write in Simplest Form.
y/xy =
3ab 2 /12ab =
2mn/6m =
24x 2 y/8xy =

Assignment #23
Pages 183: 23-43 odd.
Pages 188: 19-35 odd and 36.

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Section 4.3 And 4.4 Plus Warm Ups

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Section 4.3 And 4.4 Plus Warm Ups — Presentation Transcript