1. Thursday, August 16, 2018 Find the LCM using the ladder method.
64 and ) 48 and 72

2. Homework Answers

3. Multiplying Fractions and Mixed Numbers

4. Multiplying Fractions
Multiply the numerators, multiply the denominators, and simplify the fraction. 1 2 1 3 1 x = 6 3 5 1 2 3 x = 10

5. Multiplying Fractions by a whole number3 4
Change the whole number to a fraction. 2 x 2 1 3 4 6 1 1 x = = 4 2

6. Simplifying Before Multiplying If any numerator and denominator have a common factor, you can simplify before multiplying. This will keep you from working with big numbers a lot of the time. 1 2 7 3 8 x 4 1 7 3 4 3 x = 28

7. Simplifying Before Multiplying1 1 3 3 7 x 1 1 1 7 1 x = 7

8. Simplifying Before Multiplying1 1 5 6 3 5 x 1 2 1 2 1 1 x = 2

9. Multiplying Mixed Numbers
Rename the mixed numbers as improper fractions. Simplify then multiply. 19 1 4 76 9 1 4 4 9 x 8 x = 1 1 19 9 1 19 2 = x = 9 9

10. You Try…. 1) 1 8 1 9 3 12 4 5 1 2) 1 x x = = 72 5 1 3 1 3 6 7 2 7 3) 4) x = 6 x 2 6 2 =

11. Notes: Keep this sheet in the Math section of your binder
Notes: Keep this sheet in the Math section of your binder. Just remember….. Although it is not in these notes, it is always better to simplify before you multiply.

12. Exponents and Prime Factorization

13. What is an exponent?
An exponent is a little number high and to the right of a regular or base number. 3 4
Exponent
Base

14. Definition of Exponent
An exponent tells how many times a number is multiplied by itself. 3 4
Exponent
Base 4
= 3 x 3 x 3 x 3 3

15. What is Exponential Form?
Expressed in terms of a designated power
Ex: 2 3
This is written in exponential form

16. What is Standard Form?
When you simplify/solve the expression you put it in standard form.
Ex: 2 3 = 2 x 2 x 2 = 8
8 is standard form

17. How to read an Exponent
This exponent is read three to the fourth power. 3 4
Exponent
Base

18. How to read an Exponent
This exponent is read three to the 2nd power or three squared. 3 2
Exponent
Base

19. How to read an Exponent
This exponent is read three to the 3rd power or three cubed. 3 3
Exponent
Base

20. Let’s see who can read these exponents…3 2 6 7 2 3 5 4

21. How would we write this in exponential form?3
2 x 2 x 2 = 2

22. How would we write this in exponential form?2
3 x 3 = 3

23. How would we write this in exponential form?4
5 x 5 x 5 x 5 = 5

24. How to Multiply an Exponent to Find the Standard Form4 3
= 3 x 3 x 3 x 3 9 27 81

25. Write in Standard Form 2 4 16 =

26. Write in Standard Form 3 2 8 =

27. Write in Standard Form 2 3 9 =

28. Write in Standard Form 3 5
125 =

29. Now Let’s Look at Prime Factorization

30. Prime and Composite Numbers
Prime numbers are
numbers that only have
two factors: one, and the
number itself.
EXAMPLES:
3, 5, 7, 11, 31
Composite numbers
have more than two
factors.
EXAMPLES:
6, 15, 18, 30, 100

31. A Product of Primes
Every composite number can be expressed as a product of prime numbers.
This is called prime factorization.

32. The product of the primes or primes factorization for 15 is
Example
15 is a composite number.
The product of the primes or primes factorization for 15 is
3 x 5

33. Let me show you an example: Prime Factorization of 100.
100 ÷ 2 = 50. Two is the first prime number that goes into 100.
2 is a prime number, so we are done with it.
2 X 50
Now we deal with the 50. Divide it by 2 to get the next factors.
25 is not divisible by the first prime, 2. The next prime, 3, does not work either. We must divide by 5 to get a factor.
2 X 25
5 x 5
Both numbers are prime, leaving us with all primes.

34. What’s the Answer?
Just list the circled prime numbers in order from least to greatest with a multiplication sign between them.
2 x 2 x 5 x 5

35. Exponential Form
We have just listed our prime factorization for 100 as being 2 x 2 x 5 x 5. This is repeated multiplication. Repeated multiplication can be expressed with exponents.
2 x 2 can be expressed in exponential form: 22
5 x 5 can be expressed as 52
Put it together, and 2 x 2 x 5 x 5 is more simply put as
22 x 52

36. Let’s do this one together…
420
2 x 210
2 x 105
Expanded Form:
2 x 2 x 3 x 5 x 7
3 x 35 or
22 x 3 x 5 x 7
5 x 7
Exponential Form:

37. Now, You Try! Find the Prime Factorization and Exponent of 16?
/ \
2 8
/ \
2 4
/ \
2 2
The prime factors of 16 are: 4
or 2
2 x 2 x 2 x 2

38. Class Practice

39. Class Practice Answers

40. Homework Time! You may use a calculator for Section C of homework.
There is no work/justification needed on tonight’s homework.