Download Factoring Integers Study Guide Key

Mayansky/Finizio
Period 5/6
Algeo I
Quiz Date: 2/11/05
Sections 5.1, 7.1, and 7.2
Study Guide
(KEY)
Sample Problem #1: Factoring Integers
Give all the positive factors of 56
Step #1: Think of all the positivefactors of
56 and write them out.
56  1  56
28  2  56
Factors of 56
14  4  56
8  7  56
Step #2: List all the positive factors of 56 in
order from least to greatest.
1, 2, 4, 7, 8, 14, 28, and 56
Sample Problem #2: Prime Factorization
Find the Prime Factorization of 100
Step #1: Set up a Factor Tree
100
Think of factor of 100 (10 x 10). Since theses #’s
are not prime you must keep going.
10 10
Think of factor of 10 (5 x 2). Since theses #’s are
prime you STOP.
5 2 5 2
Step #2: Write your prime numbers in Exponential Form
2 2  52
Answer
Sample Problem #3 Ratios
Write the Ratio in Simplest Form
32: 48
32
48
Step #1: Rewrite the ration in Fractional Form.
2
3
Step #2: Reduce the fraction to lowest terms. (in this case you can divide
both numbers by 16.)
Sample Problem #4 Ratios
Write the Ratio in Simplest Form
25x : 20x
25 x
20 x
Step #1: Rewrite the ration in Fractional Form.
25 x  5 x 5

20 x  5 x 4
Step #2: Reduce the fraction to lowest terms. (in this case you can divide
both numbers by 5x.) Therefore divide both the bottom and the top number
by 5x
5
4
Step #3: Final Answer
Sample Problem #5 Ratios
Write the Ration in Simplest Form
9x2 y
6 xy 2
9x2 y
6 xy 2
3x 2 y
2 xy 2
3 x  x  y
2 x y  y
3 x  x  y
2 x y  y
3x
2y
Step #1: Reduce the Coefficient Numbers before worrying about exponents.
In this case you can divide both numbers by 3.
2
Step #2: Write your exponents in expanded form. (ex. Write x as
x x )
Step #3: Cancel out the exponents.
Step #4: In this case you can cancel out one set of x’s and one set of y’s. Leaving
you with one x on the top of your fraction and one y on the bottom of your fraction.
Final Answer
Sample Problem #6: Ratios
Simplify Ratio
20 min : 2hours
Step #1: Convert Hours to Minutes: 2 hours = 120 minutes
20min :120min
1: 6
Step #2: Reduce: Since 20 can be divided into both 20 and 120 you are left with a ratio of
1:6. Remember “min.” cancel out because they are on both sides of the ratio
Sample Problem #6 Proportions
Solve
3 5

x 4
Step #1: Cross multiply. Multiply x  5 and 3  4 . Remember to keep an equal
sign in between both of these answers.
5x  12
Step #2: Solve for “X”. In this case you have to divide both sides of your equation
by 5.
5
x
5
12
5
Final Answer
Sample Problem #7: Proportions
Solve
x4 2

3
15
Step #1: Cross multiply. Multiply 3  2 and 15( x  4) . Remember to keep an
equal sign in between both of these answers.
6  15( x  4)
Step #2: Distribute the 15 to remove parenthesis.
6  15x  60
Step #3: Add 60 to both sides of the equation.
60
60
66  15x
15
Step #4: Divide both sides by 15 in order to isolate “x”.
15
x  4.4
Final Answer
Sample Problem #8: Word Problems
Solve
Maria drove 111 mi in 3 hours. About how far could she drive in 5 hours?
Step #1: Set up a chart that looks like the one below. In case #1 use the information given to you in the
problem. Use “X” to take the place of your unknown
Miles
Hours
Case #1
111
3
Case #2 (unknown)
X
5
Step #2: Set up a proportion using the information from the chart.
111 x

3
5
Step #3: Solve the Proportion.
3x  555
x  185
Step #4: Add your Label
185miles
Practice Problems
List the Factors
List the Factors
List the Factors
List the Factors
1. 22
2. 24
3. 40
4. 64
1, 2,11, 22
1, 2,3.4, 6,8,12, 24
1, 2, 4,5,8,10, 20, 40
1,2,4,8,16,32,64
Prime Factorization
Prime Factorization
Prime Factorization
Prime Factorization
5. 16
6. 34
7. 120
8. 128
2 17
23  3  5
27
Simplify Ratio
Simplify Ratio
Simplify Ratio
Simplify Ratio
9. 5:15
10. 18: 24
11. 20t : 35t
3: 4
4:7
24
1: 3
Simplify Ratio
Simplify Ratio
27 m5
45m 2
3M 3
5
Simplify Ratio
Simplify Ratio
6y
15.
9y
60 y 3
16.
12 y 2
5
3
12.
64a b
13.
16ab 4
72rs
14.
12r 2 s 2
4a 2
b3
6s 3
r
Simplify Ratio
Simplify Ratio
Simplify Ratio
Simplify Ratio
17. 20min :3hours
18. 18cm :1.8m
19. 9days : 3weeks
20. 1lb : 7oz
1: 9
1:10
3: 7
16 : 7
Solve
Solve
Solve
y 4
21. 
3 7
8 4
22. 
5 3x
15a 45

23.
36 12
x5 3

24.
4
2
5
6
a 9
x  11
Solve
Solve
Solve
y
12
7
x
Solve
25. 5 
4  3y
5
y  7
26.
3  2 y 1 y

8
5
y
5y
2
3
7
18
27.
3  2x
 3
3  2x
x0
Solve
28.
15a 45

36 12
a 9
Word Problems
1.
Six oranges cost $.99. How much do ten oranges cost?
$1.65
2.
A car that sold for $11,800 has a sales tax of $767. How much does a car cost if it’s sales tax is
$637?
$9,800
3.
a recipe for 2 dozen whole-wheat muffins requires 600 g of flour. How many muffins can be
made with 900 g of flour?
3dozen
4.
A truck uses 8 L of gasoline to go 120 km. How much gasoline will it use to go 300 km?
20L
5.
At a fixed interest rate, an investment of $4000 earns $210. How much do you need to invest at
the same rate to earn $336?
$6, 400