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Reduce All Fractions to Lowest Terms

1. 5/2

Keep the common denominator, add the
numerators
, reduce.

2. 23/20

a. Use common denominator of 20.

b. use “ the formula

3. 7/12

Use common denominator of 12

4. 2/35

a. Use C.D. of 35

b. Use the formula


 

5. 4/3

a. Multiply numerators , multiply denominators;
reduce

b. reduce first


 

6. 7/6

Invert and multiply

You could also reduce before you multiply
 

7. 1

Invert and multiply


 

8. -1/20

Using the formula:

B. Numbers

1. Define “rational number” A fraction ; a number
that can be written as the ratio of two integers .
It will be a terminating or repeating decimal.

2. Circle the integers : 2, -2, 0
Integers are not fractions, but they can be positive
or negative.

3. -|-8| = -(8) 3. -8

Circle T or F

4. |12| = |-12| 4. T
5. -(-8) = 8 5. T
6. -5 < -4 6. T
7. |-5| ≥ |-4| 7. T
8. 4 ≤ 4 8. T

C. Perform the indicated operations

1. 2 - (-6) = 2 + 6 1. 8
2. -4 + 7. Start at -4, go 7 steps right. 2. 3
3. -7 - (-10) = -7 + 10 3. 3
4. -6 - 3. Start at -6; go 3 steps left. 4. -9
5. 7 + (-5) = 7-5 5. 2
6. (4)(3) 6. 12
7. (4)(-3) 7. -12
8. (-4)(-3) 8. 12
9. -12 ÷ (-4) = -12·(-1/4)> multiplying two
negatives gives a positive
9. 3
10. -2/3 ÷ (1/3) = -2/3·(3/1) 10. -2

D. Use the order of Operations

1. 3 + 2·4 = 3 + 8 1. 11
2. 12 - 3(4 - 1)
= 12 - 3(3)
= 12 - 9
2. 3
3. 1 + 3[17 - 3(2 + 3)]
= 1+ 3[17 - 3(5)]
= 1+ 3[17 - 15]
= 1+ 3[2]
= 1+ 6
3. 7
4. 4 (7 - 5)
= 4(2)
4. 8

E. Simplify each expression . Write “CBS” if it cannot be simplified

1. 4n + 8x + 5x + 3n
Combine like terms
1. 7n + 13x
2. 3ab + 4a. Unlike terms 2. CBS
3. 4a + 3b - 5 + 2(a + 2b + 1)
remove brackets
=4a + 3b - 5 + 2a + 4b + 2
combine like terms
3. 6a + 7b - 3
4. 5x + 3x2 Unlike terms 4. CBS

F. Properties
1. Which property says that a + b = b + a
1. commutative

2. Which property says that (ab)c = a(bc)
2. associative

3. use the distributive property to rewrite: -3(- 4y + 5)
3. 12y - 15

G. Rewrite each equation by : removing fractions, decimals and brackets and combining like terms
You need not solve


3x - 20 = 4
1. 3x - 20 = 4

3(x - 2) = 12 || distribute bracket
3x - 6 = 12 || +6
2. 3x - 6 = 12

Multiply x 4
3x + 2 = 8
 
3. 3x + 2 = 8
4. .4x + 4.2 = 5
Move all decimals one place
4x + 42 = 50
4. 4x + 42 = 50
5. .3 + .04x = .42
Move all decimals two places
30 + 4x = 42
5. 30 + 4x = 42

H. Linear Equations . Solve each of the following for x

1. x - 8 = 12
add 8 to both sides
1. x = 20
2. x - 2 = -7
add 2 to both sides
2. x = -5
3. 5x -5 = 20
add 5 to both sides
5x = 25
divide by 5
3. x = 5
4. -3x = -12

divide by -3.
negative ÷ negative = positive

4. x = 4
5. -6x + 5 = 29
subtract 5
-6x = 24
divide by -6
x = -4
5. x = -4

multiply by 4
3x - 8 = 4. add 8
3x = 12. divide by 3
x = 4
6. x= 4

Multiply by 4
3(x - 2) = 12. Distribute to remove bracket
3x - 6 = 12. Add 6
3x = 18. Divide by 3
x = 6

7. x = 6
8. 8x - 4 = 5x + 11
subtract 5x
3x - 4 = 11. add 4
3x = 15. divide by 3
x = 5
8. x = 5
9. 5x – 4 = 8x - 16
subtract 5x
-4 = 3x -16. add 16
12 = 3x. Divide by 3
4 = x
9. x = 4
10. -.7x + 5 = .3x + 2
multiply by 10 (move all decimals one place)
-7x + 50 = 3x + 20. add 7x
50 = 10x + 20.   subtract 20
30 = 10x    divide by 10
3 = x
10. x = 3

I. Inequalities. Solve and Graph

1. 4 + 3x ≥ 11  1. x 7/3
3x ≥ 7
x ≥ 7/3

2. 2 - 4x > 14   2. x < -3
-4x > 12. Divide negative 4. Reverse the inequality
x < -3

3. 0 < 4x + 12 ≤ 20   3. -3 < x  2
subtract 12 from all three parts
-12 < 4x ≤ 8. Divide by 4
-3 < x ≤2

 

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