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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) = 75  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 + 3x^{2} 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. 
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 
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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