ALGEBRA
Algebra involves the use of letters and symbols as well as numbers.
Operation with signed numbers
For operation with signed numbers (+ or -)
A. Addition:
1. For number with the same sign, add and keep the same sign in the
answer.
2. For numbers with different signs , subtract and give the answer the
sign of the higher number.
Ex. 4+5=9
-24+13=-11
B. Subtraction:
Combine the two signs of the subtrahend (taking the subtraction sign as a
negative sign )
[- and -= +]
[- and += -]
Then use the rules for addition
Ex. -4 – (-2) = -4 +2=-2 [- (-2) becomes a +2 because of two negative
signs]
-4 – (+2) = -4 -2 =-6
C. Multiplication:
1. The product of an odd number of negative numbers is negative
2. The product of an even number of negative numbers is positive
Ex.
(-3)*(-2)*(-5) = -30 has 3 negative signs = negative
(-3)*(-2)*(-5)*(-4) = 90 has 4 negative signs = positive
D. Division
If the two numbers have the same sign, the quotient is positive; if
otherwise, the quotient is negative.
Ex.
Solving Algebra Equations
X, Y, Z-the letters in an algebraic expression are called variables or unknowns
There are 4 axioms (truths) of algebra by which you solve equation
A. Addition Axiom: If you add the same number or ex pression to each side of
an equation, the equation remains equal.
Ex.
X – 15 =30
X – 15 +15 = 30+15
X+ 0 = 45
X = 45
X – 14 =21
X -14 +14 = 21+ 14
X = 35
Addition’s Practice Problems
1) U – 4 = 8
2) M – 12=14
3) Y -9 = -21
B. Subtraction Axioms: If you subtract the same number or expression from
each side of an equation the equation remains equal.
Ex.
3 + x = 12
3-3+x = 12-3
x = 9
4+ y = -16
4-4+y = -16 -4
y = -20
Subtraction - Practice Problems
1) 5 + G = 20
2) W + 21 = 45
3) S + 3 = 56
C. Multiplication Axiom : If you multiply each side of an equation by the same
umber or expression, the equation remains equal.
Ex.
Multiplication - Practice Problems
D. Division Axiom : If each side of an equation is divided by the same number
or expression, the equation remains equal.
Ex. 3X = 12
Division - Practice Problems
1) 5S = 20
2) 2W = -16
3) -4Y = -28
ORDER OF OPERATIONS
1. First remove grouping symbols (parentheses, brackets ) starting with the
innermost grouping symbols.
2. Perform the operations of multiplication and division, moving from left to
right.
3. Perform the operations of addition and subtraction, moving from left to
right.
(symbol / meant divide)
Ex.
[5 – 2(5*2)] / [(20/2)] +5
[5- 2(10)] / (10) +5
5 - 2 + 5
3+5
8
Rule:
a(b+c) = a*b +a*c
2x(y+3) = 2x(y) + 2x(3) = 2xy + 6x
x(x-1) = x(x) + x(-1) = x2-x
Answer Key
Fundamental’s Answer Key
1. B 2. C. 3. D 4. B 5. B 6. C 7. D 8. D.
Fraction ’s Answer Key
1. A 2. B 3. D 4. A 5. B 6. D
Decimal’s Answer Key
1. B 2.B 3. A 4. D 5. C 6. C
Percentage, Ratio, and Proportion’s Answer Key
1. C 2. C 3. B 4. A 5. B 6. D
Algebra Addition’s Answer Key
1. U = 12
2. M = 26
3. Y = -12
Algebra Subtraction’s Answer Key
1. G = 15
2. W = 16
3. S = 53
Algebra Multiplication’s Answer Key
1. X = 20
2. X = -21
3. X = 100
Algebra Division’s Answer Key
1. S = 4
2. W = -8
3. Y = 7
