Expressions
A numerical expression is a mathematical statement involving only numbers and one or more operation symbols.
Numerical expressions contain only constants and arithmetic operations (+, –, x, ÷), and sometimes grouping symbols like parentheses. They represent a single value.
Example:
Question1: Evaluate the sum of 7 and 8.
Answer 1: 7+8= 15
Question 2: Evaluate the difference of twenty-two and eight divided by two
Answer 2: (22-8)÷2 =14÷2 = 7
Question 3: add fourteen and six, then multiply by 3
Answer 3: (14+6)x3 = (20)x3 = 60
Algebra is a branch of mathematics that substitutes letters for numbers.
An algebraic expression is is a mathematical phrase that contains one or more numbers, one or more letters (variables), and one or more arithmetic operations. The letters stand for numbers that are unknown.
Example:
- Expression: 2 x + 3
- Phrase: Three more than twice a number
- 3 is a constant, x is a variable and 2 is a coefficient of x
To evaluate algebraic expressions you must substitute the given value for the variable.
Example:
If x = 6, what is 2x+3 ?
Answer: 2(6) + 3 = 12 + 3 = 15
Equivalent Expressions
Two expressions are equivalent if the value of both the expressions remains the same for any value of x.
Example: 3(x + 4) and 3x + 12 are equivalent expressions
if x =1, 3(1+4) = 3(5) = 15 and 3(1) + 12 = 3 + 12 = 15 (OK)
if x =2, 3(2+4) = 3(6) = 18 and 3(2) + 12 = 6 + 12 = 18 (OK)
etcetera.
Simplifying Expressions
To simplify an expression we need to rewrite the expression with the fewest terms possible.
Example:
Simplify -(3x + 2) + 4(x + 3)
-3x -2 + 4(x + 3) (Distribute)
-3x -2 + 4x + 12 (Distribute)
-3x + 4x – 2 + 12
-3x + 4x + 10 (Add the numbers)
1 x + 10 (combine like terms)
Solution: x + 10 (We don’t need the 1 as coefficient)
Algebraic Equations
Example of an algebra problem:
When 3 is added to two times a number, the result is 13. Find the number.
Equation: 2x +3 = 13
The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation.
To isolate the variable, we must reverse the operations acting on the variable.
2x +3 -3 = 13 -3 (Subtract 3 from both sides)
2x = 10 (Simplify)
2x ÷ 2 = 10 ÷ 2 (Divide both sides by the same factor)
x = 5 (Simplify)
Solution x= 5
Plug the answer back into the problem to see if it works.
2(5) + 3 = 10 + 3 = 13 (OK)
Evaluating Numerical Expressions
Numerical Expressions 1
Numerical Expressions 2
Numerical Expressions 3
Numerical Expressions 4
EX01 Expressions
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EX03 Expressions_2
EX04 Expressions_3
EX05 Expressions_4
EX06 Expressions_5
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