Expressions

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

EX02      Expressions_1

EX03      Expressions_2

EX04      Expressions_3

EX05      Expressions_4

EX06      Expressions_5

EX07      Expressions_6