Form and evaluate algebraic expressions

Expression

\(\displaystyle 2p^2-5\)

Value

\(\displaystyle p=-4\)

Predict the value when the pronumeral is negative. Only the pronumeral is squared

Rule A adds eight to x, then divides the whole sum by four. Rule B divides eight by four, then adds x. Try zero, four and negative four. Follow the solid A line and dashed B line

What does the comparison show?

Translate words into operations

An expression describes a calculation without an equals sign. Forming chooses the correct operations; evaluating carries them out for assigned values

1. 1Name the operation A sum adds, a difference subtracts, a product multiplies and a quotient divides \(\displaystyle 3x=3\times x\)
2. 2Keep the order Four less than a quantity means start with that quantity and subtract four \(\displaystyle x-4\)
3. 3Group before dividing The fraction bar divides the entire numerator by the denominator \(\displaystyle \frac{x+8}{4}\)

Form an expression: add eight to x, then divide the whole sum by four

Expression

\(\displaystyle \frac{x+8}{4}\)

Value

\(\displaystyle x=-5\)

Evaluate the grouped expression. Give an exact fraction or decimal

Calculate the whole numerator before dividing

Form an expression: square t, multiply that square by three, then subtract twice t

Expression

\(\displaystyle 3t^2-2t\)

Value

\(\displaystyle t=-3\)

Now evaluate the expression with a new negative value

Substitute the negative value at both occurrences, keeping it in brackets

Keep signs and the scope of a power

Brackets tell you what is squared. A leading minus outside a square remains outside. Division by zero is undefined

1. 1Square the whole bracket Multiplying two negative factors gives a positive result \(\displaystyle (-3)^2=9\)
2. 2A minus outside is different Here the square is evaluated before the leading minus \(\displaystyle -3^2=-9\)
3. 3Replace every pronumeral Substitute both values before combining the numerator \(\displaystyle \frac{2a-b}{3}\)
4. 4Check the denominator Do not evaluate a quotient when its denominator is zero \(\displaystyle \frac{6}{x-2}\quad(x\ne2)\)

Expression

\(\displaystyle \frac{2a-b}{3}\)

Values

\(\displaystyle a=-4,\quad b=7\)

Evaluate using both assigned values

Keep the entire numerator together and substitute each value once

Pronumeral

\(\displaystyle n\)

Which expression means five less than twice n?

Expression

\(\displaystyle 2x^2+1\)

Value

\(\displaystyle x=-3\)

Find the first incorrect calculation in this attempt

Expression

\(\displaystyle \frac{6}{x-2}\)

Value

\(\displaystyle x=2\)

Can this expression be evaluated at the assigned value?