Notation, evaluation and algebraic models
Interpret grouped algebraic notation and define a letter before substituting a value.
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A letter represents a number
The notation ab means a × b; a²b means a × a × b. If a = −2 and b = 3, then a²b = (−2)² × 3 = 12. Brackets preserve the negative base. The fraction (3 + y)/5 divides the entire sum by 5; it differs from 3 + y/5.
Translate a stated relationship
A notebook costs n dollars. Three notebooks and a fixed two-dollar charge cost 3n + 2 dollars. If n = 4, substitute to get 14 dollars. The expression alone does not claim a particular n; an equation adds a condition.
A rectangle has width w and length w + 3. Its perimeter is 2w + 2(w + 3). At w = 5, the width is 5, length 8 and perimeter 26 length units. Writing w + (w + 3) would count only two of its four sides.
Check your understanding 1 The bracket changes what is divided
Evaluate (3 + y)/5 and 3 + y/5 at y = 7.
Show answer
The first is (3 + 7)/5 = 2. The second is 3 + 7/5 = 4.4. The same digits and operation symbols have different grouping.
Label the quantity
A formula value needs its meaning and unit. A numerical expression for total cost is not a count of notebooks, and a perimeter is not an area. Define the letter and interpret the output before trusting a substituted answer.
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