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Algebra 1

Unit 1

Expressions and Real Numbers

5 topics · 21 practice questions · Free responseNot yet reviewed

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Notes

The real numbers

Real numbers include rational numbers (fractions, integers, terminating or repeating decimals) and irrational numbers (like $\pi$ and $\displaystyle \sqrt{2}$). Properties such as commutative, associative, identity, inverse and distributive let you rewrite expressions without changing their value.

Simplifying expressions

  • Follow the order of operations: grouping, exponents, multiplication and division left to right, then addition and subtraction left to right.
  • Evaluate by substituting values for variables. Use parentheses when you substitute a negative: $(-2)^2 = 4$.
  • Combine like terms (same variable, same power) and use the distributive property $a(b + c) = ab + ac$ to clear parentheses.

Signs and fractions

Subtracting is adding the opposite. A product or quotient of two negatives is positive. To divide fractions, multiply by the reciprocal.

Topics in this unit

Each topic has its own short notes and practice.

Practice

Simplify $3 + 6^2 \div 4 - 1$.
Which property is shown by $x \cdot 1 = x$?
Evaluate $\displaystyle \frac{m - n}{2}$ for $m = -3$ and $n = 7$.
Simplify $2(3x - 4) - (x + 5)$.
A phone plan costs $25 a month plus $0.10 per text. Which expression gives the cost for $t$ texts?
$\displaystyle \frac{2}{3} \div \frac{4}{9} =$

Free response

Write your answer first, then open the scoring guide.

Free-response question

A school club sells T-shirts for $12 each and hoodies for $28 each. It spent $150 on supplies.

(a) Write an expression for the club's profit if it sells $t$ T-shirts and $h$ hoodies.

Show the answer and scoring guide

Profit is money in minus money out: $12t + 28h - 150$.

Check off the points you earned:

(b) Evaluate your expression for 20 T-shirts and 6 hoodies. Show your work.

Show the answer and scoring guide

$12(20) + 28(6) - 150 = 240 + 168 - 150 = 258$. The profit is $258.

Check off the points you earned:

(c) Is the profit for 0 shirts and 0 hoodies a rational number? Explain.

Show the answer and scoring guide

Yes. The profit is $-150$, an integer, and every integer is rational because it can be written as $\displaystyle \frac{-150}{1}$.

Check off the points you earned: