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Foundations of Algebra flashcards
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- What is a variable?Variables and Expressions
- A symbol for a number in a stated domain.
- What is a coefficient?Variables and Expressions
- A numerical factor multiplying a variable.
- What is a constant term?Variables and Expressions
- A term without a variable.
- What separates terms?Variables and Expressions
- Addition or subtraction signs.
- What does “less than” often reverse?Variables and Expressions
- The order of subtraction.
- Why use parentheses in a translation?Variables and Expressions
- To keep a named group together.
- What is twice n?Variables and Expressions
- 2n.
- Why define a variable with units?Variables and Expressions
- To give the expression a clear meaning.
- What is evaluation?Variables and Expressions
- Substituting values and calculating the expression.
- Why parenthesize a negative substitution?Variables and Expressions
- To preserve the sign and intended exponent.
- What value makes 1/x undefined?Variables and Expressions
- x=0.
- What is (−2)²?Variables and Expressions
- 4.
- What comes first in order of operations?Order of Operations and Properties
- Grouping symbols.
- Do multiplication and division share a priority?Order of Operations and Properties
- Yes, work left to right.
- What is −3²?Order of Operations and Properties
- −9.
- What is (−3)²?Order of Operations and Properties
- 9.
- What is the commutative property?Order of Operations and Properties
- Changing order in addition or multiplication.
- What is the associative property?Order of Operations and Properties
- Changing grouping in addition or multiplication.
- What is the distributive property?Order of Operations and Properties
- a(b+c)=ab+ac.
- Can subtraction operands be swapped without changing value?Order of Operations and Properties
- Generally no.
- What are like terms?Order of Operations and Properties
- Terms with matching variable factors and exponents.
- What are equivalent expressions?Order of Operations and Properties
- Expressions equal on every input in their common domain.
- Can x and x² terms combine as like terms?Order of Operations and Properties
- No.
- What is a counterexample?Order of Operations and Properties
- An input showing a claimed equality fails.
- What is an additive inverse?Integers, Fractions, and Absolute Value
- The number that sums with a given number to zero.
- What is −(−7)?Integers, Fractions, and Absolute Value
- 7.
- What sign has a product of two negatives?Integers, Fractions, and Absolute Value
- Positive.
- Is division by zero defined?Integers, Fractions, and Absolute Value
- No.
- What is a rational number?Integers, Fractions, and Absolute Value
- A ratio of integers with a nonzero denominator.
- Why use a common denominator?Integers, Fractions, and Absolute Value
- To add or subtract equal-sized fractional parts.
- What is a reciprocal?Integers, Fractions, and Absolute Value
- A nonzero number multiplied by its reciprocal gives one.
- Is a repeating decimal rational?Integers, Fractions, and Absolute Value
- Yes.
- What is absolute value?Integers, Fractions, and Absolute Value
- Distance from zero on the real number line.
- Can absolute value be negative?Integers, Fractions, and Absolute Value
- No.
- What is the distance between a and b?Integers, Fractions, and Absolute Value
- abs(a−b).
- What are the solutions to abs(x)=4?Integers, Fractions, and Absolute Value
- x=4 and x=−4.
- What is an equation?Equations as Balance
- A statement equating two expressions.
- What is a solution?Equations as Balance
- A permitted value making an equation true.
- How do you check a solution?Equations as Balance
- Substitute it into the original equation.
- Does an expression have an equals sign?Equations as Balance
- No.
- What is the addition property of equality?Equations as Balance
- Adding the same amount to both sides preserves equality.
- What is an inverse operation?Equations as Balance
- An operation undoing another.
- Why can you not divide an equation by zero?Equations as Balance
- Division by zero is undefined.
- How do you solve x+7=12?Equations as Balance
- Subtract seven from both sides.
- What should a context variable include?Equations as Balance
- Meaning and unit.
- What is a fixed fee?Equations as Balance
- An amount independent of usage.
- What is a rate?Equations as Balance
- Amount per one unit of input.
- Why check a context solution?Equations as Balance
- To ensure the number satisfies the equation and makes sense.