Essential Math Foundations flashcards

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Nested operations and signsOrder of Operations and Signed Numbers: A leading minus outside a square stays outside.
When should I use signed-number arithmetic?Order of Operations and Signed Numbers: Add and subtract signed numbers accurately.
What method supports nested operations and signs?Order of Operations and Signed Numbers: −a² = −(a²), but (−a)² = a²
Grouping and powersOrder of Operations and Signed Numbers: Do the inside first, then the power, then multiply.
Signed-number arithmeticOrder of Operations and Signed Numbers: Subtracting a negative moves you upward.
What must I check in order of operations and signed numbers?Order of Operations and Signed Numbers: Evaluate powers before a leading negative; division by zero is undefined
What method supports grouping and powers?Order of Operations and Signed Numbers: a(b + c)² means a × ((b + c)²)
What method supports signed-number arithmetic?Order of Operations and Signed Numbers: a − (−b) = a + b
When should I use nested operations and signs?Order of Operations and Signed Numbers: Distinguish a negative base from a negative sign outside a power.
When should I use grouping and powers?Order of Operations and Signed Numbers: Evaluate expressions with parentheses and exponents.
Mixed-number products and reciprocal divisionFractions, Decimals, and Mixed Numbers: Turn the mixed number into one fraction; flip the divisor.
When should I use equivalent fractions and decimals?Fractions, Decimals, and Mixed Numbers: Convert fractions to decimals by division.
What method supports mixed-number products and reciprocal division?Fractions, Decimals, and Mixed Numbers: (a/b) ÷ (c/d) = ad/(bc), b,c,d ≠ 0
Adding fractionsFractions, Decimals, and Mixed Numbers: Match the size of the pieces before counting them.
Equivalent fractions and decimalsFractions, Decimals, and Mixed Numbers: A fraction bar means divide.
What must I check in fractions, decimals, and mixed numbers?Fractions, Decimals, and Mixed Numbers: A denominator must be nonzero; convert a mixed number to an improper fraction before multiplying
What method supports adding fractions?Fractions, Decimals, and Mixed Numbers: a/b + c/d = (ad + bc)/(bd)
What method supports equivalent fractions and decimals?Fractions, Decimals, and Mixed Numbers: a/b = (ka)/(kb), b ≠ 0, k ≠ 0
When should I use mixed-number products and reciprocal division?Fractions, Decimals, and Mixed Numbers: Use improper fractions and reciprocals in a multistep calculation.
When should I use adding fractions?Fractions, Decimals, and Mixed Numbers: Find a common denominator before adding.
Percent as a multiplierRatios, Proportions, and Percent Foundations: A percent tells you what fraction of the whole to take.
When should I use ratio parts?Ratios, Proportions, and Percent Foundations: Convert a part-to-part ratio to a part-to-whole fraction.
What method supports percent as a multiplier?Ratios, Proportions, and Percent Foundations: part = (p/100) × whole
Solving a proportionRatios, Proportions, and Percent Foundations: Scale both sides of the ratio by the same factor.
Ratio partsRatios, Proportions, and Percent Foundations: Add the parts to find the whole.
What must I check in ratios, proportions, and percent foundations?Ratios, Proportions, and Percent Foundations: Keep the ratio order and identify the whole used as the percent base
What method supports solving a proportion?Ratios, Proportions, and Percent Foundations: a/b = c/d ⇒ ad = bc
What method supports ratio parts?Ratios, Proportions, and Percent Foundations: first share = a/(a + b)
When should I use percent as a multiplier?Ratios, Proportions, and Percent Foundations: Find a percentage of a whole.
When should I use solving a proportion?Ratios, Proportions, and Percent Foundations: Find an unknown value in equal ratios.
Scientific notationExponents, Roots, and Scientific Notation: Multiply the front numbers, combine powers of ten, and normalize.
When should I use integer exponents?Exponents, Roots, and Scientific Notation: Evaluate powers and zero exponents.
What method supports scientific notation?Exponents, Roots, and Scientific Notation: (a × 10^m)(b × 10^n) = ab × 10^(m+n)
Roots and powersExponents, Roots, and Scientific Notation: The root symbol has one principal output; an equation can have two solutions.
Integer exponentsExponents, Roots, and Scientific Notation: A negative exponent moves the power into a denominator.
What must I check in exponents, roots, and scientific notation?Exponents, Roots, and Scientific Notation: Use principal nonnegative square roots; scientific notation requires 1 ≤ |a| < 10
What method supports roots and powers?Exponents, Roots, and Scientific Notation: √(u²) = |u|
What method supports integer exponents?Exponents, Roots, and Scientific Notation: a^(−k) = 1/a^k, a ≠ 0
When should I use scientific notation?Exponents, Roots, and Scientific Notation: Multiply and normalize numbers in scientific notation.
When should I use roots and powers?Exponents, Roots, and Scientific Notation: Recognize the principal square root and square-root equations.
Translate a constraintTranslating Words into Mathematical Expressions: Name the unknown, model both amounts, and make them equal.
When should I use verbal operations?Translating Words into Mathematical Expressions: Translate a phrase into an expression with correct order.
What method supports translate a constraint?Translating Words into Mathematical Expressions: initial + change × time = final
Fixed and variable chargesTranslating Words into Mathematical Expressions: Start with the fixed cost and add rate times quantity.
Verbal operationsTranslating Words into Mathematical Expressions: Read the phrase for which quantity starts the subtraction.
What must I check in translating words into mathematical expressions?Translating Words into Mathematical Expressions: Define variables and units before translating; subtraction and division depend on order
What method supports fixed and variable charges?Translating Words into Mathematical Expressions: cost = fixed fee + rate × quantity
What method supports verbal operations?Translating Words into Mathematical Expressions: b less than kx means kx − b
When should I use translate a constraint?Translating Words into Mathematical Expressions: Turn a contextual relationship into an equation and solve.
When should I use fixed and variable charges?Translating Words into Mathematical Expressions: Build an expression for a fixed charge plus a rate.