Applied Mathematics for Business: Class 1 - Basic Arithmetic (Part 1)

Flashcards reviewing sets of numbers, number line and absolute value, order of operations, fractions, and fundamental algebraic operations.

What is a natural number?

A counting number: 1, 2, 3, …

What numbers make up the set of integers?

All positive integers, negative integers, and zero.

Define a rational number.

A number that can be expressed as a/b where a is an integer and b ≠ 0.

Define an irrational number.

A number that cannot be written as a fraction of two integers.

What is a real number?

All rational and irrational numbers.

What is an imaginary number?

The square root of a negative number (e.g., i = sqrt(-1)).

What is absolute value?

The distance from zero on the number line; |a| equals a if a ≥ 0, and −a if a < 0.

Where is the origin on the number line?

The point 0.

What does BEDMAS stand for?

Brackets/Parentheses, Exponents, Division, Multiplication, Addition, Subtraction.

If grouping symbols are present, what is the general order of operations?

Work inside innermost grouping symbols first, then apply exponents, then multiplication/division left-to-right, then addition/subtraction left-to-right.

State the Commutative Law for addition and multiplication.

Order of terms does not matter: a + b = b + a; ab = ba.

State the Associative Law for addition and multiplication.

Grouping does not affect the result: (a + b) + c = a + (b + c); (ab)c = a(bc).

State the Distributive Law.

Multiplication distributes over addition: a(b + c) = ab + ac (and a(b − c) = ab − ac).

What is the additive identity?

0, since a + 0 = a.

What is the multiplicative identity?

1, since a × 1 = a.

What is the additive inverse of a number x?

−x, since x + (−x) = 0.

What is the multiplicative inverse of a nonzero number x?

1/x, since x × (1/x) = 1.

What is a common fraction?

A fraction representing part of a whole, with a numerator over a denominator.

What is an equivalent fraction?

Fractions with the same value obtained by multiplying numerator and denominator by the same number.

What does it mean to reduce a fraction to lower terms?

Simplify by dividing numerator and denominator by their greatest common factor.

What is the Lowest Common Denominator (LCD)?

The least common multiple of the denominators; used to add/subtract fractions with different denominators.

How is the LCD determined in the notes' method?

Divide denominators by integers ≥ 2 until they are all reduced to 1; multiply the divisors to obtain the LCD.

How do you convert a common fraction to a decimal?

Divide numerator by denominator; continue to the desired decimal places or until it terminates or repeats (repeat shown with a bar).

How do you convert a mixed number to a decimal?

Convert the fractional part to decimal form and add to the whole number.

What is a complex fraction?

A fraction where the numerator or denominator contains a fraction; evaluated using the standard order of operations.

What is a monomial?

A single term: a constant times one or more variables; the constant is the coefficient.

What is a polynomial?

A sum of finitely many monomials.

What is a binomial?

A polynomial with exactly two terms.

What are like terms?

Terms with the same variable(s) raised to the same power; coefficients can be combined.

How do you add or subtract like terms?

Add or subtract their coefficients while keeping the same variables.

What is multiplication of monomials?

Multiply coefficients and multiply variables by adding exponents.

How do you multiply a polynomial by a polynomial?

Multiply each term of one polynomial by each term of the other, then collect like terms.

What is division of monomials?

Quotient of numerical coefficients and quotient of the variables (subtract exponents).

How do you divide a polynomial by a monomial?

Divide each term of the polynomial by the monomial.

What is division of two fractions?

Multiply the first fraction by the reciprocal of the second: (a/b) ÷ (c/d) = (a/b) × (d/c).

Why add or subtract fractions with different denominators using the LCD?

It provides a common denominator to combine fractions.

What is a coefficient in a term like -7C?

The numerical factor multiplying the variable; for -7C, the coefficient is -7.

How do you identify and combine like terms in an expression?

Identify terms with the same variable and exponent, then add their coefficients.

What is a monomial in multiple variables called?

A single term involving several variables (e.g., 3CD).

What is a polynomial with exactly one term called?

Monomial.

What is a polynomial with exactly two terms called?

Binomial.

How do you multiply monomials with polynomials?

Distribute the monomial across all terms of the polynomial.

What is the product of two polynomials?

A polynomial obtained by distributing every term of one polynomial by every term of the other and collecting like terms.

What is the division of a monomial by another monomial?

Divide coefficients and subtract exponents of like variables.

What is the quotient when dividing a polynomial by a monomial?

Each term of the polynomial divided by the monomial.

What is the reciprocal of a fraction a/b (with a,b ≠ 0)?

b/a.

Why is the LCD useful when adding/subtracting fractions?

It provides a common denominator to combine fractions.

What is the decimal representation of 9/8?

1.125.