Mathia Vocabulary Module 1

The _______________ states that for any numbers a, b, and c, a(b + c) = ab + ac.

• Expressions

• Common Factor

• Composite Number

• Distributive Property

Answer explanation

The Distributive Property states that a(b + c) = ab + ac, illustrating how multiplication distributes over addition. This is a fundamental property in algebra, making 'Distributive Property' the correct choice.

An ______ is a mathematical sentence that uses an equals sign to show that two expressions are the same as one another. It can contain numbers, variables, or both in the same mathematical sentence.

• Equation

• Expression

• Exponent

• Equivalent Fraction

Answer explanation

An equation is a mathematical sentence that uses an equals sign to indicate that two expressions are equal. It can include numbers and variables, making 'equation' the correct choice over the other options.

A number is _____ if it has exactly two distinct factors: 1 and the number itself.

• Composite

• Prime

• Fraction

• Multiple

Answer explanation

A number is prime if it has exactly two distinct factors: 1 and itself. Composite numbers have more than two factors, while fractions and multiples do not fit this definition. Therefore, the correct answer is 'Prime'.

A number is _______ if it has more than 2 factors.

• Composite

• Prime

• Even

• Odd

Answer explanation

A number is composite if it has more than two factors, meaning it can be divided by numbers other than 1 and itself. In contrast, a prime number has exactly two factors. Therefore, the correct answer is composite.

The _______ is the number or variable that is repeatedly multiplied.

• Exponent

• Variable

• Base of Power

• Multiple

Answer explanation

The base of power is the number or variable that is multiplied by itself. In expressions like a^n, 'a' is the base, while 'n' is the exponent. Therefore, the correct answer is 'Base of Power'.

The _______ of two whole numbers is the largest whole number that is a factor of both numbers.

• Greatest Common Factor

• Least Common Multiple

• Base of Power

• Distributive Property

Answer explanation

The Greatest Common Factor (GCF) of two whole numbers is the largest whole number that divides both numbers without leaving a remainder. It is the correct term for the definition provided in the question.

An ______ is any symbolic mathematical form that may include constants, variables, and operators.

• Equation

• Expression

• Exponent

• Exterior Angle

Answer explanation

An expression is a symbolic mathematical form that can include constants, variables, and operators. Unlike an equation, which states a relationship between two expressions, an expression itself does not include an equality sign.

A _______ is a whole number that is a factor of two or more integers or expressions.

• Common Factor

• Common Multiple

• Common Denominator

• Common Tangent

Answer explanation

A common factor is a whole number that divides two or more integers without leaving a remainder. It is the correct choice as it directly relates to factors of integers, unlike the other options.

A ______ is a multiple that is shared by two or more integers or expressions.

• Common Denominator

• Common Factor

• Multiplication

• Common Multiple

Answer explanation

A common multiple is a number that is a multiple of two or more integers. It is the correct term for a shared multiple, distinguishing it from a common factor, which refers to shared divisors.

The _______ of two whole numbers is the smallest whole number that is a multiple of both numbers.

• Least Common Multiple

• Greatest Common Factor

• Least Common Multiple

• Distributive Property

Answer explanation

The Least Common Multiple (LCM) of two whole numbers is the smallest whole number that is a multiple of both numbers. This makes 'Least Common Multiple' the correct answer, as it directly defines the concept in the question.