Properties of Multiplication Quiz

Adding or subtracting terms with the same variable and exponent.

Multiplying a number outside parentheses by each term inside the parentheses.

Combining like terms and applying the distributive property to simplify expressions.

Operations that undo each other.

Finding the quotient of two rational numbers.

The number being divided.

The number that divides another number.

The result of a division.

A constant, a variable, or a product of a number and a variable.

Terms having the same variables raised to the same powers but may differ in their numerical coefficients.

Terms that do not have the same variables or exponents of variables.

The numerical factor that multiplies a variable in a term.

A statement of equality between two expressions.

Equations that have the same solution(s).

A combination of variables, constants, and arithmetic operations.

Operations that change the form of an equation or inequality, but maintain the solution(s).

The order of factors doesn't change the product. For any rational numbers 'a' and 'b', a × b = b × a.

Grouping of factors doesn't change the product. For any rational numbers 'a', 'b', and 'c', a × (b × c) = (a × b) × c.

Multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. For any rational numbers 'a', 'b', and 'c', a × (b + c) = (a × b) + (a × c).

Any number multiplied by zero equals zero. For any rational number 'a', a × 0 = 0.

Any number multiplied by one equals itself. For any rational number 'a', a × 1 = a.

To multiply fractions, multiply the numerators and the denominators.

To multiply decimals, multiply as if they were whole numbers and then count the total decimal places in the factors to place the decimal point in the product.

If the signs of the dividend and divisor are the same, the quotient is positive (+). If the signs are different, the quotient is negative (-).

To find the absolute value of the quotient, divide the absolute value of the dividend by the absolute value of the divisor.

The reciprocal of a rational number is found by inverting the numerator and denominator.

Division by zero is undefined in the set of rational numbers.

Multiplying the dividend by the reciprocal of the divisor.

Both the dividend (28) and divisor (4) are positive. The quotient is 7 because 28 ÷ 4 = 7.

The dividend (-10) is negative and the divisor (2) is positive. The quotient is -5 because 10 ÷ 2 = 5, and the signs are different.

The numerical coefficient of -x² is -1. Coefficients are the numbers that multiply variables. In this case, the coefficient is -1 because it's essentially -1 * x².

The like terms are 3x² and -5x². They both have the same variable (x) and the same exponent (2).

All of these terms are unlike because they either have different variables or different exponents.

The order in which you add three or more numbers does not affect the sum. (a + b) + c = a + (b + c)

Multiplying any number by -1 results in its opposite. -1 × a = -a

An even number of negative factors results in a positive product. An odd number of negative factors results in a negative product.

When simplifying expressions involving parentheses, use the Distributive Property first to remove the parentheses.

After distributing, combine terms with the same variable and exponent. Use the Associative and Distributive Properties.