Multiplying and dividing rational numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero.

Front

How do you multiply two rational numbers?

Back

To multiply two rational numbers, multiply their numerators together and their denominators together. For example, (2/3) * (4/5) = (2*4)/(3*5) = 8/15.

Front

What is the result of multiplying a positive rational number by a negative rational number?

Back

The result is a negative rational number. For example, (3/4) * (-2/5) = -6/20 = -3/10.

Front

What is the result of dividing a rational number by another rational number?

Back

To divide two rational numbers, multiply the first number by the reciprocal of the second number. For example, (3/4) ÷ (2/5) = (3/4) * (5/2) = 15/8.

Front

What happens when you multiply a rational number by zero?

Back

The result is always zero. For example, (5/6) * 0 = 0.

Front

What is the reciprocal of a rational number?

Back

The reciprocal of a rational number a/b is b/a, provided that a and b are not zero.

Front

How do you simplify the product of two rational numbers?

Back

To simplify the product, divide the numerator and denominator by their greatest common divisor (GCD). For example, (6/8) * (4/6) = (6*4)/(8*6) = 24/48 = 1/2 after simplification.

Front

What is the rule for multiplying two negative rational numbers?

Back

The product of two negative rational numbers is a positive rational number. For example, (-1/2) * (-3/4) = 3/8.

Front

How do you convert a mixed number to an improper fraction?

Back

To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. For example, 2 1/3 = (2*3 + 1)/3 = 7/3.

Front

What is the result of dividing a negative rational number by a positive rational number?

Back

The result is a negative rational number. For example, (-3/4) ÷ (2/5) = (-3/4) * (5/2) = -15/8.