Multiplying and Dividing Rationals Flashcard Review

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 the numerators together and multiply the denominators together. For example, (a/b) * (c/d) = (a*c)/(b*d).

Front

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

Back

The result is a negative rational number.

Front

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

Back

To divide two rational numbers, multiply the first rational number by the reciprocal of the second. For example, (a/b) ÷ (c/d) = (a/b) * (d/c) = (a*d)/(b*c).

Front

What happens when you multiply a rational number by zero?

Back

The result is always zero.

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, factor both the numerator and denominator and cancel any common factors.

Front

What is the difference between multiplying and dividing rational numbers?

Back

Multiplying combines the values, while dividing determines how many times one number is contained within another.

Front

What is an example of multiplying two negative rational numbers?

Back

(-2/3) * (-4/5) = 8/15, which is positive.

Front

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

Back

Multiply the whole number by the denominator, add the numerator, and place that over the original denominator. For example, 2 1/3 = (2*3 + 1)/3 = 7/3.