Warm-up: Operations with Rational Numbers

Front

What is a rational number?

Back

A rational number is any number that can be expressed as the quotient or fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

Front

How do you multiply two fractions?

Back

To multiply two fractions, multiply the numerators together and the denominators together. For example, \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \).

Front

What is the simplest form of a fraction?

Back

A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

Front

How do you divide fractions?

Back

To divide fractions, multiply by the reciprocal of the second fraction. For example, \( \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} \).

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \).

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, add the numerator, and place that over the original denominator. For example, \( 2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3} \).

Front

What is the result of multiplying a negative fraction by a positive fraction?

Back

The result is a negative fraction. For example, \( -\frac{2}{3} \times \frac{4}{5} = -\frac{8}{15} \).

Front

What happens when you divide a negative number by a positive number?

Back

The result is a negative number. For example, \( -6 \div 2 = -3 \).

Front

What is the result of dividing two negative fractions?

Back

The result is a positive fraction. For example, \( -\frac{3}{4} \div -\frac{1}{2} = \frac{3}{2} \).

Front

How do you simplify the fraction \( \frac{-30}{36} \)?

Back

To simplify \( \frac{-30}{36} \), divide both the numerator and denominator by their greatest common divisor, which is 6. Thus, \( \frac{-30 \div 6}{36 \div 6} = \frac{-5}{6} \).