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 add two fractions with the same denominator?

Back

To add two fractions with the same denominator, keep the denominator the same and add the numerators. For example, \( \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} \).

Front

How do you subtract two fractions with different denominators?

Back

To subtract two fractions with different denominators, first find a common denominator, convert the fractions, and then subtract the numerators. For example, \( \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \).

Front

What is the process to multiply two fractions?

Back

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

Front

What is the process to divide two fractions?

Back

To divide two fractions, multiply the first fraction 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 a mixed number?

Back

A mixed number is a whole number combined with a proper fraction. For example, \( 2 \frac{1}{2} \) is a mixed number.

Front

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

Back

To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient is the whole number, and the remainder over the original denominator is the fraction.

Front

What is the reciprocal of a fraction?

Back

The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \), provided that \( a \neq 0 \) and \( b \neq 0 \).

Front

How do you simplify a fraction?

Back

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). For example, \( \frac{8}{12} = \frac{2}{3} \) after dividing by 4.

Front

What is the least common denominator (LCD)?

Back

The least common denominator (LCD) is the smallest multiple that is common to the denominators of two or more fractions.