Mastering Rational Number Operations

A rational number is any number that can be expressed as the quotient or fraction $$\frac{a}{b}$$ , where $$a$$ is an integer and $$b$$ is a non-zero integer.

To divide two rational numbers, multiply the first number by the reciprocal of the second number. For example, to divide $$\frac{7}{9}$$ by $$\frac{2}{3}$$ , calculate $$\frac{7}{9} \times \frac{3}{2} = \frac{7 \times 3}{9 \times 2} = \frac{21}{18} = \frac{7}{6}$$ .

$$\frac{5}{8} = 0.625$$ .

To add $$\frac{3}{4}$$ and $$\frac{2}{3}$$ , find a common denominator (12): $$\frac{3}{4} = \frac{9}{12}$$ and $$\frac{2}{3} = \frac{8}{12}$$ . Thus, $$\frac{9}{12} + \frac{8}{12} = \frac{17}{12}$$ .

To multiply two rational numbers, multiply their numerators and denominators. For example, $$\frac{2}{5} \times \frac{3}{4} = \frac{2 \times 3}{5 \times 4} = \frac{6}{20} = \frac{3}{10}$$ .

To subtract $$\frac{5}{6}$$ from $$\frac{7}{8}$$ , find a common denominator (24): $$\frac{7}{8} = \frac{21}{24}$$ and $$\frac{5}{6} = \frac{20}{24}$$ . Thus, $$\frac{21}{24} - \frac{20}{24} = \frac{1}{24}$$ .

The reciprocal of a rational number $$\frac{a}{b}$$ is $$\frac{b}{a}$$ , provided that $$a \neq 0$$ .

To convert a fraction to a decimal, divide the numerator by the denominator. For example, $$\frac{5}{8} = 5 \div 8 = 0.625$$ .

The least common denominator (LCD) is the smallest multiple that two or more denominators share. It is used to add or subtract fractions.

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD). For example, $$\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}$$ .