Mastering Rational Number Operations

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

To convert a fraction to a decimal, divide the numerator by the denominator.

To multiply a fraction by a whole number, multiply the numerator of the fraction by the whole number and keep the denominator the same.

To add two fractions with different denominators, find a common denominator, convert the fractions, and then add the numerators.

The least common multiple (LCM) is the smallest multiple that two or more numbers share. It is used to find a common denominator when adding fractions.

To subtract one fraction from another, ensure they have a common denominator, then subtract the numerators and keep the denominator the same.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator, add the numerator, and place that result over the original denominator.

To simplify a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).

The greatest common divisor (GCD) is the largest positive integer that divides two or more integers without leaving a remainder.

To solve a word problem involving fractions, identify the fractions involved, determine the operation needed (addition, subtraction, multiplication, or division), and apply the appropriate mathematical rules.