Lesson 5.3 The rational numbers

Rational numbers – set of all numbers which can be expressed in the form a/b, where a and b are integers and b is not zero. A rational number is reduced to its lowest terms or simplified when the numerator or denominator have no common divisors other than 1.

Reduce to lowest terms

Mixed number – the sum of an integer and a rational number. Improper fraction – a rational number whose numerator is greater than its denominator.

Convert to an improper fraction. Write as a mixed number.

Rational Numbers and Decimals – a decimal that terminates or repeats is a rational number Terminating Decimal Repeating Decimal

Express as a decimal 3/85/11 Expressing terminating decimals as fractions. – Use denominators of 10, 100, 1000, 10000, …

Express a repeating decimal as a quotient of integers 1.Let n = the repeating decimal 2.Multiply both sides of the equation by 10 if one digit repeats, by 100 if two digits repeat and so on 3.Subtract the equation in step 1 from the equation in step 2 4.Divide both sides of the equation in step 3 by the number in front of n and solve for n.

Multiplying Rational Numbers Dividing Rational numbers – Multiply by the reciprocal

Adding and subtracting Rational numbers with common denominators. Adding Rational Numbers with unlike denominators – Find the least common denominator