Set of Rational Numbers Section 6.1 Set of Rational Numbers numerator denominator

Uses of Rational Numbers Example Division problem or solution to a multiplication problem 2x = 3, x = 3/2 Part of a whole Joe received ½ of Mary’s salary Ratio The ratio of girls to boys is 9/6 or 3/2 Probability When you toss a coin, the probability of landing on heads is ½

Rational Number Models

Definition Proper fraction A fraction where Improper fraction A fraction such that

Equivalent or Equal Fractions Equivalent fractions are numbers that represent the same point on a number line.

Fraction Strips

Fundamental Law of Fractions Let be any fraction and n a nonzero whole number, then

Example Find a value for x such that

Example Write each of the following fractions in simplest form if they are not already so: a. b. c. d.

Equality of Fractions Two fractions and are equal if and only if ad = bc.

Ordering Rational Numbers If a, b, and c are integers and b > 0, then if and only if a > c. If a, b, c, and d are integers and b > 0, d > 0, then if and only if ad > bc.

Denseness of Rational Numbers Given rational numbers there is another rational number between these two numbers. Find two fractions between

Addition of Rational Numbers Section 6.2 Addition of Rational Numbers Area model

Addition/Subtraction with Like Denominators If are rational numbers, then

Addition/Subtraction with Unlike Denominators If are rational numbers, then

Example Find each of the following sums: a. b.

Example (continued) c. d.

Example Find each difference. a. b.

Mixed Numbers Numbers that are made up of an integer and a fractional part of an integer. A mixed number is a rational number, and therefore, it can always be written in the form

Example Change each of the following mixed numbers to improper fractions. a. b.

Example Change to a mixed number.

Properties of Addition for Rational Numbers Properties of the additive inverse for rational numbers are analogous to those of the additive inverse for integers.

Example Add or subtract. Write answers in simplest form. a.

Example (continued) b.

Example (continued) c.

Estimation A sixth-grade class is collecting cans to take to the recycling center. Becky’s group brought the following amounts (in pounds). About how many pounds does her group have all together? The front-end estimate is 1 + 3 + 5 = 9. The adjustment is The adjusted estimate is 9 + 2 = 11.

Example Estimate each of the following. a. b.