Rational NumbersMath 9

What is a Rational Number?Rational Numbers

ReviewNatural Numbers or Counting Numbers → 1, 2, 3, 4, 5, 6, 7….

Integers →

Rational NumbersA rational number is any number that can be written in the form , where m and n are integers and n ≠ 0.

Interesting Facts● We use the same symbol to represent a negative number as we do for

subtraction. Ex. (-4) is the same as -4.● The same number with different symbols are said to be opposite. Ex. (-4)

and (+4).● When you add opposites, they always equal zero.● Any number that can be written as a fraction with an integer numerator

and a non-zero denominator is a rational number.● Irrational numbers are those that cannot be written as fractions, such as

√2 or 𝜋. That’s because they don’t have a pattern.

Example OneIs ⅓ rational or irrational? Why?

Note

Example TwoWrite each number as a decimal.

3/8 = 5/9 = -7/10 = 8/-3 =

Example ThreeFind 2 rational numbers between each pair of numbers.

A.

B.

C.

D.

AssignmentPage 100

#’s 5, 7, 8, 9, 10, 13, 16, 22, 23

Adding Rational NumbersRational Numbers

Example FourWhich rational number is less?

3/4 or 3/5

-2.34 or -2.3

Adding FractionsTo add rational numbers in fraction form, you must use a common denominator.

Ex.

Common DenominatorsPlan A

● Multiply the denominators (3 x 5 = 15)● This is not always the common denominator

Plan B

● Find the lowest common multiple● 3 → 3, 6, 9, 12, 15, 18, 21, 24● 5 → 5, 10, 15, 20, 25, 30

LOWEST COMMON MULTIPLE IS 15

ExamplesHow do we turn

mixed fractions into improper fractions?

Examples

Assignment

Page 111

#’s 3, 5, 7, 9, 11 (a, c, e), 13, 17

Subtracting Rational NumbersRational Numbers

Subtracting Fractions

To subtract rational numbers in fraction form, you must use a common denominator.

Ex.

Common Denominators

Plan A

● Multiply the denominators (3 x 4 = 12)● This is not always the common denominator

Plan B

● Find the lowest common multiple● 3 → 3, 6, 9, 12, 15, 18, 21, 24● 4 → 4, 8, 12, 16, 20, 24

LOWEST COMMON MULTIPLE IS 12

Examples

Examples

Assignment

Page 119

#’s 3, 4, 5, 6, 7, 8, 9, 11, 13

Multiplying Rational NumbersRational Numbers

Multiplying Fractions

When we multiply fractions, we multiply the numerators and multiply the denominators, then reduce if possible.

Ex.

Examples

Remember!

When multiplying integers:

+ x + = ++ x - = -- x - = +

Examples

Assignment

Page 127

#’s 3, 5, 7, 9, 14, 15

Dividing Rational NumbersRational Numbers

Dividing Fractions

When we divide fractions, we multiply the reciprocal.

Reciprocal:

Ex.

Examples

Remember!

When dividing integers:

+ ÷ + = ++ ÷ - = -- ÷ - = +

Examples

Assignment

Page 134

#’s 3, 4, 7, 11, 12, 17, 18

Order of Operations with Rational Numbers

Rational Numbers

Examples

(-0.8) + 1.2 ÷ (-0.3) x 1.5 & (-3.2) - 0.9 ÷ [0.7 - (-1.2)]2

Examples

ExamplesWrite each number as a decimal.

Assignment

Page 140

#’s 3, 4, 8, 9, 11, 12 (a, c), 16 (b), 17

Review

● Page 144 → #’s 5 - 10, 16 - 19, 20 (a), 21, 23● Chapter 3 Self Test● Practice Test → Page 146