RATIONAL NUMBERS

NATURAL NUMBERS {1, 2, 3,…} + {0}

= WHOLE NUMBERS {0, 1, 2, 3,…} + NEG. WHOLE NOS.

= INTEGERS {…-2, -1, 0, 1, 2,…} + PURE FRACTIONS

= RATIONAL NUMBERS

A RATIONAL NUMBER is any number that can be written in the form a/b, where a & b are

integers and b ≠ 0. OR a RATIONAL NUMBER is any number that

can be written as a fraction.

RATIONAL NUMBERS

GRAPHING THE NUMBER SETS ON THE NUMBER LINE

NATURAL NUMBERS(or counting numbers)

0 2 4 6-2-4-6

RATIONAL NUMBERS

GRAPHING THE NUMBER SETS ON THE NUMBER LINE

WHOLE NUMBERS

0 2 4 6-2-4-6

RATIONAL NUMBERS

GRAPHING THE NUMBER SETS ON THE NUMBER LINE

INTEGERS

0 2 4 6-2-4-6

RATIONAL NUMBERS

EXAMPLES OF RATIONAL NUMBERS

51

5

- 71

7

01

0

5

2fraction

aalready

0.310

3

3.03

1

RATIONAL NUMBERS

GRAPHING THE NUMBERS ON THE NUMBER LINE

0.5

0 2 4 6-2-4-6

RATIONAL NUMBERS

GRAPHING THE NUMBERS ON THE NUMBER LINE

8/3

0 2 4 6-2-4-6

RATIONAL NUMBERS

GRAPHING THE NUMBERS ON THE NUMBER LINE

–32/5

0 2 4 6-2-4-6

RATIONAL NUMBERS

GRAPHING THE NUMBERS ON THE NUMBER LINE

{-3, -2, 0, 5}

0 2 4 6-2-4-6

RATIONAL NUMBERS

GRAPHING THE NUMBERS ON THE NUMBER LINE

{0, 2, 4, 6,…}

0 2 4 6-2-4-6

RATIONAL NUMBERS

The ABSOLUTE VALUE of any number is its distance from zero on the number line.

The absolute value of 3 is written |3|

0 2 4 6-2-4-6

|3| = 3, because

3 units

RATIONAL NUMBERS

The ABSOLUTE VALUE of any number is its distance from zero on the number line.

0 2 4 6-2-4-6

|-3| = 3, because

3 units

RATIONAL NUMBERS

Evaluate: |-2 + 7| = |5|

Evaluate: 3 + |-4| + |4| = 3 + 4 + 4

Evaluate: x + |x + 4| + 3, if x = -7

= -7 + |-3| + 3 = -7 + 3 + 3 = -1

= 5

= 11

ADDING & SUBTRACTING RATIONAL NUMBERS

ADDINGADDING

Same Signs: Add their absolute values and use their common sign.

6 + (+3) = 9

-6 + (-3) = -9

4 + (+8) = 12

-20 + (-45) = -65

ADDING & SUBTRACTING RATIONAL NUMBERS

ADDINGADDING

Different Signs: Subtract their absolute values and use the sign of

the larger.6 + (-3) = 3

-6 + (+3) =

-3

3 + (-7) = -4

-20 + (+45) =

25

ADDING & SUBTRACTING RATIONAL NUMBERS

SUBTRACTINGSUBTRACTING

The ADDITIVE INVERSE of a number is its opposite.

The additive inverse of 6 is -6

The additive inverse of -3 is 3

The additive inverse of 1/2 is -1/2

The additive inverse of -6.25 is 6.25

ADDING & SUBTRACTING RATIONAL NUMBERS

SUBTRACTINGSUBTRACTING

The ADDITIVE INVERSE of a number is its opposite.

ADDITIVE INVERSE PROPERTYFor every number a, a + (-a) = 0

4 + (-4) = 0

10 + (-10) = 0

ADDING & SUBTRACTING RATIONAL NUMBERS

SUBTRACTINGSUBTRACTING

To subtract signed numbers, add the opposite.

(A.T.O.) and use the rules of addition.6 – (+3) = 6 + (-3) = 3

6 – (-3) = 6 + (+3) =9

-8 – (+2) = -8 + (-2) = -10

-30 – (-50) = -30 + (+50) =

20

REVIEW

5 is a rational number

YES

TRUE OR FALSE

REVIEW

0 is the smallest natural number.

NO, 1 is the smallest

TRUE OR FALSE

REVIEW

-1 is the largest negative integer.

YES

TRUE OR FALSE

REVIEW

Name a rational number that is not

an integer.Any fraction

½, 0.6, 2.3, etc

TRUE OR FALSE

REVIEW

Name a whole number that is not a

natural number.

0

REVIEW

Name a whole number that is not

an integer.

NOT POSSIBLE

ADDING & SUBTRACTING

RATIONAL NUMBERS

FLASH CARDS

8 + (+3)

11

FLASH CARDS

5 + (-3)

2

FLASH CARDS

-7 + (-2)

-9

FLASH CARDS

-5 + (+2)

-3

FLASH CARDS

-7 + (+8)

1

FLASH CARDS

-3 + (-5) + (+2)

-6

FLASH CARDS

7 + (-3) + (-6)

-2

FLASH CARDS

20 + (+30) + (-50)

0

FLASH CARDS

-5 + (-3) + (-2)

-10

FLASH CARDS

2 + (-1) + (8)

9

FLASH CARDS

7 - (+1)

6A.T

.O.

FLASH CARDS

9 - (-1)

10A.T

.O.

FLASH CARDS

-20 - (+10)

-30A.T

.O.

FLASH CARDS

-5 - (-8)

3A.T

.O.

FLASH CARDS

11 - (+8)

3 A.T.O

.??

FLASH CARDS

25 - (-10)

35A.T

.O.

ABSOLUTE VALUES

FLASH CARDS

|-1|

1

FLASH CARDS

|0|

0

FLASH CARDS

|5| + |-2|

7

FLASH CARDS

|-2+(-3)|

5

FLASH CARDS

|2| + |-1| + |8|

11

FLASH CARDS

|2 - 1| + |-1 + 3|

3

FLASH CARDS

|10 - 3| - |-1 - 3|

3

FLASH CARDS

3 + 5xif x = -2

-7

FLASH CARDS

x + |-x| - |-x+2|if x = -2

-4