Real Numbers

Classifying Real Numbers

100

Which of these numbers is a NATURAL number? a) 2/3 b) -3 c) 7 d) 0

7 is a natural/counting number

200

Which of the following is a whole number? a) 0.8 b) 1/2 c) -5 d) 12/3

12/3 = 4 ; 4 is a whole number

300

Which of the following is an integer? a) -4/9 b) 12 c) 0.67 d) 1/4

12 is an integer. Integers are whole numbers or their opposites.

400

Why is "Pi" an irrational number?

"Pi" is an irrational number because its decimal goes on forever and never repeats. Also, it cannot be written as a fraction.

500

Is the square root of 81 a rational or irrational number? How do you know?

The square root of 81 is a rational number because it is equal to 9 and 9 can be written as a fraction, 9/1.

Comparing and Ordering Real Numbers

100

Compare using <, >, or =. -5.4 ____ 6.7

-5.4 < 6.7 (Negative numbers are always smaller than positive numbers.)

200

Compare using <, >, or =. 0.76 _____ 0.2345

0.76 > 0.2345

300

Compare using <, >, or =. 4/5 _____ 0.80

4/5 = 0.80

400

Order the following numbers from least to greatest: 1/2, 0.12, -8, 0, -1.3

-8, -1.3, 0, 0.12, 1/2

500

Order these numbers from greatest to least: 3.9, -4, 1.22, 1/4, -12

3.9, 1.22, 0.25, -4, -12

Integers

100

Find the sum: -18 + -12

-30 (Same signs, you add and give the sign)

200

Find the difference: -12 - (-9)

-3 (Keep, Change, Change; Follow the rules of addition) -12 + (+9) (Different signs, subtract, and give the sign of the bigger number)

300

A submarine is located at 400 meters below sea level. If the submarine ascends125 meters, what is its current location?

-400 + 125 = -275 meters

400

-4 x 3 + (-16)

-12 + (-16) = -28

500

-120 - (-46)

-74

Absolute Value

100

Find |-10|.

10

200

Find |175|.

175

300

Find |-6 x -8|.

48

400

|-10 + -3| + |-8 - -2|

13 + 6 = 19

500

|4 x -5| - |12 + -10|

20 - 2 = 18

Order of Operations

100

Find the value of the following expression: 14 + 3 x 6 - 17

15

200

Find the value of this expression: 13 - (2 x 4) + 15

13 - 8 + 15 5 + 15 20 The value of this expression is 20.

300

|12 + -4| x 3

8 x 3 = 24

400

4 + 19 - 4 x 2(-4 + -2)

4 + 19 - 4 x 2 x -6 4 + 19 - 8 x -6 4 + 19 - (-48) 23 - (-48) 71 The value of this expression is 71

500

Find the value of the following expression: ([3 x -5] + -11) x 4

(-15 + -11) x 4 -26 x 4 -104 The value of this expression is -104