Unit 1: Number Systems Review

Vocabulary

100

Categorize the number:  Square root 121

Irrational

Rational

Integer

Whole

Natural

Categorize the number:  Square root 121=11

Irrational

Rational-Yes

Integer-Yes

Whole-Yes

Natural-Yes

200

Categorize the number:  (-2)³

Irrational

Rational

Integer

Whole

Natural

Categorize the number:  (-2)³=-8

Irrational

Rational=Yes

Integer=Yes

Whole

Natural

300

What number is whole but is not natural?

0

400

Is the number, 

3.47171717171...

rational?  Explain your reasoning in one sentence.

Yes.  3.47171717171... is rational because the decimal pattern repeats.

500

Prove that 1.5 is a rational number.  

1.5=3/2

1.5 is a rational number because the decimal is finite.  1.5 can be written as a ratio, 3/2.

Fractions

100

Find the sum.

-7  3/5  +  4  1/3  

-7  3/5     +  4  1/3  

-7  9/15   +  4  5/15

-3  4/15

200

Find the difference.

-8  5/6  -  1  3/4

-8  5/6      -    1  3/4

-8  10/12   -   1  9/12  

 -9  19/12

-10  7/12

300

Find the product of   1  7/9  and -3  3/4.

(1  7/9)(-3  3/4)

(16/9)(-15/4)

REDUCE!

(4/3)(-5/1)=  -  20/3

                =  -  6  2/3

400

Subtract 10  1/6  from 6  5/9.

6 5/9  -  10  1/6  

6 5/9      -    10  1/6 

-10  1/6    +  6  5/9

-10  3/18  +  6  10/18 

-9  21/18  +  6  10/18

-3  11/18

500

Find the quotient.

-1  1/9   /    -2  1/12

-1  1/9   /    -2  1/12

-10/9    /     -25/12

-10/9   *     -12/25

-2/3     *     -4/5  =  8/15

                 Answer:  8/15

Decimals

100

2.31  -  (-9.75)

2.31  -  (-9.75)

2.31  +   9.75

9.75  +   2.31

12.06

200

Find the difference.

-10.25  -  13.9

-10.25  -  13.9

-13.90

-10.25

_______

-24.15

300

The product of -1.53 and 6.

(-1.53)(6)

-1.53

*    6

_____

-9.18

400

Find the quotient.

0.792 divided by -0.04.

0.792 / (-0.04)  Multiply by 100/100

79.2 / (-4)  =  -19.8

500

-13.1-(-7.05)+0.9

-13.1-(-7.05)+0.9

-13.1+ 7.05  +0.9

-13.1+ 7.95

-5.15

Order of Operations

100

-10  +  8  -  (-1)

-10  +  8  -  (-1)

-10  +  8  +  1

-10  +  9

-1

200

1  -  (4/5)²

1  -  (4/5)²

1  -  16/25

9/25

300

-12  +  (-6)²  /  (-9)  

-12  +  (-6)²  /  (-9) 

-12  +  36    /    (-9)

-12  +  (-4)

-16

400

10¹  -  (-2)(-9)  - 1⁰

10¹  -  (-2)(-9)  - 1⁰

10   -   18         -1

10   -   19

-9

500

(-5)(-4)  /  (-10)  -  (-7)²

(-5)(-4)  /  (-10)  -  (-7)²

       20  /  (-10)   -  49

                     -2  -  49

                          -51

Word Problems

100

A scuba diver was swimming 15 feet below sea level.  The swimmer dove an additional 9 feet to get a better look at a shipwreck.  What is the depth the diver is swimming now?

-15-9

-24 feet

200

The temperature in the morning was -5 degrees Celsius.  By noon, the temperature rose to 8 degrees Celsius.  How much did the temperature rise?

8-(-5)

8+5

13

Answer:  13 degrees Celsius

300

A mountain climber descends down the mountain 300 meters each hour.  How far will they descend in 4 hours?

-300(4)=-1200 meters

400

A hiker started at an elevation of 500 meters.  She descended 350 meters by the first hour and descended an additional 425 meters by the second hour.

500-350-425

500-725

-275 meters

500

The elevation at the start of the hiking trail is 32 feet below sea level.  At the end of the trail the elevation 119 feet.  What is the change of elevation?

119-(-32)

119+32

151 feet