Competency 15: Number Concepts & Operations

Question 1

Odd numbers

Answer 1

cannot be divided by 2 without having a remainder of 1. A remainder of 0 is not possible when dividing an odd number by 2. EX) 9,21,35

Question 2

Even numbers

Answer 2

Can be divided by 2 with no remainder. EX) 2,4,16

Question 3

Prime numbers

Answer 3

Have exactly 2 numbers that divide them evenly, 1 and the actual number itself. 1 is not considered prime & 2 is the only even prime #. EX) 3,7,11.

Question 4

Composite numbers

Answer 4

Have more than exactly 2 numbers that divide them evenly Ex) 4,15,49

Question 5

Number operations

Answer 5

Adding, subtracting, multiplying or dividing.

Question 6

Integers

Answer 6

Set of whole numbers and their opposites.. The number line can be used to represent a set of these. Positive & negative whole numbers. Ex) +5, -13,+23,-1258

Question 7

Rational Numbers

Answer 7

Real number that can be expressed as a ratio of integers/ in the form: a/b where “a” and “b” are integers and “b” does not equal 0. They can be expressed as fractions, decimals, and integers. Decimals are either terminating or repeating. Ex) 24, since 48/2; 5.2, since 26/5; 0.777…, since 7/9. 5=5/1, 25=1/4, .333=1/3. 2.40 (represents a fixed # of digits), 1/7=0.142857142857 (Contains a repeating decimal part)
3.14159265..(pie) is not one, since the decimal does not begin to repeat from some point.

Question 8

Algorithm

Answer 8

Step-by-step procedure used to get a certain result, often with several steps that repeat. Adding two numbers together is one kind.

Question 9

Whole Numbers

Answer 9

The counting numbers and 0 (0,1,2,3,4,5…)

Question 10

Place Value

Answer 10

The location of a digit within a number determines its value.
Ex) Ones place-8
Tens place-80
Hundreds place-800

Question 11

Expanded Form

Answer 11

The sum of a number’s place values: 1,729=1000+700+20+9.

Question 12

Rounding

Answer 12

Estimating the closest number to a given whole number, with all zeros to the right of the desired place value. Ex) 17 rounded to nearest ten is 20.

Question 13

Commutative Property

Answer 13

Changing the order of numbers being added or multiplied gives the same answer (12+7 is the same as 7+12 & 3x9 same as 9x3.)

Question 14

Associative Property

Answer 14

The grouping of numbers in addition or multiplication does not change the answer, such as (2 X 4) X 3 = 2 X (4 X 3)

Question 15

Distributive Property

Answer 15

Multiplication and division may be distributed over addition and subtraction. 10 X (50+3)=(10X50)+ (10X3) and (30-18) / 3 = 30/3 - 18/3.

Question 16

Zero Property of Addition

Answer 16

Adding 0 to a number equals the original number. (43+0=43)

Question 17

Zero Property of Multiplication

Answer 17

Multiplying a number by 0 equals 0. (43 X 0=0)

Question 18

Irrational Numbers

Answer 18

Values that can not be expressed as a ratio of 2 integers. Always non-terminating & non-repeating. Ex) 5.347658953 (no repeating #s)
I=R-Q

Question 19

T o F: Each real number can be expressed in either a decimal or a fractional form.

Answer 19

True

Question 20

Decimal Numbers

Answer 20

Contain a decimal point that separates the place value of ones from tenths. Can also contain commas that underline other place values. EX) 2,300.34. 0.4553. 444,456.09. Often used to indicate the number of significant figures.

Question 21

Fractional Numbers

Answer 21

Do not contain decimal points. They have a division bat either horizontal or slashed (a/b). The number a is the numerator & the number b is the denominator. A fraction is expressed Numerator/Denominator. A fractional form is not defined if the denominator is 0.

Question 22

Fractions can be classified as…

Answer 22

1) Proper
2) Improper
3) Mixed number

Question 23

Proper fraction

Answer 23

if a

Question 24

Improper fraction

Answer 24

if a>b. Ex) 6/4, 7/2

Question 25

Mixed number

Answer 25

Contains a whole number and a proper fraction. 2 2/3, -5 1/7

Question 26

Natural numbers

Answer 26

Denoted by N where N=(1,2,3,4,…) The minimum value is 1 and they increase in value by 1. Infinite. Sometimes called positive or non-negative.

Question 27

Whole Numbers

Answer 27

Adding zero to the set of natural numbers produces a set of these denote by W where W=(0,1,2,3,4…). Infinite.

Question 28

Integers

Answer 28

Whole numbers with their opposites denoted by Z where Z=(…-4,-3,-2,-1,0,1,2,3,4…) Infinite & doesn’t have max or min values.

Question 29

Rational Numbers

Answer 29

Contain numbers that can be converted into decimal forms that terminate or contain fixed repeated parts. Denoted by Q. (-10, -1, -1/2,0,3.4,10) Can be placed on a number line & can be positive or negative.

Question 30

Quantity can be expressed as a…

Answer 30

fraction or a decimal. Ex) Mass of 1/20 kilogram=1/20kg, 60 mph, 3.5h.

Question 31

To convert a decimal to a fraction

Answer 31

identify the place value of the last digit in the decimal. Then create a fraction by placing the digits portion in the numerator and the place value as the denominator. EX) 3.2=3 & 2 10ths= 3 2/10 = 3 1/5. 2.04=2 & 4 hundredths=2 4/100 = 2 1/25. 0.027=27 thousandths=27/1000 (cannot simplify)

Question 32

To convert a fraction to a decimal

Answer 32

2 options:

1) If the numerator is a multiple of 10 (10, 100, 1,000), then simply place the digits behind the decimal so the last digit is in the correct place. Ex) 5/10=6.5. 23/50=46/100=0.46. 2/1000=0.002.
2) If the numerator is not a multiple of 10, then divide the numerator by the denominator to get the decimal. Ex) 8 3/15= 8.2. 1/3=0.333. 1/4=0.25.

Question 33

Percent

Answer 33

Or part of 100, represents a ratio of part of a quantity with reference to the whole value. EX) A class contains 25 students. If 20 students are present, express that in terms of percent. (Part/Whole Quantity=20/25, then multiply the ratio by 100: 20/25 x 100=80, thus 80% of students are present.

Question 34

Converting fractions to a percent

Answer 34

Percent means per hundred, so a fraction can be expressed out of 100. Ex) 5/100=5%, 46/100=46%, 2/100=2%

Question 35

Converting decimals to a percent

Answer 35

Percent can also be thought of as 2 decimal places behind the decimal (the hundredths place). A decimal is multiplied by 100 by moving the decimal two places right.
Ex) 0.25 X 100=25%
0.30 X 100=30%

Question 36

Concerting percent to decimals

Answer 36

Divide by 100 by moving the decimal 2 places left.
Ex) 46% / 100 = 0.46
2%/100=0.02

Question 37

Relative Percent Change

Answer 37

(Final Value-Initial Value/Final Value) X 100%
Ex) due to a heavy rain, a water level in a tank raised from 1.2m to 1.5m. Calculate percent change. Initial value=1.2m & final value=1.5m. (1.5-1.2/1.5) x 100=20%

Question 38

Relative Percent Error

Answer 38

(Expected value-measured value/expected value) x 100%. Ex) a student measured acceleration due to gravity to be 9.0m/s2. If the accepted value is 9.8m/s2, calculate percent error. Accepted value=9.8m/s2 Measured value=(9.0m/s2.
9.8/s2-9.0m/s2/9.8m/s2) x 100%=8.2%

Question 39

Roots

Answer 39

Zeros of a function
Solutions of an algebraic equation
Results of exponentiation when the exponent is a fractional proper or improper.

Question 40

Power

Answer 40

An expression of the form a^b, where a is called the base and b is the exponent/power. If exponent is whole #, then it tells how many times the base must be multiplied by itself to evaluate the power. ex) 4^3=4x4x4=64. y^2-y x y.

Question 41

Scientific Notation

Answer 41

Used to express very large or very small quantities by applying a power with the base of 10. a x b^n where:
a is called the magnitude of the value: -10<a></a>