Math review

Question 0

Product of integers:

Even * Even =

Odd * Odd =

Even * Odd =

Answer 0

Even * Even = Even (2*2=4)

Odd * Odd = Odd (1*1=1)

Even * Odd = Even (2*1=2)

Question 1

Multiple

Answer 1

A multiple is divisible by each of its divisors/factors “25 is a multiple of: 1,5,25, and their negatives.”

Question 3

Sum of integers:

Even + Even =

Odd + Odd =

Even + Odd =

Answer 3

Even + Even = Even (2+2=4)

Odd + Odd = Even (1+1=2)

Even + Odd = Odd (2+1=3)

Question 4

Prime number

Answer 4

1. x>1 and
2. Only 2 positive factors, 1 and x
   i. e. 2,3,5,7,11,13,17,19,23,29

1 is not prime number.

2 is only prime number that is even.

Question 5

Composite number

Answer 5

1. x>1 and
2. Not prime number
   i. e., 4,6,8,9,10,12,14,15,18,20,21

Question 6

Rational number

Answer 6

Any number that can be made by dividing one integer by another. The word comes from “ratio”. Examples: 1/2 is a rational number (1 divided by 2, or the ratio of 1 to 2)

Question 7

Mixed number

Answer 7

A number that is the sum of a whole number and a proper fraction is called a mixed number. i.e. 4 3/8 = (4/1)+(3/8) = ((4*8)+3)/8 = 35/8

Question 8

Exponent basics

Answer 8

(-) Number ^ even number = (+)

(-) Number ^ odd number = (-)

-3^2= -9

a^0 = 1 (a ≠ 0)

0^0=undefined

(a)(a^-1)=1

(a ≥ 0, m ≥ 0, n > 0)

Careful!!

1. (a + b)^n ≠ a^n + b^n
2. (a – b)^n ≠ a^n – b^n

Question 9

Square root Basics

Question 10

Cube root and n-th root

Answer 10

For ODD-order roots, there is exactly 1 root for every number a (i.e. cubed root).

• cubed root of 8 = cubed root of 8
• cubed root of -8 = cubed root of -8

If n is odd then .

For even-order roots, there are exactly 2 roots for every positive number a and NO root for any negative number a (i.e. fourth root).

fourth root of 8 = (+) and (-) fourth root of 8

fourth root of -8 = NONE

If n is even then .

Distributing (a ≥ 0 and b ≥ 0)

Careful!

Question 11

Rational number

Answer 11

can be expressed as a TERMINATING or REPEATING decimal

however, not every decimal is terminating or repeating (i.e. Square root of 2 = 1.4142135… = IRRATIONAL number)

Question 12

Real number

Answer 12

Rational number (integer, fraction, decimal) + Irrational number

Question 13

Triangle Inequality

Answer 13

Geometrically, the right-hand part of the triangle inequality states that the sum of the lengths of any two sides of a triangle is greater than the length of the remaining side.