Math Concepts

Question 1

Prime Number

Answer 1

whole number whose only divisors are itself & 1

Question 2

Composite number

Answer 2

one that has at least one other factor besides itself & 1

Question 3

Proper fraction

Answer 3

a fraction whose numerator is less than its denominator

Question 4

Improper fraction

Answer 4

fraction where the numerator is greater than or equal to the denominator

Question 5

How to multiply two fractions?

Answer 5

multiply the two numerators and the two denominators

2/5 x 5/7 = 10/21 because 2x5=10 and 3x7=21

Question 6

How to divide two fractions?

Answer 6

multiply the first fraction by the reciprocal of the second

27/4 ‘/’ 3/2 => 27/4 x 2/3 (reduces to) => 9/2 x 1/1 = 9/2 or 4 1/2

Question 7

How to add fractions with same denominator?

Answer 7

to add fractions with the same denominator, add their numerators and preserve the denominator

3/4 + 1/4 = 4/4 = 1

Question 8

How to add fractions with different denominator?

Answer 8

find a way to change them so that the denominators are the same

1/2 + 1/4 => (1/2 x 2/2 = 2/4) => 2/4 + 1/4 = 3/4

Question 9

How to add fractions with very different denominators?

Answer 9

1/2 + 1/3 = (1/2 x 3/3) + (1/3 x 2/2) = 3/6 + 2/6 = 5/6

Question 10

How to subtract fractions w/ same denominator?

Answer 10

keep the common denominator and subtract the second numerator from the first

3/4 - 1/4 = 2/4

Question 11

How to subtract fractions with different denominators?

Answer 11

if different, change the fractions so that they have the same denominator

7/8 - 1/4 => 7/8 - (1/4 x 2/2 = 2/8) = 5/8

Question 12

How to multiply decimals?

Answer 12

multiply them as if they were whole numbers, then add up their decimal places and insert a decimal point the same number of places from the right in the solution

Question 13

How to divide decimals?

Answer 13

to divide by a whole number, all you have to do is keep the decimal point in the solution directly over the decimal point in the dividend (the number being divided)

Question 14

How to convert fraction to decimal?

Answer 14

move the decimal two spaces to the right and add the percent sign

17% => 0.17
250% => 2.50

Question 15

How to convert percent to decimal?

Answer 15

since percent means hundredths, you can convert percent to a decimal by dropping the percent sign and moving the decimal by dropping the percent sign and moving the decimal point two places to the left

5. 5% => 0.055
6. 3% => 0.003

Question 16

How to convert fraction to a percent?

Answer 16

first change the fraction to a decimal then move the point two places to the right and add the percent sign

7/8 => .875 => 87.5%

Question 17

What is the formula for simple interest?

Answer 17

i = p x r x t

i means interest or income
p means principal or money invested
r means rate of interest in percent
t means time (in years)

Question 18

Absolute Value

Answer 18

the unsigned or undirected value of a number

|-3| = |3| = 3

Question 19

What happens with the signs when you add?

Answer 19

even + even = even
odd + odd = even

even + odd = odd
odd + even = odd

Question 20

What happens with the signs when you subtract?

Answer 20

even - even = even
odd - odd = even

even - odd = odd
odd - even = odd

Question 21

What happens with the signs when you multiply?

Answer 21

pos x pos = pos
odd x odd = pos

pos x neg = neg
neg x pos = neg

Question 22

Monomial

Answer 22

an algebraic expression with one and ONLY ONE term

2abfg | x^2y^4 | (2)(3)xyz | xyz/3

Question 23

Binomial

Answer 23

an algebraic expression with two and ONLY TWO terms separated by either plus or minus signs

2x-3y | x^2-4y^2 | ab+4a^2 | abcd+5d

Question 24

Trinomial

Answer 24

An algebraic expression with three and ONLY THREE terms separated by either plus or minus signs

x^2+2x-7 | 3x-4y+z

Question 25

Polynomial

Answer 25

Any algebraic expression with MORE than ONE term.

2x+3y | abc-7d-8ce | 2x-3y-4z+4a-2b

Question 26

Similar Terms

Answer 26

terms are similar or like when they have the SAME LITERAL FACTORS raised to the same powers

3x and 2x are like terms; 3x and 2x^2 are NOT
3x2 and -x^2 are like terms; 3x^2 and x are NOT
x^2z and -7x^2z are like terms; x^2z and -7xz are NOT

Question 27

How to multiply algebraic expressions

Answer 27

multiply the numerical factors )also called coefficients) and then multiply the variables. When multiplying one power of x by another power of x, simply add the exponents.

(2x^2)(3x^5) => (2)(3) = 6 & (x^2)(x^5) = x^7 => 2+5 = 7

Question 28

How to divide the algebraic expressions

Answer 28

divide the coefficient and then divide the variables. When dividing one power of x by another power of x simply subtract the exponents.

x^5/x^3 => 5-3 = 2 => x^2

8x^3/4x => (8/4 = 2)/(4/4 = 1) * (x^3 - x^1 = x^2)/(x/x = 1) = 2 * x^2 = 2x^2

Question 29

How to factor?

Answer 29

factoring should be ONLY prime factors.

50 = (1)(50) is incorrect because neither 1 nor 50 is prime
50 = (2)(25) is incorrect because 25 is not prime
50 = (5)(10) is incorrect because 10 is not prime
50 = (2)(5)(5) is the CORRECT factorization because 2 and 5 are indeed prime numbers

Question 30

How to find Greatest Common Factor

Answer 30

GCF –

75x^2 + 30x

1) find common factors of the numbers
75x^2 = 355xx
30x = 235*x

2) see what is in all of the numbers
3, 5, x

3) multiply these terms
35x = 15x

4) finish factoring
=15x(5x + 2)

Question 31

Factoring the difference of two squares

Answer 31

the special product of the sum of two numbers and the difference of the same two numbers equals the difference of the squares of these numbers

(a + b)(a - b) = a^2 - b^2

Question 32

Law of Exponents

Answer 32

x^0 = 1

x^-1 = 1/x 
x^-2 = 1/x^2
x^-3 = 1/x^3

x^a * x^b = x^a + b

x^a / x^b = x^(a - b) = 1 / x^b - a

x^a * y^a = (xy)^a

(x/y)^a = x^a / y^a

(x^a)^b - x^ab

Question 33

Laws of Square Roots

Answer 33

√a^2=a

√a√b=√ab

√a / √b = √a / b

Question 34

How to Foil

Answer 34

First Outer Inner Last - FOIL

positive L, positive O + I
x^2 + 4x + 3 = (x + )(x + )

positive L, negative O + I
x^2 - 4x + 3 = (x - )(x - )

negative L, negative O + I
x^2 - 4x - 3 = (x + )(x - )

negative L, positive O + I
x^2 + 4x - 3 = (x + )(x - )

Question 35

Sum of angles in a polygon

Answer 35

The sum of ANY polygon can be found using: 180(n - 2)

n = number of sides

Triangle: 180(3 - 2) = 180
Quadrilateral: 180(4 -2) = 360
Pentagon: 180(5 - 2) = 540
Hexagon: 180(6 - 2) = 720
[...]

Question 36

Special Right Triangles

Answer 36

Most common triangles:
(leg-leg-hypotenuse)

3-4-5 ;; 1-1-√2 ;; √3-1-2

30-60-90 triangles
The short side, opposite the 30° angle, is always half the hypotenuse. The longer leg is always the square root of 3 times longer than the shorter leg.

45-45-90
The two legs are always equal because this is an isosceles triangle, and the hypotenuse is always the square-root of two times any leg.

Question 37

Rule of Exponents

Answer 37

Rule 1: x^-a = 1 / x^a
==> 4^-3 = 1 / 4^-3 = 1 / 64
==> 1 / 2^-a = 2^a

Rule 2: (x^a)(x^b) = x^a+b
==>(3^2)(3^4) = 3^(2+4) = 3^6 = 729
==> (y^3)(y^-1) = y^2

Rule 3: x^a / x^b = x^(a-b) = 1 / x^(b-a)
==> 5^7 / 5^4 = 5^(7-4) = 5^3 = 125
==> t^3 / t^8 = t^-5 = 1 / t^5

Rule 4: x^0 = 1
==>7^0 = 1
==> -3^0 = 1
NOTE: 0^0 is undefined

Rule 5: (x^a)(y^a) = (xy)^a
==> 2^3 * 3^3 = 6^3 = 216
==> (10z)^3 = 10^3z^3 = 1000z^3
NOTE: uses common exponents

Rule 6: (x / y)^a = x^a / y^a
==> (3 / 4)^2 = 3^2 / 4^2
==> (r / 4t)^3 = r^3 / 64t^3

Rule 7: (x^a)^b = x^ab
==> (2^5)^2 = 2^10 = 1024
==> (3y^6)^2 = (3^2)(y^6) = 9y^12