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Math Memorizations > Math Concepts > Flashcards

Math Concepts Flashcards

1
Q

Prime Number

A

Number that has exactly 2 factors.
Only positive integers.
2 is the only prime number. Every even prime number greater than 2 has at least 3 factors.
First 8 prime numbers: 2,3,5,7,11,13,17,19

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2
Q

Factor Foundation Rule

A

If c is divisible by primes a and b, then c is divisible by (a*b)

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3
Q

“Greatest number than x must be divisible by”

A

LCM

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4
Q

Double Cross Method

A

Use when adding fractions and when finding when a fraction is greater than or equal to other fractions

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5
Q

What percent

A

x/100

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6
Q

What percent of

A

turn what percent into x/100, then multiply.

ex: What percent of 200 is 60 = (x/100)200=60

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7
Q

x% of

A

1) Convert x% into decimal/fraction
2) Multiply, or
1) find a power of 10 of x%
2) multiple/divide to get to x%

ex: 30% of 200 = 0.30x200 = 60
30% = 20x3 = 60

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8
Q

percent change formula

A

Percent change (as percent of original)
=
Change in value/Original Value

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9
Q

Unknown Multiplier

A

The number by which you multiply the ratio to get to the actual number.

*Always the same for all parts of a ratio

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10
Q

Least common multiple (LCM)

A

The LCM of 2 numbers is the smallest number that is a multiple of both numbers

i.e: 3 & 10 = 30
6 & 9 = 18

*If x is divisibke by A & by B, then x is divisible by the LCM of A & B no matter what

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11
Q

The double cross Method

A

1) Draw arrows and multiple
2) Add the numerators
3) Simplify

ex: 5/6 + 3/8 = ((58) + (36))/(6*8) = (40 + 18)/48 = 58/48=29/24

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12
Q

Double Cross Fraction Comparison

A

1) set the fractions up near each other
2) Multiple “up” the arrows. Be sure to put the resulting number at the top of each respective error
3) Compare the numbers. The side with the bigger number is the bigger fraction

ex: 3/5 and 4/7
(37) and (45) = 21 and 20.
Since 21 is greater than 20, 3/5 is greater than 4/7

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13
Q

Improper fraction to mixed number

A

1) rewrite the number as a sum
2) Split the fraction

ex:

1) 13/4 = 12/4 + 1/4 = 3 + 1/4 =3 1/4
2) 11/6 = 6/6 + 5/6 = 1 5/6
3) 100/11 = 99/11 + 1/11 = 99 1/11

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14
Q

Mixed Number to Improper fraction

A

Shortcut:
((denom) (integer) + num)/denom

ex:
7 3/8 => ((8) (7) +3)/8= 59/8

Note: I already do it this way

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15
Q

% decrease of 50%

A

= New percent of 50%

= Multiple original value by 0.5 or 1/2

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16
Q

Divide a number by (+) 10^-x

A

When dividing any number by a negative power of 10, move the decimal to the right

ex:
53.0447/10^-2 = 5304.47

17
Q

Multiple a number by (+)10^x

A

When multiplying any number by a positive power of 10, move the decimal to the right of the specified number of places

ex:
3.9742 x 10^3 = 3,974.2

18
Q

Multiple a Decimal & a Big Number

A

When one number is very big and the other is very small, you can trade powers of 10 from the big one to the small one.

Similar to: Move one decimal point to the left and the other to the right.

ex:
4,000,000 x 0.0003 = 400 x 3 = 120
50,000 x 0.007 = 50 x 7 = 350

19
Q

Numerator and Denominator Rules

A

1) (up arrow) numerator, -denom => (up arrow) fraction
2) (up arrow) denom, =numer => (down arrow) fraction
3) adding same value to both numer & denom => fraction goes toward 1

a) if fraction <1, then fraction increases as it approaches 1
b) if fraction >1, then fraction decreases as it approaches 1

20
Q

Interest Formula

A

Total Amount = P(1 + r/n)^nt

P = Principal, r = rate (in decimal form), n = number of times/year, t= number of years

21
Q

Multiply a number by (+) 10^-x

A

When multiplying any number by a negative power of 10, move the decimal to the left

e.x: 6782.01 x 10^-3 =6.78201

22
Q

Exponent base

A

Fractional Base: When base id (+) proper decimal/fraction, the exponent (up arrow) the value of the expression (down arrow)

Compound base: an exponent can be distributed a product (10^3 = (2x5)^3 = 2^3 x 5^3)

Base of -1: (-1)^odd = -1
(-1)^even = 1

Negative base: the exponent does not distribute unless the (-)ve sign is inside the parenthesis

23
Q

Combining exponential terms

A

When multiplying 2 exponential terms, w/the same base, add the exponents

When dividing 2 exponential terms w/the same base, subtract the exponent

Any base to the 0 power = 1

0^0 is undefined

X^-3 = 1/x^3

When you raise an exponential term, multiply the exponents

24
Q

Divide 2 decimals

A

Write the division as a fraction

Move the decimals in the same direction on the top and the bottom

Ex.: 300/0.05 = 30,000/5 = 6000
12.39/0.003 = 12,390/3=4130

25
Q

Expression

A

Represents a value

Does not contain an equal sign

To simplify:
1)	Combine like terms
2)	Find a common denominator
3)	Pull out a common factor
Cancel common factors
26
Q

High school algebra rule

A

1) N variables require N equations to solve
2) Good to use when P.S.
Does not always work w/D.S

27
Q

Odd exponents

A

Less than -1=> result is smaller
Between -1 and 0 =>result is bigger
Between 0 and 1 =>result is smaller
Greater than 1 => result is bigger

Odd exponents preserve the sign of the original expression

28
Q

Even exponents

A

Less than -1=> result is bigger
Between -1 and 0 => result I bigger
Between 0 and 1 => result is smaller
Greater than 1 => result is bigger

Even exponents hide the sign of the original number

An integer raised to a positive even power, is always a perfect square

29
Q

Equation I xI = a

A

When you have an equation in the form I x I =a with a>0, then x=+/- a

30
Q

Divide a number by (+) 10^x

A

When dividing any number by a positive power of 10, move the decimal to the left the specified number of places.

e.x: 4,162.9 /10^2 = 41.629

31
Q

Sector Area/Circle Area=

A

Arc Length/Circumference

32
Q

The Triangle Inequality Theorem

A

The sum of any 2 sides of a triangle must be greater than the measure of the third side

33
Q

Relationship between triangle side lengths and angles

A

Sides correspond to their opposite angles. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle.

34
Q

Parallelogram

A

Any 4-sided figure in which the opposite sides and a parallel and equal. Opposite angles are also equal, and adjacent angles add up to 180 degrees.

Perimeter=Sum of all sides
Area=base x height

35
Q

For any even number of consecutive integers,

A

the sum of all the integers is never a multiple of the number of integers

36
Q

Triple Venn diagrams can be solved with the following formula:

A

Sum of totals in three individual categories – (sum of items in exactly two categories) - (2 * number of items in all three categories) + Neither = Total

Math Memorizations (5 decks)

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