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Mathematics: Formulas & Terms > 2. Fundamental Math Formulas & Rules > Flashcards

2. Fundamental Math Formulas & Rules Flashcards

1
Q

What is the essential rule when Adding Expressions with Variables?

A
  1. In order to add 2 expressions that involve variables, it must be the case that the expressions are identical except for the numerical coefficient of the expression. (These are often called “like terms.”)
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2
Q

What is rule 1 of 3 when working with Addition and Subtraction Parity?

A
  1. If you add or subtract 2 numbers that are even, then the result will be even
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3
Q

What is rule 2 of 3 when working with Addition and Subtraction Parity?

A
  1. If you add or subtract 2 numbers that are odd, then the result will be even
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4
Q

What is rule 3 of 3 when working with Addition and Subtraction Parity?

A
  1. If you add or subtract 2 numbers that have a different parity (one of the numbers is even and the other number is odd), then the result will be odd
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5
Q

What is the formula for the Area of a Circle?

A
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6
Q

What is the formula for the Circumference of a Circle?

A
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7
Q

What is the essential rule when Converting from a Mixed Number to an Improper Fraction?

A
  1. Multiply the whole number by the denominator and add the numerator
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8
Q

What is the essential rule when Converting from an Improper Fraction to a Mixed Number?

A
  1. The numerator is the dividend, and the denominator is the divisor. Divide, and make the quotient into the whole number part of the mixed number. Make the remainder the numerator of the fraction, and keep the divisor as the denominator
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9
Q

What is the essential rule when Converting from Decimals to Fractions?

A
  1. Write any whole numbers by themselves. Next, write what is to the right of the decimal point (leaving off the decimal point) as the numerator (the top of the fraction). Determine which place the last digit of the decimal is in (tenths, hundredths, thousandths, etc.). The denominator (the bottom of the fraction) is the number that corresponds to that place. If the last digit was in the hundredths place, the denominator would be 100. If the last digit was in the tenths place, the denominator would be 10.
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10
Q

What is the essential rule when Converting from Fractions to Decimals?

A
  1. Perform long division by dividing the denominator (the number on the bottom) into the numerator (the number on the top). Keep using more 0’s after the decimal point (as needed) until the answer comes out even or the numbers begin repeating
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11
Q

What is the essential rule when Converting from Percents to Decimals?

A
  1. Take the percent amount, move the decimal point 2 places to the left, and remove the percent sign
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12
Q

What is rule 1 of 3 when Converting from Percents to Fractions?

A
  1. Use the percent amount as the numerator (the top number) of the fraction
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13
Q

What is rule 2 of 3 when Converting from Percents to Fractions?

A
  1. Always make the denominator (the bottom number) 100.
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14
Q

What is rule 3 of 3 when Converting from Percents to Fractions?

A
  1. Simplify the fraction if needed
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15
Q

What is the essential rule when dividing Expressions with Variables?

A
  1. For any nonzero number x and any 2 integers a and b, x to the a/x to the b = x to the (a - b). In other words, you subtract the exponents when you divide 2 like varables
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16
Q

What is the Divisibility Rule for 2?

A
  1. A number is divisible by exactly 2 when its last digit is divisible by 2; in other words, a number is divisible by exactly 2 when the last digit of the number is a 0, 2, 4, 6, or 8
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17
Q

What is the Divisibility Rule for 3?

A
  1. A number is divisible by exactly 3 when the sum of all the digits of the number is divisible by 3.
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18
Q

What is the Divisibility Rule for 4?

A
  1. A number is divisible by exactly 4 when the number created from its last 2 digits is divisible by 4
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19
Q

What is the Divisibility Rule for 5?

A
  1. A number is divisible by exactly 5 when its last digit is divisible by 5; in other words, a number is divisible by exactly 5 when the last digit of the number is a 0 or 5.
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20
Q

What is the Divisibility Rule for 8?

A
  1. A number is divisible by exactly 8 when the number created from its last 3 digits is divisible by 8
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21
Q

What is the Divisibility Rule for 9?

A
  1. A number is divided by exactly 9 when the sum of all the digits of the number is divisible by 9
22
Q

What is the Divisibility Rule for 11?

A
  1. A number is divisible by exactly 11 when the alternating sum of all the digits of the number is divisible by 11
23
Q

What is the Essential Fact of Exponentiation?

A
  1. a to the 1 = a for any number a, and as long as a does not equal 0, a to the zero power = 1.
24
Q

What is the essential rule for Finding the Greatest Common Factor?

A
  1. Factor numbers to their prime factorization. Find the smaller occurrence of each prime number in the factors. Multiply these together to obtain the greatest common factor
25
Q

What is the essential rule for Finding the Least Common Denominator?

A
  1. Factor numbers to their prime factorization. Find the greatest occurrence of each prime number in the factors. Multiply these together to obtain the least common denominator
26
Q

What is the essential rule in How to Cross Multiply?

A
  1. Write the ratios as fractions. Multiply the numerator of the first fraction with the denominator of the second fraction. Then, multiply the denominator of the first fraction with the numerator of the second fraction. If you drew lines to show which numbers where being multiplied together, it would make an X in the center, or a cross - hence the term “cross multiply.”
27
Q

What is the formula to find the Midpoint of a Line Segment?

A
  1. Use the coordinates of the 2 endpoints as x and y
28
Q

What is rule 1 of 3 when working with Multiplication Parity?

A
  1. If you multiply 2 even numbers together, then the answer you get is an even number
29
Q

What is rule 2 of 3 when working with Multiplication Parity?

A
  1. If you multiply 2 odd numbers together, then the answer you get is an odd number
30
Q

What is rule 3 of 3 when working with Multiplication Parity?

A
  1. If you multiply an even number and an odd number, then the answer you get is an even number
31
Q

What is the essential rule when Multiplying Expressions with Variables?

A
  1. For any nonzero number x and any 2 integers a and b, x to the a times x to the b = x to the (a +b). In other words, you add the exponents when you multiply 2 like variables
32
Q

What is rule 1 of 6 when working with Operations with Signed Numbers?

A
  1. If you are subtracting a negative number, the number turns into a positive. For example, +3 - (-5) becomes +3 +5.
33
Q

What is rule 2 of 6 when working with Operations with Signed Numbers?

A
  1. When you are adding a negative number and a positive number, subtract the 2 numbers and take the sign of the number that has a larger absolute value.
34
Q

What is rule 3 of 6 when working with Operations with Signed Numbers?

A
  1. When you are adding 2 numbers that are both negative, add their absolute values together and put a negative sign in front
35
Q

What is rule 4 of 6 when working with Operations with Signed Numbers?

A
  1. When you multiply or divide 2 numbers that are both positive, the answer is positive
36
Q

What is rule 5 of 6 when working with Operations with Signed Numbers?

A
  1. When you multiply or divide 2 numbers that are both negative, the answer is positive
37
Q

What is rule 6 of 6 when working with Operations with Signed Numbers?

A
  1. When you multiply or divide 2 numbers that have different signs, the answer is negative
38
Q

What is rule 1 of 3 when working with Operations with Square Roots?

A
  1. You can multiply the numbers under the square root symbols if the 2 are being multiplied. For example, square root 20 x square root 5 = square root 100.
39
Q

What is rule 2 of 3 when working with Operations with Square Roots?

A
  1. If there is addition or subtraction under the radical symbol, you cannot break the numbers into separate square roots. For example, square root 16 - 4 is not the same as square root 16 - square root 4.
40
Q

What is rule 3 of 3 when working with Operations with Square Roots?

A
  1. You can only add or subtract square roots if the number under the radical symbol is the same
41
Q

What is rule 1 of 3 when working with Parallelograms?

A
  1. The sum of the degrees of the angles inside a parallelogram, rectangle, or square is always 360 degrees
42
Q

What is rule 2 of 3 when working with Parallelograms?

A
  1. The area of any parallelogram, rectangle, or square is equal to b x h, where b is the base and h is the height
43
Q

What is rule 3 of 3 when working with Parallelograms?

A
  1. The perimeter of any such object is the sum of the lengths of the 4 legs
44
Q

What is the formula for the Rule of Fractional Exponents?

A
  1. a to the b/c = (a to the b) to the 1/c and a to the b/c = (a to the 1/c) to the b
45
Q

What is the formula for the Rule of Negative Exponents?

A
  1. a to the -b = 1/a to the b
46
Q

What are the 6 steps in the Order of Operations?

A
  1. Parenthesis
  2. Exponents
  3. Multiplication (left to right)
  4. Division (left to right)
  5. Addition (left to right)
  6. Subtraction (left to right)
47
Q

What is the formula for the Slope of a Straight Line?

A
48
Q

What is the rule for the Sum of Degrees for a Regular Polygon?

A
  1. It is exactly 180 times the number that is 2 less than the number of legs. It can be written as 180 x (L - 2), where L is the number of legs (sides) in a polygon
49
Q

What is the essential rule of Theoretical Probability?

A
  1. If a sample space has n equally likely outcomes and an event A occurs in m of these outcomes, then the theoretical probability of event A is denoted by p(A) and is given by p(A) = m/n
50
Q

What is rule 1 of 3 when working with Triangles?

A
  1. The sum of the degrees of the angles inside a triangle is always 180 degrees
51
Q

What is rule 2 of 3 when working with Triangles?

A
  1. The area of a triangle is equal to 1/2 x b x h, where b is the base and ha is the height of the triangle
52
Q

What is rule 3 of 3 when working with Triangles?

A
  1. The perimeter of a triangle is the sum of the lengths of the 3 legs

Mathematics: Formulas & Terms (6 decks)

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