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28 Cards in this Set

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Order of Operations
What is the sequence in which you perform math operations in a complicated expression?
Parentheses
Exponents
Multiplication and
Division
Addition and
Subtraction
How do you add (or subtract) fractions with the same denominator?
Add (or subtract) the numerators.

Example: 3/5 + 1/5 = 4/5
How do you add (or subtract) fractions with different denominators?
Change the form of the fraction so that the 2 denominators are alike. You do this by multiplying one or both fractions by 1, in the form 2/2 or 5/5, etc. Example: 3/5 + 1/2 = 6/10 + 5/10 = 11/10.
How do you multiply 2 fractions?
Simply multiply the numerators together and multiply the denominators together.
Example: 3/4 x 2/5 = 6/20 (= 3/10)
How do you divide by a fraction?
Flip the 2nd fraction over and then multiply.

Example: 7 / 5/3 = 7 x (3/5) = 21/5
How do you find the decimal equivalent of a fraction?
The fraction bar represents division. Use your calculator to divide the numerator by the denominator.

Example: 2/3 = 2 ÷ 3 = 0.666...
When is a fraction undefined?
A fraction is considered undefined when its denominator is zero because it is meaningless to divide a number by zero.

Example: 4/(x-3) is undefined when x=0.
How do you use cross multiplication?
When both sides of an equation are in fractional form, you can cross multiply to produce an equivalent equation with no fractions. This makes algebra easier. Ex: 3/5 = 4/x. Cross multiply to get 3x = 20 so x = 20/3.
What are percentages?
A percentage expresses a quantity as a fraction in hundredths of another quantity. For example, if a slice is 35% of a pie, the slice is 35/100 of the whole pie. If you know any 2 of these quantities, you can solve for the 3rd.
How do ratios work?
Ratios relate parts to parts. For example, suppose a garden consists of ross and daffodils in the ratio of 4:5. In fractional terms, the garden contains 4/9 roses and 5/9 daffodils. Here's how to solve problems with ratios: If there are 4x roses and 5x daffodils, there are 9x flowers overall. By solving for x, you can determine the values of roses, daffodils, or total flowers.
How do proportions work?
When 2 quantities are related proportionally, they always produce the same quotient (i.e. a/b = c/d). If you know any 3 of the unknowns, you can solve for the 4th by cross multiplying. Just remember to make sure that the same quantity is found on TOP of both fractions and that the units match.
What does it mean that x and y are in direct variation (or x varies directly as y)?
It means x and y are related proportionally. They will always produce the same quotient. You can express this relationship like a proportion. Given any 3 of the quantities, you can solve for the 4th by cross multiplying.
When can you add or subtract exponential terms?
You can only add or subtract exponential terms when they have the same base and exponent. For example, x² + 3x² = 4x².
How do you multiply 2 exponential terms with the same base?
Add the exponents.
For example, x² x x¹ = x³
How do you multiply exponential terms with different bases and the same exponent?
Multiply bases and don't change the exponent.
For example, 3ª x 4ª = 12ª
How do you divide exponential terms with the same base?
Subtract the exponents.
Example: x³ ÷ x² = x¹
How do you divide exponential terms with the same base?
Subtract the exponents.
Example: x³ ÷ x² = x¹
How dd you raise an exponential term to another power?
Multiply the exponents.

For example (x²)ˆ8 = xˆ16 (note: read this as x² to the 8th power = x to the 16th power)
How do you convert a decimal number into scientific notation?
1. Move the decimal point until the number's value is between 1 and 10 - in other words, until there is only one digit to the left of the decimal point.
2. Count the number of places the decimal point must be moved to return the number to its original position. If the decimal point must be moved to the right, make it positive; if left, then negative. Example: .0034 = 3.4 x 10^(-3)
In a square root, what is the number under the radical sign (ã) called?
The radicand.
What is the square root sign (ã) called?
Radical.
What are the associative property for addition and the associative property for multiplication?
The associative properties state that it doesn't matter how you GROUP values when you add them or multiply them together. For example, (a+b)+c = a+(b+c) for addition and (ab)c=a(bc) for multiplication.
What does the distributive property state?
For any real numbers a, b and c,
a(b+c) = ab + ac.
What are the commutative property for addition and the commutative property for multiplcation?
The commutative properties state that ORDER doesn't matter. For addition, a+b=b+a (e.g. 3+6=6+3). For multiplication, ab=ba (e.g. 3x6 = 6x3).
How can you simplify a square root if the radicand is a MULTIPLE of a perfect square (example: the square root of 72)?
The root of the perfect square can be pulled out of the radical.

For example, the square root of 72 = the square root of (36 x 2) = 6 x the square root of 2.
How do you add or subtract square roots?
Example: 2(the square root of 5)+ 3(the square root of 5)
You can add or subtract square roots only when they have the same radicand. Example: 2(the square root of 5)+ 3(the square root of 5) = 5(the square root of 5)
How do you multiply square roots? Example: (the square root of 5) x (the square root of 7)
Multiply the radicands and keep the product under the radical. Example: (the square root of 5) x (the square root of 7) = the square root of 35.
When is a radicand a perfect square?
A radicand is a perfect square if it can be expressed as an integer. For example, the square root of 25 is 5.