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18 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Denominator
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A value or object that is being divided. Used in a fraction.
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Denominator = Nenner
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Numerator
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The value on the top of a fraction.
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Numerator = Zähler
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Finite and Infinite
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Something is said to be finite if it has an end. Something is said to be infinite if it has no end.
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For example, 1.5 has a finite number of digits after the decimal point. On the other hand, the decimal representation of has an infinite number of digits after the decimal point.
finite = endlich infinite = unendlich |
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Digits
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Digits are the basic symbols that we use to write numbers. There are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
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Numbers
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Numbers are created by combining one or more digits.
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For example, 13 is a two-digit number, 817 is a three-digit number, and −54,000 is a five-digit number.
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Decimal
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A decimal is any number that we represent using a string of digits with a decimal point (as opposed to fractions).
Decimals generally fall between consecutive integers, but we can also represent integers as decimals, by using trailing zeros. |
For example, the decimal 2.6 is between the integers 2 and 3, but we could also represent the integer 3 as a decimal with any number of trailing zeros: 3.00, or 3.00000.
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Fraction
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Like decimals, fractions are a way of expressing values that fall between consecutive integers.
A fraction consists of a number on top, a “slash” or “line” that represents the division operation, and a number underneath this line. The value on the top of a fraction is called the “numerator.” The numerator is a value or object that is being divided. The value on the bottom of a fraction is called the “denominator.” The denominator represents the number of equal portions that an object is divided into. The value of a fraction is equal to the numerator divided by the denominator. |
Fraction = Bruch
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Integer
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Integers include whole numbers and the negative counterparts of whole numbers.
All whole numbers are integers; not all integers are whole numbers (for example, -1 is not a whole number because it is negative). |
examples are: ... -3, -2, -1, 0, 1, 2, 3, ...
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Whole numbers
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Whole numbers include 0 and all positive numbers that do not have to be written as fractions or decimals.
Put differently, whole numbers are all non-negative integers. |
such as: 0, 1, 2, 3, 4 and so on
whole numbers = ganze zahlen |
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Place value
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Our standard way of writing numbers is called the decimal number system. In this system, each place to the left and to the right of the decimal point represents a power of ten.
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For example, 10^0 = 1 = one, 10^1 = 10 = ten, and 10^2 = 100 = one hundred.
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Parenthesis
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Klammerwert
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Order of Operations
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This means that in the presence of multiple operations, we must perform the operations in the correct order in order to arrive at the correct solution.
PEMDAS = Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. 1. Perform any operations inside of any parentheses. (Absolute value signs count as parentheses.) 2. Evaluate any exponents. 3. Do any multiplication and/or division (moving left to right). 4. Do any addition and/or subtraction (moving left to right). |
PEMDAS = Please Excuse My Dear Aunt Sally.
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Proper Fraction
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A proper fraction falls between 0 and 1. All proper fractions are positive. The numerator of a proper fraction is always smaller than its denominator (both must be positive).
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Examples: 1/6, 2/3, 19/20
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Mixed Number
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A combination of an integer and a proper fraction. Can also be thought of as the sum of a positive integer and a fraction.
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Example of mixed number: 1x3/2
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How to best compare fractions with different denumerators and numerators?
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In order to compare fractions with different numerators and denominators, we need to find a common denominator. We can then compare the fractions by comparing their numerators.
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What is an improper fraction?
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The denominator is smaller than the enuminator, so that the decimal value of the fraction is <0 or >=1.
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What is a proportion?
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An equation with a ratio on each side.
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Questions on proportions are often solved using cross-multiplication.
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What is an Associative Property?
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If the numbers or terms involved can be grouped inside parentheses in any way without changing the value of the group.
Addition and multiplication are both associative operations. Subtraction and division, however, are not associative. |
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