1. General Flashcards
Mathematics
The abstract science of quantity, structure, space, and change.
Pure Mathematics
The study of mathematical concepts without concern for practical applications in the real world.
Applied Mathematics
The application of mathematical concepts by various fields such as physics, engineering, medicine, biology, finance, business etc.
Arithmetic
The study of numbers, their operations, and properties.
Operations of Arithmetic
Addition, Subtraction, Multiplication, and Division.
Addition
An operation that combines numbers to find their total.
Addens
Numbers being combined in an addition.
Sum
The result of an addition.
Subtraction
An operation that finds the difference between two quantities.
Minuend
The number to be subtracted from.
Subtrahend
The number that subtracts.
Difference
The result of a subtraction.
Multiplication
An operation of repeated addition of groups of equal sizes.
Factors
Numbers multiplied to get a product.
Product
The result of a multiplication.
Division
An operation that splits a quantity into equal parts or groups.
Divisor
A number that divides another number.
Dividend
A number that is divided by another number.
Quotient
The result of a division.
Remainder
The remaining quantity left over after a division.
What are properties of arithmetic?
Mathematical laws that describe how numbers interact when used in arithmetic operations.
Properties of Arithmetic
Commutative, Associative
Distributive, Identity, and Inverse.
Commutative Property
States that the order of numbers being added or multiplied does not affect the result.
Associative Property
States that the order in which numbers are grouped when adding or multiplying does not affect the result.
Distributive Property
States that multiplying a sum/difference by a number is the same as multiplying the addens/minuend/subtrahend by the number, and then adding/subtracting the products.
Identity Property
States that the sum of any number and zero is the orginal number. And the product of any number and one is the original number.
Inverse Property
States that every number has an additive inverse (Opposite) that, when added, gives zero. And every non zero number has a multiplicative inverse (Reciprocal) that, when multiplied, gives one.
Fraction
A numerical quantity that is not a whole number.
Numerator
The number of equal parts of a whole that you have/consider.
Denominator
The number of parts that a whole is equally divided into.
Proper Fraction
A fraction where the denominator is greater than the numerator.
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator.
Equivalent Fractions
Fractions that have different numerators and denominators but are equal to the same value, representing the same portion of the whole.
Place Value
The value of a digit in a number based on it’s position.
Standard Form
A way of expressing numbers using digits. (642)
Expanded Form
A way of expressing numbers by place value. (600+40+2)
Regrouping
The process of regrouping/changing place value groups when performing addition or subtraction.
Place Value Chart
A model that organizes the values of each digit in a number based on it’s position.
Regrouping in Subtraction
Regrouping place value groups to make up for the lack of digits within a given place vlaue group.
Algorithm
A finite sequence of instructions designed to solve a specific problem.
Regrouping in Addition
Regrouping place value groups to make up for a lack of space in a given place value group.
Standard Algorithm
The standardized algorithm or system designed to perform mathematical operations.
Base 10 math/Decimal system
A numeral system that uses 10 as it’s base and contains 10 digits.
Multiplying a number by 10, 100, or 1,000
The factor multiplied by 10, 100, or 1,000 will take a 10s, 100s, or 1,000s place value.
Multiplying a number by multiples of 10, 100, or 1,000
You can break down the operation into groups, using the associative property, then multiply the number by 10, 100, or 1,000.
Multiplying in general
The operation can be simplified by using the distributive property.
Powers of ten
Numbers that are the result of multiplying 10 by itself a specific number of times.
