Mathematics is often explained in school as the language of
One of the first historical uses of math was for counting; to determine how much of something existed, e.g., there are five people, or 10 apples, etc. Later, this system was extended to measure distances so people could understand spatial relationships. However, to express the concept of quantity, a system of
, or numbers, was required. The Romans used Roman numerals, the Greeks used
The cardinal numbers are used to answers questions such as "How many?" and are:
1, 2, 3, 4, 5, 6, 7, and so on.
The ordinal numbers are used to answer questions such as "Which one?" and are:
1st, 2nd, 3rd, 4th, 5th, 6th, 7th, and so on.
The standard numerals, also known as the counting numbers, are arranged in a system of notation. The system we use now is known as the
, and every number in the decimal system can be
Each column represents the
Beyond hundreds, tens, and units, there are thousands, millions, billions, trillions, and so on. When a decimal number is greater than three digits, such as 4510 or 7900, it is typical to see a comma inserted every three digits from the right to break the number down and make it easier to read, such as 4,510 and 7,900. The comma system is extended to every three digits, as in 973,452,576,999.
Each column, whether hundreds, tens, units, or whatever, is called a number's
. If a number has 3 hundreds, no tens, and 2 units, it cannot be written as 32. It should appear as 302. The 0 is inserted into any column to
Nowadays, people often use the word "arithmetic" to mean mathematics in general. However,
actually refers to the basic operations that occur to
If I am the owner of one tomato, and after searching through the garden I find two more tomatoes, I will have increased my total of tomatoes to three. This process of combining two or more
If after collecting three tomatoes, someone comes along and steals one of my tomatoes, I shall be left with two. The process of reducing one quantity by another is called
, and the result of subtraction is called the
. So, the difference of 3
1 is 2. Subtraction is the
Increasing a quantity in terms of
is the opposite (or
) of multiplication. Rather than increasing a quantity, division is the process of determining how many times one quantity fits into another. The result of division is called the