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Basics of Arithmetic
by Ron Kurtus (11 January 2008)
Arithmetic is a fundamental branch of Mathematics that is concerned with numbers and their operations. The subject starts with counting and the number or numeric system. Then arithmetic considers the major operations on numbers, such as addition, subtraction, multiplication and division. The third area is applying these operations on fractions and decimals.
Questions you may have include:
- What is a numeric system?
- What are the major operations in arithmetic?
- What are fractions and decimals?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Counting and the numeric system
You can count objects such as your ten fingers. Each quantity has a name, such as one, two, three, and so on. Associated with those names of quantities of objects are symbols that you can write down: 1, 2, 3, and so on.
Our numeric system is based on the total number of fingers that an average person has. We write down the first ten numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and then we start over with 11, 12, 13 and so on.
The ancient Maya of Central America used a system based on 20. In other words, they counted both on their fingers and their toes. Ancient Babylonians—for some reason—used a numeric system based on 60.
Before you can start with arithmetic operations, you need to know how to count.
Arithmetic operations
The major arithmetic operations are addition, subtraction, multiplication and division.
Addition
If you have a certain number of objects and want to include another group of objects, you add them together. Counting the total amount is made easier by knowing how to add. For example, if you have three objects and want to include four more objects, you can add 3 plus 4, which equals 7. Otherwise, you will count 1, 2, 3, and then continue with the next four numbers, 4, 5, 6, 7 to reach the total of 3 plus 4.
The sign for addition is the plus sign: +. The sign for equals is: =.
Adding 6 plus 7 equals 13 is written: 6 + 7 = 13.
Subtraction
Subtraction is going in the opposite direction. If you hold up 7 fingers and then put down 3 of them, you are subtracting 3 from 7, which equals 4.
The subtraction or minus sign is: −.
Thus, 13 minus 5 equals 8 is written: 13 − 5 = 8. Other ways of indicating subtraction are: 13 less 5 and subtract 5 from 13.
Multiplication
Multiplication is repeated addition. If you add 5 with itself 3 times, you would add 5 + 5 + 5. Designating that as multiplication, you would say 3 times 5 or 3 × 5.
There are several multiplication or times signs: ×, · and *.
Division
Division is the opposite of multiplication. If you have the number 15, what number would you add 3 times to equal 15? Or you could say, what number times 3 equals 15? Dividing 15 by 3 results in 5. Or 15 ÷ 3 = 5.
There are two division signs: ÷ and /.
Fractions and decimals
Fractions and decimals are numbers less than 1 that represent an incomplete division. Fractions and decimals can both be added to whole numbers.
Fractions
Fractions are representations of incomplete division. The fraction 3/43 divided by 4. Since 4 is larger than 3, the division process stops.
A fraction can be added to a whole number, resulting in a complex fraction. For example 2 + ¾ can be rewritten as the complex fraction 2¾. It is called two and three fourths.
Fractions can be added, subtracted, multiplied and divided, but the method and rules are somewhat different than for whole numbers.
Decimals
A decimal is a representation of a fraction in the base of 10. For example, the fraction 3/10 is written as a decimal as 0.3 and 27/100 is written as 0.27.
Adding a decimal to a whole number results in a complex decimal such as 2 + 0.3 = 2.3.
The advantage of decimals is that the arithmetic operations are all pretty straightforward.
Summary
Arithmetic is a branch of Mathematics concerned with numbers and their operations. The first area in arithmetic is counting and the number or numeric system. Then it considers the major operations on numbers, such as addition, subtraction, multiplication and division. The third area is applying these operations on fractions and decimals.
Try to be number one
Resources
The following resources provide information on this subject:
Websites
Books
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Arithmetic. If you had problems, you had better look over the material again.
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