Introduction to Arithmetic
Arithmetic is a branch of mathematics which deals with study of numbers and operations on numbers.
Arithmetic topics list
- Numbers
- Number system
- Fractions
- Decimals
- Ratios
- Estimations and rounding off
- Arithmetic operations
- Factorization
- Percentages
- Interest calculations
- Interesting number patterns
- Arithmetic theorems
1. Numbers
Arithmetic is the study of numbers and it has different types of numbers e.g. natural numbers, whole numbers, integers and rational numbers. These rational numbers can be represented on a number line also.
There are another type of numbers which are prime number and composite numbers.
2. Number system
Number system or numeral system is the system which defines the symbols to help write numbers. The mathematicians has developed such number systems which we use till today. Hindu Arabic System and Roman Numerals systems are the most widely adapted numeral systems in the world.
There are place value and face value of a digit in a number, which can decide the value of a digit in a number. This also helps in determining if a number is greater or smaller than the other number.
When the numbers are larger in value there are shortcut ways to check if the numbers are divisible by any other numbers which can be found in Divisibility Rules of Numbers 2, 3, 4, 5, 6, 7, 8, 9, 10, 11.
3. Fractions
Fractions are used in maths to represent how many parts are there in a whole object.
There are different types of fractions, e.g. like fractions, unlike fractions, unit fractions etc.
The comparison of fractions can be done to check which fraction is greater or less, same like the natural numbers are compared. The fractions can also be written in ascending or descending orders.
The fractions can also be added (+), subtracted (-), multiplied (×) and divided (÷) same like other natural numbers, which can be learnt in Add, Subtract, Multiply and Divide Fractions.
4. Decimals
Decimals are the numbers which can be turned into fractions and vice versa. When quantities can not be expressed in whole number because they may also have an extra part like half, one third etc., there decimals help to express such numbers. The basics of Decimal numbers, how to write and convert them into fractions have been discussed in Read, Write Decimal Numbers. Converting Decimals to Fractions with solved examples and worksheets to practice.
5. Ratios
Ratios and proportions are the topics in arithmetic that helps in comparing two quantities. The chapter Ratio, Proportion and the Unitary method discusses how to write ratios and proportions with examples and worksheets.
6. Estimations and rounding off
Estimations those we can observe in real life while getting an estimate price list of some items that a shopkeeper or a seller provides, which contains the near prices, not the actual price of selling, to just guess how much a bill amount can reach to. Estimations are achieved by rounding numbers to their nearest whole numbers of 10, 100, 1000 etc. Steps to round off to the nearest 10, 100, 1000 can be found in the chapter Estimations by Rounding to the Nearest 10, 100 and 1000.
Decimals are no different, they can also be rounded to their tenths, hundredths etc. places or to a whole number. What are the steps to round a decimal number have been explained in Rounding off Decimal Numbers to the Nearest Places.
7. Arithmetic operations
How to add whole numbers using number line and the downward method where numbers are added by placing the digits of numbers under their ones, tens, hundreds or thousandths places. Learn how to use carryover while working on sums of numbers in the chapter Addition, Subtraction of Numbers on Number Line and Downward.
Addition, subtraction and multiplication operations on decimal numbers with their how to steps can be found in the chapter Decimals Addition, Subtraction, Multiplication and Division.
To add, subtract, multiply and divide integers, it is important to know about what are integers, their number line representation also. Arithmetic operations on integers varies depending upon if the participating integers in an operation are all positives or negatives or are of different signs. The details with solved examples and practice worksheets can be downloaded from Integers and Their Arithmetic Operations with Examples.
8. Factorization
Factorization is the fundamental technique of telling if a number has its multiples. Lowest common multiple (LCM) and highest common factor (HCF) are the chapters which use the concept of factorization.
9. Percentages
Percentage in arithmetic teaches about how to write percentages and how to convert percentages into fractions and decimals. There are formulas to calculate percentages on profits, loss, discounts and profit, loss and discount percentages and how to find the different prices like cost price, selling price, effective cost price are discussed in details in the chapter Profit Loss Discount Marked Price & Calculate Percentage.
10. Interest calculations
The day to day bank operations relies on interest calculations which comes under the branch of arithmetic. How do banks calculate interest on principal and formulas to find simple interest and compound interests can be read in the chapter Simple, Compound and Rate of Interest with Examples.
11. Interesting number patterns
As these patterns are completely related to numbers, which makes them a part of study under the branch arithmetic. There are magical pattern of 9, magical pattern of 11, magical pattern of 3367 and interesting pattern of Pascal's triangle, which is in fact a special set of numbers which can be arranged in rows and columns and produce a triangle of numbers. Pascal's triangle was introduced by a famous french mathematician and philosopher, Blaise Pascal.
12. Arithmetic theorems
Arithmetic has a famous theorem to study which is the Fundamental theorem of arithmetic which was introduced by Kamal al-Din Hasan ibn Ali ibn Hasan al-Farisi from Euclid's proposition 30, proposition 31 and proposition 32.
