Division
Distributing a quantity into some equal parts such that each part contains equal amount is called division.
In another way, you are given 8 chocolates and told to distribute them among your four friends such that each of them gets equal number of chocolates. Then you will give 2 hocolates to each of your friend. You separate a quantity (Here 8 chocolates) into four parts (Here your friends) such that each of the parts contains equal amount,
You have 60 books and you want to keep them into 5 drawers such that each drawer contains equal number of books. How will you find how many books should you keep in each drawer?
Solution: To find solution first see the quantity that is to be distributed (Here 60 books) then find the number of parts among which quantity is to be distributed (Here 5 drawers)
Now divide the quantity by the number of parts. Therefore, the amount each \[\text{Parts contains}=\frac{\text{Total quantity}}{\text{Number of parts}}=\frac{60}{5}=12\]
By the division we easily find that we should keep 12 books in each drawer.
Terms Related to Division
The quantity that is to be divided is called DIVIDEND. Number of parts in which the quantity is to be divided is called DIVISOR. The amount that each group gets is termed as QUOTIENT. The extra amount which is left after equal distribution is called REMAINDER.
Divide 8 by 3 and find the terms, dividend, divisor, quotient, remainder.
Solution: \[Divisor\,\to 3\overset{2}{\overline{\left){\begin{align} & 8 \\ & \underline{6} \\ & 2 \\ \end{align}}\right.}}\begin{matrix} \to Quotient \\ \to Dividend \\ \begin{align} & \\ & \to \operatorname{Re}mainder \\ \end{align} \\ \end{matrix}\]
Here, Dividend = 8, Divisor = 3, Quotient = 2, Remainder = 2
Relation between the Terms of Division
\[\text{Dividend}=\text{Divisor}\times \text{Quotient}+\text{Remainder}\]
Divide 504 by 15 and verify the relation
Solution: \[\begin{align} & 15)5\,0\,4(33 \\ & \,\,\,\,\,\,\,\frac{-\,4\,5}{\begin{align} & 0\,5\,4 \\ & \frac{-\,4\,5}{\,\,\,0\,9} \\ \end{align}} \\ \end{align}\]
Dividend = 504, Divisor = 15, Quotient = 33, Remainder = 9
Thus \[\text{5}0\text{4}=\text{15}\times \text{33}+\text{9}\]
Or \[\text{5}0\text{4}=\text{495}+\text{9}\]Or\[\text{5}0\text{4}=\text{5}0\text{4}\]
Operation on Division
Divide 256458 by 35.
Step 1: Consider the first digit of the dividend from left. If the digit is smaller than the divisor, multiply the divisor by 0. Place the product below the number and the multiplier in the quotient side. Now subtract the product from the number.
\[\begin{align} & \text{35})\text{256458}(0 \\ & \,\,\,\,\,\,\,\frac{-\,\,0}{\,\,\,\,2} \\ \end{align}\]because 2 (the first digit of the dividend from left) is smaller than 35
Step 2: Bring down the second digit of the dividend and write it right to the difference. Now compare the formed more... 
Multiplication
When a quantity is added to itself number of times, use operation of multiplication to find the resulting quantity. Look at the following problems:
If one box contains 20 pencils, how many pencils are there in 154 boxes?
Solution:
To answer the question we will have to add the number of pencils contained by all 154 boxes.
Thus 20 + 20 + 20 + 20 ...... 154 times
Or 20 x 154 = 3080
There are 3080 pencils in 154 boxes.
Find the correct option for \[\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}+\mathbf{7}\].
(a)\[\text{7}\times \text{7}\]
(b) \[\text{7}\times \text{9}\]
(c)\[\text{7}\times \text{8}\]
(d) \[\text{9}\times \text{9}\]
(e) None of these
Answer (b)
Explanation-\[~\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}+\text{7}=\text{7}\times \text{9}\]
Terms Related to Multiplication
In the multiplication, the number which is multiplied is known as MULTIPLICAND, the number by which the multiplicand is multiplied is known as MULTIPLIER and the answer or the result of multiplication is known as PRODUCT.
\[\text{45}\times \text{5}=\text{225}\]. Here 45 is the multiplicand, 5 is the multiplier and 225 is the product.
Multiplication of a Number by Power of 10
Power of 10 = 10, 100, 1000, 10000 ......
Step 1: Write the required number and power of 10 in multiplication form Like\[\text{4568}\times \text{1}00\].
Step 2: Put as many zeroes extreme right to the number, as contained by the power of 10. For example like\[\text{4568}\times \text{1}00=\text{4568}00\]
Multiply 89456 by 1000
Solution: The power of 10 contains three zeroes. Therefore, put three zeroes extreme right to the number 89456.
Thus\[\text{89456}\times \text{1}000\text{ }=\text{ 89456}000\]
Operation on Multiplication
Step 1: Write the multiplier below the multiplicand and put a sign of multiplication.
\[\,\,\,\,\,\,\,\,\,\,\,\begin{matrix} \text{Like} & \begin{align} & \text{4566}0\text{8} \\ & \underline{\times \,\,\,\,\,\,\,\text{546}} \\ \end{align} \\ \end{matrix}\]
Step 2: Now multiply the multiplicand with the first digit of multiplier more... 
Introduction
In this chapter you will study about two important arithmetic operations "multiplication and division". Multiplication is repeated addition of a specific quantity whereas division is a distribution of a quantity into some equal parts. Let us study them. 
Subtraction
Subtraction is the method by which we know the remaining after taken away some quantity from a certain quantity.
Operation of Subtraction on the Numbers
Subtract 4564569 from 9875469
Step 1: Arrange the digits of the numerals as per the place value chart.
| T-C | C | T-Th | Th | H | T | O | |||||||||||||||||||||||||||||||||||||||||
| 9 | 8 | 7 | 5 | 4 | 6 | 9 | |||||||||||||||||||||||||||||||||||||||||
| 4 | 5 | 6 | 4 | more...
 Addition
Addition is one of the very common arithmetic operation used in mathematics. Addition is the operation to know the total quantity when two or more than two quantities are taken together.
 Operation of Addition on the Numbers:
Add 6072564 and 2545623
Step 1: Arrange the digits of the numbers in place value chart:
|
Introduction
In our daily life, we come across many activities when we need to apply the method of addition and subtraction. We are aware of numbers and number system now we will discuss about two simple Arithmetic operations addition and subtraction. 
Rules to Write Roman Numerals
Rule 1: If a symbol is repeated in a Roman Numeral, the value of the numeral is obtained by adding the value of the symbols. For example
II = 1 + 1 = 2, III = 1 + 1 + 1 = 3
Rule 2 : In a Roman numeral, if a symbol at the left having greater value than the symbol at the right, add the values of these two symbols. For example
VI = 5 + 1 = 6 , XI = 10 + 1 = 11
Find the value of the Roman numeral XV. Solution:
Rule 3: In a Roman numeral, if a symbol at the right having greater value than the symbol at the left, difference of their value is the resulting value. For example 
Rule 4: The symbols I, X, C and M can be repeated in a Roman numeral whereas V, L and D cannot be repeated. Note: No symbols can be repeated more than three times. 
See the following table:
Introduction
The numerals, we use is commonly known as hindu -Arabic Numerals. 0, 1, 2, 3, 4, 5,6, 7, 8, 9 _ _ _ _ etc. are example of hindu-Arabic numerals. In ancient time Romans developed a system of numerations (numbering) which is known as Roman Numerals. I, II, III, IV, V, VI, VII, VIII, IX, _ _ _ etc. are example of Roman Numerals.
Roman numerals are formed by using the following symbols:
Puzzle Related to Numerals
There are different ways to solve a puzzle by finding a proper relation between the given information.
What is missing number in the centre of square?
Solution:
20 + 10 = 30
What is the missing number in the square?
(a) 23
(b) 22
(c) 25
(d) 28
(e) None of these
Answer (c)
Explanation
\[5\times 5=25,\,40-15\,\,=\,25,\,\,25-0=25,\,\,20\,+\,5\,=25\] 
Number series
Around us, there are different kinds of things. They are in the form of clothes, wrapping papers, carpets and many more. A pattern of the things can be in different shapes or design repeated in a particular way. For example, look at the series of shapes given below:
There are four groups of picture shown above and each group has circles and squares in this way the first group has one square and one circle, second has two squares and one circle, third has two square and two circles, and fourth has three squares and two circles. Therefore, according to the above pattern the fifth group of the following pattern will have three squares and three circles. Numbers can also be in patterns as given below:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, _ _ _ _ _ _ _ _ _ .
The system or the relation between the consecutive numbers is very simple, adding 2 to a number gives the next number. In this chapter, we will see many more system of relation of numbers.
System Charts and Tables of Numbers
Row Column
