Arithmetic: It is one among the oldest and elementary branches of mathematics,
originating from the Greek word ‘arithmos’ means number. It deals with numbers and the basic
operations- addition, subtraction, multiplication, and division, between them.
Components
of Arithmetic:
3.
Decimals
5.
Percentages
8.
Surds
10. Integers
Arithmetic operations:
The basic operations under
arithmetic are addition and subtraction, division and multiplication although the subject
involves many other modified operations.
Addition (+)
Addition is among the basic operations in arithmetic. In simple
forms, addition combines two or more values into a single term, for example: 2
+ 5 = 7, 6 + 2 = 8.
The procedure of adding more than two values is called
summation and involves methods to add n number of values.
The identity element of addition is 0, which means that
adding 0 to any value gives the same result. The inverse element of addition is
the opposite of any value, which means that adding opposite of any digit to the
digit itself gives the additive identity. For instance, the opposite of 5 is -5,
therefore 5 + (-5) = 0.
Subtraction (−)
Subtraction can be labelled as the inverse of addition.
It computes the difference between two values, i.e, the minuend minus the
subtrahend. If the minuend is greater than the subtrahend, the difference is
positive. If the minuend is less than the subtrahend, the result is negative,
and 0 if the numbers are equal.
Multiplication (×)
Multiplication also combines two values like addition and
subtraction into a single value or the product. The two original values are
known as the multiplicand and the multiplier, or simply both as factors.
The product of a and b is expressed as a·b or a x b. In
software languages wherein only characters are used that are found in
keyboards, it is often expressed as, a*b (* is called asterisk).
Division (÷)
Division is the inverse of multiplication. It computes
the quotient of two numbers, the dividend that is divided by the divisor. The
quotient is more than 1 if the dividend is greater than divisor for any
well-defined positive number, else it is smaller than 1.
Arithmetic Problems
Question 1: The sum of two numbers is 50
and their difference is 30. Find the numbers.
Solution: Let the numbers be x and y.
Now, as per the given situation,
x + y = 50……………………(i)
and x – y = 30………………(ii)
We can write, x = 50-y, from eq.(i),
Therefore, putting the value of x in eq(ii), we get,
50 – y – y = 30
50 -2y = 30
2y = 50-30= 20
y = 20/2 = 10
and x = 50 – y = 50-10 =40
Therefore, the two numbers are 40 and 10.
Question 2: Solve 25+5(27÷3)-9
Solution: 25 + 5(27 ÷ 3) – 9
= 25
+ 5(9) – 9 = 25 + 45 – 9
=70 – 9 = 61
Concept of 70% of 30 is 21
70 is the percent.; 30 is the base ; 21 is the part.
To determine the percentage: we have to divide the numerator by denominator and then multiply the resultant to 100.
Percentage formula = (Numerator/Denominator)×100
Example: 2/5 × 100 = 0.4 × 100 = 40 per cent
Question 3: Calculate 10% of 80.
10% of 80 = 10/100 × 80 = 8
Another Methods:
(1)
Find the value of 5% of 575
Solution:-
(5×575)
÷100 =2875÷100=28.75
(2) Find the value of 20% of 500
Solution:- 20 × 5 = 100
(3) How to multiply-
(i) 65 by 65
(ii)
105 by 105
Solution:-
(i) After 6 number is 7. So 1st multiply 6 by 7,
Means 42 and then put 25. So answer is 4225.
(ii) After 10
is 11. So 1st mutiply10 by 11
Means 110 and then put 25. So answer is 11025.
[NOTE:-
We may apply if last digit is 5 with any
same number]
Question 4: Suman has a monthly salary of Rs.1200. She
spends Rs.280 per month on food. What percent of her monthly salary does she
save?
Solution- Suman’s monthly salary = Rs.1200
Savings of Suman = Rs. (1200 – 280) = Rs. 920
Fraction of salary she saves = Rs. (920÷1200)
Percentage of salary she saves = (920÷1200) ×100 =76.667 %
Solution: The number 12345 can be expressed as:
12345 = 1 × 10000 + 2 × 1000 + 3 × 100 + 4 × 10 + 5 × 1
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