Class Notes: Arithmetic in Mathematics
Introduction to Arithmetic:
Arithmetic is the branch of mathematics that deals with numbers and the basic operations
used to manipulate them. The primary operations of arithmetic include addition, subtraction,
multiplication, and division. These fundamental operations form the foundation of more
complex areas of mathematics and are essential for problem-solving in daily life.
Basic Operations in Arithmetic:
1. Addition (+): Addition is the process of finding the total or sum by combining two or
more numbers. The numbers being added are called addends, and the result is called
the sum.
Example:
o 5+7=12 In this case, 5 and 7 are the addends, and 12 is the sum.
2. Subtraction (−): Subtraction is the operation of removing objects from a collection. It
represents the difference between two numbers. The number from which another
number is subtracted is called the minuend, and the number being subtracted is the
subtrahend. The result is known as the difference.
Example:
o 10−4=6 Here, 10 is the minuend, 4 is the subtrahend, and 6 is the difference.
3. Multiplication (×): Multiplication is the process of combining equal groups. It is a
shortcut for repeated addition. The numbers being multiplied are called factors, and
the result is called the product.
Example:
o 4×3=12 In this case, 4 and 3 are the factors, and 12 is the product.
, 4. Division (÷): Division is the process of splitting a number into equal parts. The
number being divided is the dividend, the number by which it is divided is the
divisor, and the result is the quotient.
Example:
o 15÷3=5 Here, 15 is the dividend, 3 is the divisor, and 5 is the quotient.
Properties of Arithmetic Operations:
1. Commutative Property:
o Addition: a+b=b+a
o Multiplication: a×b=b×a
This property states that the order in which two numbers are added or multiplied does
not affect the result.
Example:
o 3+5=5+3=8
o 2×4=4×2=8
2. Associative Property:
o Addition: (a+b)+c=a+(b+c)
o Multiplication: (a×b)×c=a×(b×c)
The associative property indicates that how numbers are grouped in an operation does
not change the result.
Example:
o (2+3)+4=2+(3+4)=9
o (3×2)×5=3×(2×5)=30
3. Distributive Property: The distributive property links addition and multiplication,
stating that a number multiplied by a sum is the same as multiplying each addend
separately and then adding the results.
o Multiplication over addition: a×(b+c)=a×b+a×c
Example:
o 3×(4+2)=(3×4)+(3×2)=12+6=18
Introduction to Arithmetic:
Arithmetic is the branch of mathematics that deals with numbers and the basic operations
used to manipulate them. The primary operations of arithmetic include addition, subtraction,
multiplication, and division. These fundamental operations form the foundation of more
complex areas of mathematics and are essential for problem-solving in daily life.
Basic Operations in Arithmetic:
1. Addition (+): Addition is the process of finding the total or sum by combining two or
more numbers. The numbers being added are called addends, and the result is called
the sum.
Example:
o 5+7=12 In this case, 5 and 7 are the addends, and 12 is the sum.
2. Subtraction (−): Subtraction is the operation of removing objects from a collection. It
represents the difference between two numbers. The number from which another
number is subtracted is called the minuend, and the number being subtracted is the
subtrahend. The result is known as the difference.
Example:
o 10−4=6 Here, 10 is the minuend, 4 is the subtrahend, and 6 is the difference.
3. Multiplication (×): Multiplication is the process of combining equal groups. It is a
shortcut for repeated addition. The numbers being multiplied are called factors, and
the result is called the product.
Example:
o 4×3=12 In this case, 4 and 3 are the factors, and 12 is the product.
, 4. Division (÷): Division is the process of splitting a number into equal parts. The
number being divided is the dividend, the number by which it is divided is the
divisor, and the result is the quotient.
Example:
o 15÷3=5 Here, 15 is the dividend, 3 is the divisor, and 5 is the quotient.
Properties of Arithmetic Operations:
1. Commutative Property:
o Addition: a+b=b+a
o Multiplication: a×b=b×a
This property states that the order in which two numbers are added or multiplied does
not affect the result.
Example:
o 3+5=5+3=8
o 2×4=4×2=8
2. Associative Property:
o Addition: (a+b)+c=a+(b+c)
o Multiplication: (a×b)×c=a×(b×c)
The associative property indicates that how numbers are grouped in an operation does
not change the result.
Example:
o (2+3)+4=2+(3+4)=9
o (3×2)×5=3×(2×5)=30
3. Distributive Property: The distributive property links addition and multiplication,
stating that a number multiplied by a sum is the same as multiplying each addend
separately and then adding the results.
o Multiplication over addition: a×(b+c)=a×b+a×c
Example:
o 3×(4+2)=(3×4)+(3×2)=12+6=18
