Solve the problems involving integer

Basic Arithmetic Operations Involving Integers

1.2

Basic Arithmetic Operations Involving Integers

Addition of integers:

Positive integers is represented by moving towards the right.
Negative integers is represented by moving towards the left.

Subtraction of integers:

Positive integers is represented by moving towards the left.
Negative integers is represented by moving towards the right.

Example

Solve:

(i)

\(\begin{aligned}6-(-7)&=6+7 \\\\&=13. \end{aligned}\)

(ii)

\(\begin{aligned}-21+(3)&=-21+3 \\\\&=-18. \end{aligned}\)

Multiplication of integers:

Operation	Sign of the product
\((+)\times(+)\)	\(+\)
\((+)\times(-)\)	\(-\)
\((-)\times(+)\)	\(-\)
\((-)\times(-)\)	\(+\)

Division of integers:

Operation	Sign of the quotient
\((+)\div(+)\)	\(+\)
\((+)\div(-)\)	\(-\)
\((-)\div(+)\)	\(-\)
\((-)\div(-)\)	\(+\)

In general,

The product or quotient of two integers with the same signs is a positive integer.
The product or quotient of two integers with different signs is a negative integer.

Example

Calculate:

(i)

\(\begin{aligned}9\times(-11)&=-(9\times11) \\\\&=-99. \end{aligned}\)

(ii)

\(\begin{aligned}-48\div(-8)&=+(48\div8) \\\\&=6 \end{aligned}\)

Combined basic arithmetic operations of integer:

Example

Solve:

(i)

\(\begin{aligned}&\space49\div(-8+1)\\\\&=49\div(-7) \\\\&=-7. \end{aligned}\)

(ii)

\(\begin{aligned}&\space\dfrac{22+(-4)}{-7-2} \\\\&= \dfrac{22-4}{-9}\\\\ &=\dfrac{18}{-9}\\ \\&=-2. \end{aligned}\)

Laws of arithmetic operations:

Commutative Law

\(\begin{aligned} a+b&=b+a \\\\a\times b&=b\times a \end{aligned}\)

Associative Law

\(\begin{aligned} (a+b)+c&=a+(b+c) \\\\(a\times b)\times c&=a\times(b\times c) \end{aligned}\)

Distributive Law

\(\begin{aligned} a\times(b+c)&=a\times b+a\times c \\\\a\times(b-c)&=a\times b-a\times c \end{aligned}\)

Identity Law

\(\begin{aligned} a+0&=a \\\\a\times 0&=0 \\\\a\times 1&=a \\\\a+(-a)&=0 \\\\a\times\dfrac{1}{a}&=1 \end{aligned}\)

Basic Arithmetic Operations Involving Integers

1.2

Basic Arithmetic Operations Involving Integers

Addition of integers:

Positive integers is represented by moving towards the right.
Negative integers is represented by moving towards the left.

Subtraction of integers:

Positive integers is represented by moving towards the left.
Negative integers is represented by moving towards the right.

Example

Solve:

(i)

\(\begin{aligned}6-(-7)&=6+7 \\\\&=13. \end{aligned}\)

(ii)

\(\begin{aligned}-21+(3)&=-21+3 \\\\&=-18. \end{aligned}\)

Multiplication of integers:

Operation	Sign of the product
\((+)\times(+)\)	\(+\)
\((+)\times(-)\)	\(-\)
\((-)\times(+)\)	\(-\)
\((-)\times(-)\)	\(+\)

Division of integers:

Operation	Sign of the quotient
\((+)\div(+)\)	\(+\)
\((+)\div(-)\)	\(-\)
\((-)\div(+)\)	\(-\)
\((-)\div(-)\)	\(+\)

In general,

The product or quotient of two integers with the same signs is a positive integer.
The product or quotient of two integers with different signs is a negative integer.

Example

Calculate:

(i)

\(\begin{aligned}9\times(-11)&=-(9\times11) \\\\&=-99. \end{aligned}\)

(ii)

\(\begin{aligned}-48\div(-8)&=+(48\div8) \\\\&=6 \end{aligned}\)

Combined basic arithmetic operations of integer:

Example

Solve:

(i)

\(\begin{aligned}&\space49\div(-8+1)\\\\&=49\div(-7) \\\\&=-7. \end{aligned}\)

(ii)

\(\begin{aligned}&\space\dfrac{22+(-4)}{-7-2} \\\\&= \dfrac{22-4}{-9}\\\\ &=\dfrac{18}{-9}\\ \\&=-2. \end{aligned}\)

Laws of arithmetic operations:

Commutative Law

\(\begin{aligned} a+b&=b+a \\\\a\times b&=b\times a \end{aligned}\)

Associative Law

\(\begin{aligned} (a+b)+c&=a+(b+c) \\\\(a\times b)\times c&=a\times(b\times c) \end{aligned}\)

Distributive Law

\(\begin{aligned} a\times(b+c)&=a\times b+a\times c \\\\a\times(b-c)&=a\times b-a\times c \end{aligned}\)

Identity Law

\(\begin{aligned} a+0&=a \\\\a\times 0&=0 \\\\a\times 1&=a \\\\a+(-a)&=0 \\\\a\times\dfrac{1}{a}&=1 \end{aligned}\)

Basic Arithmetic Operations Involving Integers

Basic Arithmetic Operations Involving Integers

Chapter : Rational Numbers

Topic : Solve the problems involving integer

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