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