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1.2 |
Basic Arithmetic Operations Involving Integers |
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Addition of integers: |
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- Positive integers is represented by moving towards the right.
- Negative integers is represented by moving towards the left.
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Subtraction of integers: |
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- Positive integers is represented by moving towards the left.
- Negative integers is represented by moving towards the right.
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Example |
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Solve:
(i)
\(\begin{aligned}6-(-7)&=6+7 \\\\&=13. \end{aligned}\)
(ii)
\(\begin{aligned}-21+(3)&=-21+3 \\\\&=-18. \end{aligned}\)
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Multiplication of integers: |
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Operation |
Sign of the product |
\((+)\times(+)\) |
\(+\) |
\((+)\times(-)\) |
\(-\) |
\((-)\times(+)\) |
\(-\) |
\((-)\times(-)\) |
\(+\) |
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Division of integers: |
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Operation |
Sign of the quotient |
\((+)\div(+)\) |
\(+\) |
\((+)\div(-)\) |
\(-\) |
\((-)\div(+)\) |
\(-\) |
\((-)\div(-)\) |
\(+\) |
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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.
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Example |
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Calculate:
(i)
\(\begin{aligned}9\times(-11)&=-(9\times11) \\\\&=-99. \end{aligned}\)
(ii)
\(\begin{aligned}-48\div(-8)&=+(48\div8) \\\\&=6 \end{aligned}\)
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Combined basic arithmetic operations of integer: |
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Example |
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Solve:
(i)
\(\begin{aligned}&\space49\div(-8+1)\\\\&=49\div(-7) \\\\&=-7. \end{aligned}\)
(ii)
\(\begin{aligned}&\space\dfrac{22+(-4)}{-7-2} \\\\&= \dfrac{22-4}{-9}\\\\ &=\dfrac{18}{-9}\\ \\&=-2. \end{aligned}\)
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Laws of arithmetic operations: |
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Commutative Law
\(\begin{aligned} a+b&=b+a \\\\a\times b&=b\times a \end{aligned}\)
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Associative Law
\(\begin{aligned} (a+b)+c&=a+(b+c) \\\\(a\times b)\times c&=a\times(b\times c) \end{aligned}\)
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Distributive Law
\(\begin{aligned} a\times(b+c)&=a\times b+a\times c \\\\a\times(b-c)&=a\times b-a\times c \end{aligned}\)
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Identity Law
\(\begin{aligned} a+0&=a \\\\a\times 0&=0 \\\\a\times 1&=a \\\\a+(-a)&=0 \\\\a\times\dfrac{1}{a}&=1 \end{aligned}\)
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