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| − | == Variable ==
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| − | In mathematics, a variable is a
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| − | value that may change within the scope of a given problem or set of
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| − | operations. In contrast, a constant is a value that remains
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| − | unchanged, though often unknown or undetermined.[1] The concepts of
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| − | constants and variables are fundamental to many areas of mathematics
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| − | and its ''<u>applications.</u>''
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| − | A "constant" in this context should not be confused with a
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| − | mathematical constant which is a specific number independent of the
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| − | scope of the given problem.
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| − |
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| − | One may use any letteras m,l,p,x,y,z etc to show a variable . Remeber , a
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| − | variable is a number which does not have a fixed value. For ex ,the
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| − | number 5 or the 100 or any other given number is not a variable. They
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| − | are fixed values.(constant). Similiarly the number of angles of a
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| − | triangle has a fixed value i e 3. It is not a variable.The number of
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| − | corners of a qudrilateral is fixed (4 ) it is also not a variable.
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| − | But the measurement of each side of a qudrilateral is not fixed.
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| − |
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| − | == Dependent and independent variables ==
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| − |
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| − | Variables
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| − | are further distinguished as being either a dependent variable or an
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| − | independent variable. Independent variables are regarded as inputs to
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| − | a system and may take on different values freely. Dependent variables
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| − | are those values that change as a consequence to changes in other
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| − | values in the system.
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| − |
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| − | == Expressions ==
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| − | An expression is a mathematical term or a sum or
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| − | difference of mathematical terms that may use numbers, variables, or
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| − | both.
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| − |
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| − |
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| − | === Example: ===
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| − | The following are examples of expressions:
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| − | *2
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| − | *x
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| − | *3 + 7
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| − | *2 × y + 5
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| − | *2 + 6 × (4 - 2)
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| − | *z + 3 × (8 - z)
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| − |
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| − | '''Example:'''
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| − | Gangaiah weighs 70 kilograms, and Somanna weighs k kilograms. Write an expression for their combined weight. The combined weight in kilograms of these two people is the sum of their weights, which is 70 + k.
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| − |
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| − | '''Example:'''
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| − | A car travels down the highway at 55 kilometers per hour. Write an expression for the distance the car will have traveled after h hours. Distance equals rate times time, so the distance traveled is equal to 55 × h..
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| − | Example:
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| − | There are 2000 liters of water in a swimming pool. Water is filling the pool at the rate of 100 liters per minute. Write an expression for the amount of water, in liters, in the swimming pool after m minutes. The amount of water added to the pool after m minutes will be 100 liters per minute times m, or 100 × m. Since we started with 2000 liters of water in the pool, we add this to the
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| − | amount of water added to the pool to get the expression 100 × m +
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| − | 2000.
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| − |
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| − | To evaluate an expression at some number means we
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| − | replace a variable in an expression with the number, and simplify the
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| − | expression.
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| − |
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| − | Example:
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| − | Evaluate the expression 4 × z + 12 when z = 15.
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| − | We replace each occurrence of z with the number
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| − | 15, and simplify using the usual rules: parentheses first, then
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| − | exponents, multiplication and division, then addition and
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| − | subtraction.
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| − | 4 × z + 12 becomes
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| − | 4 × 15 + 12 =
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| − | 60 + 12 =
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| − | 72
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| − | Example:
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| − | Evaluate the expression (1 + z) × 2 + 12 ÷ 3 - z
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| − | when z = 4.
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| − |
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| − |
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| − | We replace each occurrence of z with the number 4,
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| − | and simplify using the usual rules: parentheses first, then
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| − | exponents, multiplication and division, then addition and
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| − | subtraction.
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| − | (1 + z) × 2 + 12 ÷ 3 - z becomes
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| − | (1 + 4) × 2 + 12 ÷ 3 - 4 =
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| − | 5 × 2 + 12 ÷ 3 - 4 =
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| − |
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| − | 10 + 4 - 4 =
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| − | 10.
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