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Home >> Algebraic Expression >> Constants >> Multiplication of constant & variable >>

Multiplication of constant & variable

Multiplication of constant & variable

Before you study this concepts, you are advised to read:

What are Constants ?
What are Variable ?
What are Natural Numbers ?
What are Integers ?

This concept can also be referred to as:
  • Multiplication of Number and Variable
  • Multiplication of Natural Number and Variable
  • Multiplication of Integer and Variable

    So, we can call this concept with different name, but the basic concept will remain always same. And this explained in following examples:

    (Note: While multiplying a constant and variable, we generally write constants first and then variable)

    Example 1: Multiply 4 and p
    Solution: In the given question:

    4 is a constant
    p is a variable

    Multiplication expression 4 and p give us:
    4 X p

    On solving the multiplication expression, we get:
    4p



    Example 2: Solve y and 10
    Solution: In the given question:

    y is a variable
    10 is a number

    Multiplication expression we get:
    Y X 10

    On solving the multiplication expression, we get:
    10y



    Example 3: Solve 4 ( 2 X q)
    Solution: In the given question:

    4 and 2 are both constants
    q is a variable

    Multiplication expression gives us:
    4 ( 2 X q)

    Solve bracket and we get:
    4 (2q)

    Open bracket and we get:
    4 X 2q

    On solving the multiplication expression, we get:
    8q

    So by now you must have understood this concept and above example 1, 2 & 3; represent multiplication of positive integer and positive variable

    But you will also face following situation under this concept:
  • Multiplication of negative constant and variable
  • Multiplication of negative integer and negative variable
  • Multiplication of constant and negative variable

    Multiplication of negative constant and variable

    (This can also be referred as multiplication of negative integer and variable)

    Example 4: Multiply (-5) and s
    Solution: In the given question:
    -5 is a negative constant or negative integer
    s is a variable

    Multiplication expression gives us:
    (-5) X s

    Now, we have one negative integer i.e. -5 and one variable i.e. (s)
    (This is similar to Multiplication of Positive and Negative Integer)
    So we will multiply 5 and s (as explained in example 1, 2 and 3) and ignore negative sign or subtraction operator i.e. (-) & we get:
    5s

    Now we put negative sign or subtraction operator i.e. (-) to the left of 5s & we get:
    -5s

    Hence, Multiplication of (-5) and s give us (-5s)

    Multiplication of negative integer and negative variable

    Example 5: Multiply (-10) and (-t)
    Solution: In the given question:
    -10 is a negative constant or negative integer
    (-t) is a negative variable

    Multiplication expression gives us:
    (-10) X (-t)

    Now, we have one negative integer i.e. (-10) and one negative variable i.e. (-t)
    (This is similar to Multiplication of Two Negative Integers)
    So we will multiply 10 and t (as explained in example 1, 2 and 3) and put positive sign or addition operator to the left of product & we get:
    +10t

    Or we can write it as:
    10t

    Hence, Multiplication of (-10) and (-t) give us (10t)

    Multiplication of constant and negative variable

    (This can also be referred as multiplication of positive integer and negative variable)

    Example 4: Multiply 11 and (-q)
    Solution: In the given question:
    11 is a constant or positive integer
    (-q) is a negative variable

    Multiplication expression gives us:
    11 X (-q)

    Now, we have one positive integer i.e. 10 and one negative variable i.e. (-q)
    (This is similar to Multiplication of Positive and Negative Integer)
    So we will multiply 11 and -q (as explained in example 1, 2 and 3) and ignore negative sign or subtraction operator i.e. (-) & we get:
    11q

    Now we put negative sign or subtraction operator i.e. (-) to the left of 11q & we get:
    (-11q)

    Hence, Multiplication of 11 and (-q) give us (-11q)


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