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

## Multiplication of constant & variable

 Multiplication of constant & variable

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)