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)