Introduction: 

The  mathematical operation of one number times another is called Multiplication. The multiplication symbol is  “ד. For example ,multiply a and b can be expressed (a × b).It is one of the basic arithmetic operations (like  addition, subtraction and division).

There are many sets multiplication under the operation , assure the axioms that define group structure. These are closure, associativity, and the addition  of an identity element and inverses.

 

Different types of multiplication

 

  •          Multiplication of variable with exponent
  •          Multiplication of fraction
  •          Multiplication of different sign like( positive(+),negative (-))     

 

Multiplying Variables with Exponents:

Multiplication of exponent:

Exponent of 0:

If the exponent is 0 means you are not multiplying by anything and the answer is 1

For example , y0 = 1
a = 1
 

Exponent of 1:

If the exponent is 1 means  the variable itself   (example x1 = x)

Multiplying with variable of exponent :

How do you multiply this:     (a2)(a3)

We know that a2 = aa   and   a3 = aaa

so let us write out all the multiplies:  a2 a3 = aaaaa

so we can adding the exponent  : a2 a3 = a5

Multiplication of Fraction

Steps:

  • `(A/B) ` × `(C/D)` multiply the numerators and denominator respectively.
  • `(A/B) ` × `(C/D)` = `(A * C) /(B * D)`  

 For example ,   There are 3 simple steps to multiply fractions:

  1.               Multiply the top numbers (the numerators).
  2.               Multiply the  numbers in the bottom.(the denominators).
  3.               Simplify the fraction if needed.

Ex:

                  `1 / 2` × `2 / 5`

Step1. Multiply the numerator (top numbers)

           `1 / 2 ` × ` 2 / 5 ` = `(1 * 2) / (2 * 5)` = `2 /(2*5)`

Step2. Multiply the denominator (bottom numbers):  

           `1 / 2` × ` 2 / 5 `  = ` (1 * 2) / (2 * 5)`  = `2 / 10`

Step3. Simplify the fraction:

             ` 2 / 10` = `1 / 5`

Multiplication of different sign like( Positive +, Negative - ):

         Basic multiplication:

  •           Positive(+) × Positive(+) = Positive(+)      Ex:  5 × 2   =10
  •           Positive(+) × Negative(-) = Negative(-).            5 × (-2) = -10
  •           Negative(-) × Positive(+) = Negative(-).            (-5) × 2= -10
  •           Negative(-) × Negative(-) = Positive(+)             (-5) × (-2)=10

 

Multiplication exam preparation problem :

    Multiply by (y + 5) (y -2)

Step 1: multiply by y in the second factor

                   y(y-2) =  y2- 2y

Step 2: multiply by 5 in the second factor

                   5(y - 2) = 5y-10

Step 3: add step 1 and step 2

             (y + 5) (y - 2) = y2- 2y + 5y - 10

                                   = y2 + 3y - 10

 

Multiplication exam preparation problems:

 

Multiplication exam preparation problem 1:

Multiply: `1/8` ×` 88/11`

Answer: 1

Multiplication exam preparation problem 2:

Multiply: `(ab)/(bc)` × `(ac)/b`

Answer: `(a^2)/b`

Multiplication exam preparation problem 3:

Multiply: `16/256` × `32/4`

Answer: `1/2`

 

Multiplication exam preparation problem 4:

Multiply: `1024 / 256` × 20

Answer: 80

Multiplication exam preparation problem 5:

Multiply: `(8ba^2) / (b^2a)`

Answer: `(8a)/b`