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Multiplying Numbers

A multiplication is the mathematical operation of scaling a number by another number. It is the basic operations in elementary arithmetic. 

Multiplication is nothing but adding the same number again and again and this is also called repeated addition.

The word times will tell us how many times we are adding the same number to itself. 
Simple way of explaining this would be putting it as a special case of addition in which all the addends are of same size. To make this operation easy and remember it as well in short period of time we make use of multiplication table through which one can learn the times of the numbers easily. 

By applying the repeated addition model of multiplication, it becomes problematical, however, we could make use of commutative property to make the task easier.

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Multiplying Integers

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Multiplication of integers is very much like multiplication of whole numbers. The only difference is that we must determine whether the answer is negative or positive.

When we multiply two nonzero integers, they either have same signs or they have the different sign.

In that case there are two possibilities to  consider:

Multiply two integers that have same signs.

Multiply two integers that have different signs.

Multiplying Integers Examples

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Below are the examples on multiplying integers -


Whole numbers larger than zero $(1, 2, 3, 4, 5...)$ are positive integers and whole numbers lesser than zero $(-1, -2, -3, -4, -5 …)$ are negative integers.

We need not assume about zero. 

Every positive integer has a negative integer. For example, $(-5)$ is the opposite of $5$.

Multiplication Rules for integers

Rule 1: Working with the two positive numbers or two negative numbers in multiplication always provides positive answers. 

Rule 2: Working with the one positive and one negative numbers in multiplication always provides negative answer. 

→ Read More In order to solve the two digit multiplication problems, we need to recall the rules for multiplication of integers discussed above. 
Easy trick to multiply two digit integers is, multiply their absolute values then make the final answer using multiplication rules.
→ Read More

Multiplying by Two Digit Numbers Examples

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Example 1:

Multiply 

(a) $12\ \times\ -15$

(b) $-28\ \times\ 98$

(c) $50\ \times\ -17$

Solution:

Here we are given with the integers with unlike signs. We will use the rule for multiplying two integers that have unlike (different) signs i.e. The product of of two integers with unlike signs is negative.

(a) Get absolute values

$|12|$ = $12$ and $|-15|$ = $15$

Multiply $12$ and $15$

$12\ \times\ 15$ = $180$

Then make the final answer negative i.e. $-180$

$\Rightarrow\ 12\ \times\ -15$ = $-180$ Answer!!

(b) Get absolute values

$|-28|$ = $28$ and $|98|$ = $98$

Multiply $28$ and $98$

$28\ \times\ 98$ = $2744$

Then make the final answer negative i.e. $-2744$

$\Rightarrow\ 12\ \times\ -15$ = $-2744$ Answer!!

(c)
Get absolute values

$|50|$ = $50$ and $|-17|$ = $17$

Multiply $50$ and $17$

$50\ \times\ 17$ = $850$

Then make the final answer negative i.e. $-850$

$\Rightarrow\ 50\ \times\ -17$ = $850$ Answer!!

Example 2: 

Multiply

(a) $-50\ \times\ -12$

(b) $14\ \times\ 15$

(c) $-10\ \times\ - 11$

Solution: 

Here we are given with the integers with like signs.

Use multiplicative rule: The product of two integers with like signs is positive.

(a) Multiply absolute values

$|-50|$ = $50$ and $|-12|$ = $12$

$50\ \times\ 12$ = $600$

Final answer is  $-50\ \times\ -12$ = $600$

(b) Both are positive values, multiply and get the result

$14\ \times\ 15$ = $210$

(c) $-10\ \times\ -11$

$|-10|$ = $10$ and $|-11|$ = $11$

$10\ \times\ 11$ = $110$

Final answer is  $-10\ \times\ -11$ = $110$

Solved Example

Question: Solve the given numbers by using the multiplication operation: (- 29) × (- 36)
Solution:
 
Given

(- 29) × (-36)

Both are two negative numbers so, the result is also a positive numbers

We use this rule,

Negative number × Negative number = Positive number

Here we multiply (-29) into (-36), and then we get

   -29
× -36
  174 .....................29 being multiplied with 6

Now 29 being multiplied with 3 and we get 87

Now we have to add the values, then we get the result of 1044
 

Correct answer is 1044
More topics in Multiplying Numbers
3 Digit by 1 Digit Multiplication Multiplication Single Digit
Multiplying Two Digit Numbers Multiplication as Repeated Addition
Multiplication Tables Multiplication Properties
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