MATHTINIK

What is MDAS rule?

Multiplication Division Addition Subtraction.


In a mathematical equation with different operations, follow the MDAS rule. 
Multiply/Divide first before Adding/Subtracting.


Example

1 - 2 + 3 x 4 / 5 = ?

first, multiply/divide, do so in order
3 x 4 / 5 = 12 / 5
= 2.4

then add/subtract, whichever comes first
1 - 2 + (2.4) = -1 + 2.4
= 1.4


so if you use parentheses in the given equation,
(1 - 2) + (3 x 4 / 5) = ?






MULTIPLICATION OF SIGNED NUMBERS


MULTIPLICATION



Unlike Signs

Consider the example 3(-4), in which the multiplicand is negative. This means we are to add -4 three times; that is, 3(-4) is equal to (-4) + (-4) + (-4), which is equal to -12.

When the multiplier is negative, as in -3(7), we are to take away 7 three times. Thus, -3(7) is equal to -(7) - (7) - (7) which is equal to -21. For example, if 7 shells were expended in one firing, 7 the next, and 7 the next, there would be a loss of 21 shells in all. Thus, the rule is as follows: 

The product of two numbers with unlike signs is negative.

The law of signs for unlike signs is sometimes stated as follows: 

Minus times plus is minus; plus times minus is minus. Thus a problem such as 3(-4) can be reduced to the following two steps:

1. Multiply the signs and write down the sign of’ the answer before working with the numbers themselves.

2. Multiply the numbers as if they were unsigned numbers.

Using the suggested procedure, the sign of the answer for 3(-4) is found to be minus. The product of 3 and 4 is 12, and the final answer is -12. When there are more than two numbers to be multiplied, the signs are taken in pairs until the final sign is determined.

Like Signs

When both factors are positive, as in 4(5), the sign of the product is positive. We are to add +5 four times, as follows:

4(5) = 5 + 5 + 5 + 5 = 20

When both factors are negative, as in -4(-5), the sign of the product is positive. We are to take away -5 four times.


Remember that taking away a negative 5 is the same as adding a positive 5. For example, suppose someone owes a man 20 dollars and pays him back (or diminishes the debt) 5 dollars at a time. He takes away a debt of 20 dollarsby giving him four positive 5-dollar bills, or a total of 20 positive dollars in all.


The rule developed by the foregoing example is as follows: The product of two numbers with like signs is positive. 


Knowing that the product of two positive numbers or two negative numbers is positive, we can conclude that the product of any even number of negative numbers is positive. Similarly, the product of any odd number of negative numbers is negative.


The laws of signs may be combined as follows:

Minus times plus is minus; plus times minus is minus; minus times minus is plus; plus times plus is plus. Use of this combined rule may be illustrated as follows:

4(-2) - (-5) - (6) - (-3) = -720

Taking the signs in pairs, the understood plus on the 4 times the minus on the 2 produces a minus. This minus times the minus on the 5 produces a plus. This plus times the understood plus on the 6 produces a plus. This plus times the minus on the 3 produces a minus, so we know that the final answer is negative. The product of the numbers, disregarding their signs, is 720; therefore, the final answer is -720.

Try to answer the following:
1. 5(-8) = ?
2. -7(3) (2) = ?
3. 6(-1)(-4) = ?
4. -2(3)(-4)(5)(-6) = ?

Answers:

1. -40
2. -42
3. 24
4. -720