I need a real world example for multiplying integers...?

Question

For example...-4 x -6 = 24. I need a real world example for why two negatives equal a positive.

Answer 1

First you need to understand the multiplication of binomials( quantities composed of the addition or subtraction of two terms):
When given a problem like (x+1)(x+1) ( the quantity of "x +1", multiplied by the quantity of "x+1"), there are specific rules for how to multiply the two terms together. These rules are usually remembered using the acronym FOIL, which indicates in what order the individual parts should be multiplied together:

The F stands for "First" and tells us to multiply the first term inside each parenthesis together, so with (x+1)(x+1), the first step is to multiply the two x's together giving 'x*x' or x^2( the '2' being an exponent expressing that there are two 'x's multiplied together.)

The O stands for "Outer" and tells us that the second step is to multiply the outermost terms( the terms on the edges) together: In (x+1)(x+1) the outermost terms are "x" and '1', multiplied together this just gives 'x'.

The I stands for "Inner" and it says that the third step is to multiply the inner-most terms together. In (x+1)(x+1) the innermost terms are 1 and 'x'. Multiplied together this gives 1*x which is just 'x'.

The L stands for 'Last' and tells us to multi[ply the last term of each group together. In (x+1)(x+1) the last terms are 1 and 1, which multiplied together yield one.

After those for steps we simply add all the terms together. So:
(x+1)(x+1) = x^2 + x + x + 1. Notice that x+x = 2x, so:
(x+1)(x+1) = x^2 +2x +1.

Now an 'x' just indicates an unknown number, so we should be able to follow the same steps indicated in FOIL for any problem which looks like this. Let's try it for something we can easily see the answer to:

(4-3)(5-2), (four minus three) times (five minus two) is a problem which we can easily do:

4-3 = 1
5-2 = 3
so (4-3)(5-2) = 3 *1 = 3.

For the FOIL method to be valid, it must give us the same answer so let's try it:

(4-3)(5-2)
First we multiply the First terms together 4*5 = 20
Then we multiply the Outer terms together (4*-2) = -8
Now multiply the Inner terms together (-3*5) = -15
Finally, multiply the last terms together (-3*-2) = 6
Now we add them all together:

20 + (-8) + (-15) + 6
26 - 23
3, and we receive the correct answer.

Now here's the important part, let's try doing it again, except this time we'll assume that two negatives multiplied together give a negative:

First we multiply the First terms together 4*5 = 20
Then we multiply the Outer terms together (4*-2) = -8
Now multiply the Inner terms together (-3*5) = -15
Finally, multiply the last terms together (-3*-2) = -6
Now we add them all together:

20 + (-8) + (-15) + (-6)
20 + (-29)
-9, which is obviously incorrect.

You can try this problem with other hypothetical rules regarding the multiplication of negatives, and they will all come out wrong.

So for our the multiplication in situations like (a-b)(c-d), the multiplication of two negatives must give a positive and the multiplication of a negative and a positive must give a negative.

In the real world something like this could arise: I'm looking for what area would be produced if I removed 3 feet from the 45 foot length of a rectangular hallway and 4 feet from the 10 foot width of the hallway. A rectangles area(a) being length times width, this problem would look like this written symbolically:

a = length*width
a = (45-3)(10-4)

Try it yourself and you'll see that two negatives multiplied together must give a positive. I hope this helps.

Answer 2

I was just debating this with someone the other day and this is what we came up with. Multiplication is really just repeated addition. For 5 x 3, you are adding 5 three times. Start with zero because that is the additive identity. So 5 x 3 = 0 + 5 + 5 + 5.

Then, the rules for negatives in addition and subtraction can be used to explain the rules for negatives in multiplication.

1. Multiplying a negative by a positive:
-5 x 3 = 0 + (-5) + (-5) + (-5) = -15
Start with 0. Add -5 three different times.

2. Multiplying a positive by a negative:
5 x -3 = 0 - (+5) - (+5) - (+5) = -15
Start with zero. Un-add 5 three times, which means subtract 5 three times.

3. Multiplying a negative by a negative:
-5 x -3 = 0 - (-5) - (-5) - (-5) = 0 + 5 + 5 + 5 = 15
Start with zero. Un-add (subtract) -5 three times.

That goes to show that a negative times a negative has to be a positive, and didn't just get randomly defined to be such. As for a real-world application, I just saw something on another site about temperature changes.
Check out: www.intmath.com/Numbers/ 1_Integers.php
Hope this helps!

PS - In the link above, I had to add a space between the last / and the 1 to make it display correctly. Make sure to take that space back out when you paste it in your browser.

Answer 3

Why is a negative times a negative a positive?
People have suggested many ways of picturing what is going on when a negative number is multiplied by a negative number. It's not easy to do, however, and there doesn't seem to be a visualization that works for everyone.


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Debt
Debt is a good example of a negative number. One common form of debt is a mortgage in which you owe the bank money because the bank paid for your house. It is also common for an employer to deduct a mortgage payment from an employee's paycheck to help the employee keep on schedule with the payments.
Suppose $700 is being deducted each month to pay the mortgage. After six months, how much money has been taken out of the pay for the mortgage? We can figure out the answer by doing multiplication.

6 * -$700 = -$4,200

This is an illustration of a positive times a negative resulting in a negative.

Now suppose that, as a bonus, the employer decides to pay the mortgage for one year. The employer removes the mortgage deduction from the monthly paychecks. How much money is gained by the employee in our example? We can represent "removes" by a negative number and figure out the answer by multiplying.

-12 * -$700 = $8,400

This is an illustration of a negative times a negative resulting in a positive.

If one thinks of multiplication as grouping, then we have made a positive group by taking away a negative number twelve times.

Answer 4

I can't explain why two negatives equals a positive, that is just the mathematical rule of thumb for multiplying integers. Two negatives equals a positive, and three negatives equals a negative. When ever there are an even number of integers that are ALL negative, the answer will be positive. Whenever there are an odd number of integers that are ALL negative, the answer will be negative.

I hope this helps! =)

Answer 5

Integers In The Real World

Answer 6

It is my understanding that the multiplying of 2 negatives becoming a positive is theory, not application.

Math is one of the few concepts that produces a set of rules that exist to account for all options. The options do not have to be real (such as sqrt(-1) ) -

I don't think you will find any real example in our world to support your need.

Answer 7

Very good question.

If I stack two papers on top of each other with each having a hole in the middle, I would still have a hole through both papers.

Sorry, but you'll just have to tell your students that there is no real world example. It's just how the math works.

Answer 8

if you have a bag with 8 coins and take away -1 coin 4 times in a row, this would mean the same as adding -1 coin -4 times. you would end up with 12 coins. 12-8= 4, -1 times -4 = 4

Answer 9

Well its not why or mathematically but its how I was explained it when I couldn't grasp the concept. Its like in english how two negatives is positive, double negative kinda thing? Like I don't have nothing (negative and negative) means I have something (positve) not sure if this helps of is what you were looking. Mand xxx

Answer 10

Suppose you pay 2 debts of 10$

if you pay the actions of paying = -2
you ow 10$ a debt for you is -10

so if you pay the two (-2)(-10) =+20

if you have payed the debt iti is as if you earn 20$