For multiplying and dividing the rules are same. If both numbers are positive then the answer will be positive, if both numbers are negative then the answer will again be positive. If one number is positive and one is negative then the answer will be negative. Show
#+ + = +# GCfiIBPG7Aw When We Multiply:
Yes indeed, two negatives make a positive, and we will explain why, with examples! SignsLet's talk about signs. "+" is the positive sign, "−" is the negative sign. When a number has no sign it usually means that it is positive. Example: 5 is really +5 And we can put () around the numbers to avoid confusion. Example: 3 × −2 can be written as (+3) × (−2) Two Signs: The Rules"Two like signs make a positive sign, Example: (−2) × (+5)The signs are − and + (a negative sign and a positive sign), so they are unlike signs (they are different to each other) So the result must be negative: (−2) × (+5) = −10 Example: (−4) × (−3)The signs are − and − (they are both negative signs), so they are like signs (like each other) So the result must be positive: (−4) × (−3) = +12 Why does multiplying two negative numbers make a positive?Well, first there is the "common sense" explanation: When I say "Eat!" I am encouraging you to eat (positive) But when I say "Do not eat!" I am saying the opposite (negative). Now if I say "Do NOT not eat!", I am saying I don't want you to starve, so I am back to saying "Eat!" (positive). So, two negatives make a positive, and if that satisfies you, then you don't need to read any more. DirectionIt is all about direction. Remember the Number Line? Well here we have Baby Steven taking his first steps. He takes 2 paces at a time, and does this three times, so he moves 2 steps x 3 = 6 steps forward: Now, Baby Steven can also step backwards (he is a clever little guy). His Dad puts him back at the start and then Steven steps backwards 2 steps, and does this three times: Once again Steven's Dad puts him back at the start, but facing the other way. Steven takes 2 steps forward (for him!) but he is heading in the negative direction. He does this 3 times: Back at the start again (thanks Dad!), still facing in the negative direction, he tries his backwards walking, once again taking two steps at a time, and he does this three times: So, by walking backwards, while facing in the negative direction, he moves in the positive direction. Try it yourself! Try walking forwards and backwards, then again but facing the other direction. Play With ItBut maybe you would like to see it in action? Use the sliders below: numbers/images/number-line-mult.js More ExamplesExample: Money
Example: A Video of People RunningPeople Run Forward, Video Normal: All normal, people running forwards: +1 × +1 = +1
Looks like people running backwards: +1 × −1 = −1
You see people running backwards: −1 × +1 = −1
Looks like people running forwards: −1 × −1 = +1 Example: Tank Levels Rising/FallingThe tank has 30,000 liters, and 1,000 liters are taken out every day. What was the amount of water in the tank 3 days ago? We know the amount of water in the tank changes by −1,000 every day, and we need to subtract that 3 times (to go back 3 days), so the change is: −3 × −1,000 = +3,000 The full calculation is: 30,000 + (−3 × −1,000) = 30,000 + 3,000 = 33,000 So 3 days ago there were 33,000 liters of water in the tank. Multiplication TableHere is another way of looking at it. First have a play with this (explanations below): numbers/images/mult-grid.js?min=-5&max=5 Start with the multiplication table (just up to 4×4 will do):
Now see what happens when we head into negatives! Let's go backwards through zero:
Look at the "4" column: it goes -16, -12, -8, -4, 0, 4, 8, 12, 16. Getting 4 larger each time. Look over that table again, make sure you are comfortable with how it works, because ... ... now we go further to the left, through zero:
We can follow along a row (or column) and the values change consistently:
So it all follows a consistent pattern! Also see this at Real Multiplication Table. What About Multiplying 3 or More Numbers Together?Multiply two at a time and follow the rules. Example: What is (−2) × (−3) × (−4) ?First multiply (−2) × (−3). Two like signs make a positive sign, so: (−2) × (−3) = +6 Next multiply +6 × (−4). Two unlike signs make a negative sign, so: +6 × (−4) = −24 Result: (−2) × (−3) × (−4) = −24 330, 1615, 1616, 1617, 3447, 3448,331, 1618, 3170, 3171 What are the 4 rules for multiplying integers?What are the Four Rules for Multiplying Integers?. Rule 1: Positive × Positive = Positive.. Rule 2: Positive × Negative = Negative.. Rule 3: Negative × Positive = Negative.. Rule 4: Negative × Negative = Positive.. What are the rules for multiplying with negative numbers?Multiplying and dividing negative numbers can be summarized with the following rules:. Multiplying a negative and a positive results in a negative.. Multiplying two negatives results in a positive.. Dividing a negative and a positive results in a negative.. Dividing two negatives results in a positive.. When multiplying do 2 negatives make a positive?The fact that the product of two negatives is a positive is therefore related to the fact that the inverse of the inverse of a positive number is that positive number back again.
What is the plus and minus rule?When two positive integers are multiplied then the result is positive. When two negative integers are multiplied then also the result is positive. But when one positive and one negative integer is multiplied, then the result is negative.
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