What does negative times a negative equal?
The fact that a negative times a negative equals a positive can be proven mathematically using algebraic manipulation. Specifically, it can be proven using the equation x = (a) (b) + (-a) (b) + (-a) (-b), where a and b are any positive numbers and x is unknown, via factoring and reducing the expression.
Why do 2 negatives make a positive?
There is no logic behind why a negative times a negative is a positive but the identity that all real numbers must answer math without logic should not exist. I don't think you're getting the point here... a negative times a negative dosen't mean anything intuitively nor physically like does a positive integer times another.
What does a negative plus a positive make?
what does a negative plus a positive make? Summary: Adding two positive integers always yields a positive sum; adding two negative integers always yields a negative sum. To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values. The sum of any integer and its opposite is equal to zero.
When multiplying a negative and a positive?
When you multiply a negative number by a positive number then the product is always negative. When you multiply two negative numbers or two positive numbers then the product is always positive. Now we have two negative numbers, so the result is positive. How does multiplying negative and positive numbers work?
What is the rule for multiplying negative and positive numbers?
RULE 1: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive.
Does a positive times a negative make a negative?
From this, we can show that ab and –ab have opposite signs and therefore that a positive times a negative is a negative. Using the fact multiplication is commutative, a negative times a positive is also negative....Corrolary 1.a = a + 0(Axiom 3 and Axiom 1)a = −(−a)(Axiom 3)3 more rows•Mar 7, 2020
When multiplying a negative and a negative What is the answer?
positiveMultiplying a negative number and another negative number makes the product positive.
What is a negative times a negative times a negative?
Why a negative times a negative is a positive (video) | Khan Academy.
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Video transcript
Lets say you are an Ancient Philosopher who was building up mathematics who was building mathematics from the ground up And you already have a reasonable of what a negative number could or should represent and you know how to add and subtract negative numbers But now you are faced with a conundrum What happens when you multiply negative numbers? Either when you multiply a positive number times a negative number Or when you multiply two negative numbers So, for example You aren't quite sure what should happen if you were to multiply (and im just picking two numbers where one is positive and one is negative) What would happen if you were to multiply 5 times negative 3 You're not quite sure about this just yet You're also not quite sure what would happen if you multiply two negative numbers.
What is the result of multiplying a positive and a negative number?
3 x (–4) = –12. If you're multiplying a larger series of positive and negative numbers, you can add up how many are positive and how many are negative.
How to work with positive and negative integers?
Here are a few tips for working with positive and negative integers: Context can help you make sense of unfamiliar concepts. Try and think of a practical application like keeping score when you're practicing. Using a number line showing both sides of zero is very helpful ...
How to find the sum of two negative integers?
If you're calculating the sum of two negative integers, it looks like this: To get the sum of a negative and a positive number, use the sign of the larger number and subtract. For example: The sign will be that of the larger number.
Why is it important to know the rules of working with positive and negative numbers?
The rules of how to work with positive and negative numbers are important because you'll encounter them in daily life , such as in balancing a bank account, calculating weight, or preparing recipes.
What is the rule for subtracting?
The rules for subtraction are similar to those for addition. If you've got two positive integers, you subtract the smaller number from the larger one. The result will always be a positive integer:
Why do we use a number line?
Using a number line showing both sides of zero is very helpful to help develop the understanding of working with positive and negative numbers/integers. It's easier to keep track of the negative numbers if you enclose them in brackets.
1.5 Why is NEGATIVE TIMES NEGATIVE POSITIVE?
When we discover negative numbers we naturally, without question even, assume they obey the same laws of arithmetic as the ordinary positive counting numbers.
MULTIPLYING POSITIVE AND NEGATIVE NUMBERS
In the early curriculum multiplication is introduced in the context of whole counting numbers and is appropriately defined there as repeated addition. For instance, 4 × 5 is read as “four groups of five” and is computed as such: 4 × 5 = 5 + 5 + 5 + 5 = 20.
THINKING OUR WAY THROUGH THINGS
Positive times Negative : It does seem compelling to hold on to the “repeated addition” notion for the product of a negative and a positive:
THE PRECISE LOGICAL ARGUMENT AS TO WHY NEGATIVE TIMES NEGATIVE SHOULD BE POSITIVE
Once we agree that 2 × ( − 3) = − 6 (via repeated addition) and ( − 3) × 2 = − 6 (via a belief in commutativity), that negative times negative is positive is a forced logical consequence of these next two basic beliefs of arithmetic: a × 0 = 0 and a ( b + c) = a b + a c . Here’s why:
