Why A Negative And A Positive Can Equal A Positive X г Two like signs make a positive sign, so: next multiply 6 × (−4). two unlike signs make a negative sign, so: result: (−2) × (−3) × (−4) = −24. yes indeed, two negatives make a positive, and we will explain why, with examples lets talk about signs. is the positive sign, is the negative sign. I would explain it by number patterns. first, to establish that a positive times a negative is negative: 3 × 2 = 6, 3 × 1 = 3, 3 × 0 = 0. notice in each case, as we reduce the second factor by 1, the product is being reduced by 3. so for consistency the next product in the pattern must be 0 − 3 = − 3.
Why Does A Negative Times A Negative Equal A Positive Math With Mr My 6th and 7th grade students are pretty effective at calculating with negative numbers. they all know, for example, that 5 – ( 2) = 7. ask them why, and you’ll hear this: “because two negatives make a positive!”. then, if you listen carefully, you will hear something else: the low rumble of my teeth grinding together with tectonic force. Positive times negative. we can show that these facts imply what multiplication of negative numbers has to look like, in two steps. first: (4) now, we are forced to accept a new law, that negative times positive equals negative. this is because we can use the distributive law on an expression like 2*(3 ( 3)). this equals 2*(0), which is zero. Those good reasons are mathematical: we want to make sure that when we extend multiplication and addition to negative numbers the properties of operations still apply. in particular, we want the distributive property to apply. meditate on this: 3 ⋅ (5 (− 5)) = 3 ⋅ 5 3 ⋅ (− 5). the left side is really 3 ⋅ 0, so it had better be zero. Try this visual: multiplying by positives is adding to the total that number of times: so 5 times 3 is adding 5 to the total each time. 0 ( 5) ( 5) ( 5) = 15. and multiplying by a negative number is subtracting from the total that same number of times: 5 times 3 is subtracting 5 from the total each time.
Negative Times A Negative Equals A Positive Here Is Why Youtube Those good reasons are mathematical: we want to make sure that when we extend multiplication and addition to negative numbers the properties of operations still apply. in particular, we want the distributive property to apply. meditate on this: 3 ⋅ (5 (− 5)) = 3 ⋅ 5 3 ⋅ (− 5). the left side is really 3 ⋅ 0, so it had better be zero. Try this visual: multiplying by positives is adding to the total that number of times: so 5 times 3 is adding 5 to the total each time. 0 ( 5) ( 5) ( 5) = 15. and multiplying by a negative number is subtracting from the total that same number of times: 5 times 3 is subtracting 5 from the total each time. A negative number has the same length as its corresponding positive number, but is pointing the opposite direction. think of multiplying by a negative as a command to reverse your direction. so if you have a*5 it means "multiply by 5", and if you have a* ( 5) it means "reverse your direction, then multiply by 5". 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. that is, we like to believe that basic laws such as a × b = b × a a × b = b × a and a × 1 = a a × 1 = a and a × 0 = 0 a × 0 = 0 hold.
Why Does A Negative Times A Negative Equal A Positive Youtube A negative number has the same length as its corresponding positive number, but is pointing the opposite direction. think of multiplying by a negative as a command to reverse your direction. so if you have a*5 it means "multiply by 5", and if you have a* ( 5) it means "reverse your direction, then multiply by 5". 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. that is, we like to believe that basic laws such as a × b = b × a a × b = b × a and a × 1 = a a × 1 = a and a × 0 = 0 a × 0 = 0 hold.
Why Two Negatives Equal A Positive Math Arithmetic Multiplication
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