Please explain double negative mathematics?
Hi can anyone please settle an argument about my son’s homework?
He as to explain double negatives in maths (he’s only 9) I say its-
4 - -4= 8
i.e. two negatives equalled a positive were as my wife says it’s a negative and all my son wants to know is why?
Can anyone help??
Thanks
Answers:
Think about the temperature of a bath.
Use blue and red counters if it would help him.
one blue counter is -1 degree and one red is +1 degree
Play around with adding blue and red counters - just changing the temperature up and down by various amounts until he is happy.
Then introduce minus minuses
What if I take out a red? It gets colder - taking away 1degree
What if I take out a blue? It gets warmer - taking away -1degree
It normally 'clicks' at this point and you hear the penny drop and a smile will be seen!!
Good luck
I don't know why, but "minus" a minus quantity is a positive, so you're right, that 4-(-4) = 8.
when there is only one negative he's lonely and sad. But when there are two negatives they are happy, so they are positive.
Or a other way to see it: negative is equal to reverse. The reverse of 4 is -4. So when you have 4--4; you reverse two times. So actually you're back at the beginning. You just used up your minusses to reverse, so there comes a plus.
(can you follow :D ?)
two negatives only equal a positive in multiplication so the way you wrote it out you would be wrong -4(-4) actually equals 16.
two minus is postive
plus and minus is negative
why? Because maths is that way :|
Negatives are like something you owe. so if you take away something you owe, you are actually gaining something. For example, if you say I don't owe you 4 dollars anymore, then it is like gaining 4 dollars.
Another analogy uses language. If I say, the door is not unlocked, the double negatives cancel to mean, the door *is* locked. Or if you tell me NOT to watch television, but I'm NOT going to do what you say, that means, I will watch television. The two negatives cancel out.
A double negative does equal a positive, so 4--4 would indeed = 8. The reason lies in unary and binary operators. Unary operators take precedence over all binary operators. So in the sum 4--4=8, the two minuses aren't actually the same. The first minus is a binary operator, equalling subtraction, whereas the second minus is a unary operator equalling 'negative 4'. So, the second operator (negative 4) takes precedence over the binary operator (the subtraction sign) and accepts only one operand (since it is unary), the 4 and thus produces -4. Only then can the subtraction sign take an operand, so it will take 4. So in effect we have +4- (-4) = 8.
Hope this helps and is clear enough!
if you have 4 and you take away 4 you have zero.
if you take away a minus this is equivalent to grabbing the 4 on the minus side of the zero and adding to the positive one.
so, if you have 4 and then try to take away -4 you actually end up with 8. It's a good question, hopefully this might help answer it?
i think -4--4=0 because 2 minus's is a positive..what a crap teacher obviously trying to confuse the poor little boy who is brighter than the teacher..personally i would complain to the school governers or the head teacher..my daughter is a primary school teacher and no way should a nine year old get questions like that..could put him off the beauty of maths for life..mb
First off: if you subtract a negative number it is the same as adding the positive number (i.e. 4-(-4)=8, as you think). Your wife is wrong.
To explain it to your child: I would advise using a numberline. Write all the numbers from -10 to +10 in a line. On another piece of paper. Draw 4 arrows in the same direction. Show him that a 4 is the four arrows pointing positive from 0. Show him that 4+4 means starting at 4, with the 4 arrows pointing away from 0, which makes 8. Show him that subtracting a number means turning the arrows around, so that they point the opposite direction (i.e. towards 0). So 4-4=0.
Next step: show him that -4 is the four arrows pointing downwards from zero. Next add this number to 4 by putting it next to 4. It points to zero! So 4+ (-4)=0. Next remind him that to subtract a number you turn it around. So to subtract the -4, you turn it around, and put next to 4 it makes 8!
Hope that makes sense. It was the best way I could think of to explain how it works.
It might help to look at goals for, and goals against an opponent in football.
For example.
Bolton 0 : 4 Man utd.
Man utd 4 : 1 Bolton.
Now do the maths.
Man utd have scored 8 (positive) goals altogether.
Bolton have conceded 8 (negative) and scored 1 (positive).
Boltons goal difference would be -7.
If Bolton score 7 the next match they will have a 0 goal difference.Thats because their goal difference is a negative number, or, less than 0.
in addition the following basic maths rules apply
- - =+
-+ = -
+- = -
++=+
therefore,4 - -4= 4+4=8
the same rules apply for multiplication and division
i hope that this helps
Draw out a numberline. If you take a positive 4, you go left, so do the opposite - i.e. go right
(-) + (-) = (+)
(-) + (+) = (-)
and obviously.
(+) + (+) = (-)
2 negative signs together would cancel each other out or something. I dunno, but it works on a calculator.
Let's try this:
4 + 4 = 8
...-4 = .-4
4.. = 8 - 4
4.. = 8 + (- 4), (-4 = -1*4, or 1*(-4)
.- (-4)...- (-4)
4 - (-4) = 8
another way to look at it is with "times tables"
... 1. .. -1
...┌───┬───┐
..1 │.+1 │.. -1│
.-1 │. -1 │.+1 │
(-1)*(-1) = 1
-(-1) = 1
--1 = 1
1) You are right. Chalk 1 up for thr guys :)
2) Supose you have $8 & you owe someone $4. your worth is $4 ($8-$4=$4)
now supose this debt is cancelled, you subtract the debt so your net worth is now
$4-(-$4)=$8, the $8 you have in your hand.
I dodn't know whether this will work with a nine year old, but here's my explanation.
If you have minus something its like you are holding an IOU for it. So if you have -4 apples it is like you are holding a note saying that you owe somebody 4 apples.
So in 4 - (-4) it is as though you've got 4 of something . apples in my example . and you take away (i.e. you give SOMEBODY ELSE) an IOU for 4 apples.
So you have 4 apples and somebody else owes you 4 apples - so it means you own 8 apples.
Several people have said 'it's because maths is that way'. Whilst this is true, its that way for a reason.
If you start from the other end and say 'what number do you take away from 4 to get 8' you have something that sounds like a riddle, but with a bit a working out it also shows you why maths works this way:
4 - (mystery number) = 8
Call the mystery number X.
4 - X = 8
Now add X to both sides and you have
4 = 8 + X
(you can always add the same number to both sides of an equation and the equality is still true)
So X = 4 -8 = -4
So the mystery number to take away from 4 to get 8 is -4. Basically this is the same as the IOU for 4 items.
I hope that helped more than it confused.
I was taught that positive was to go right across a page and so up a number line. Negative was to go down the number line (left) or change direction.
In mixed commands positive means go in the same direction as the previous command.
Negative is to change direction. Therefore a double negative meant changing direction twice, going left, then right, so becoming positive.
A triple negative is left, right, left and so is negative since you end up pointing left.
Just think that plus (+) is go right in the first instance or stay in the direction you are sent.
Minus (-) is to change direction.
-, - therefore is +
-,-,- therefore is -
-,-,-,- is therfore +
-,+ is -
-.-.-,+ is -
-,+ is -
-.-.+ is +
Hope this helps
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He as to explain double negatives in maths (he’s only 9) I say its-
4 - -4= 8
i.e. two negatives equalled a positive were as my wife says it’s a negative and all my son wants to know is why?
Can anyone help??
Thanks
Answers:
Think about the temperature of a bath.
Use blue and red counters if it would help him.
one blue counter is -1 degree and one red is +1 degree
Play around with adding blue and red counters - just changing the temperature up and down by various amounts until he is happy.
Then introduce minus minuses
What if I take out a red? It gets colder - taking away 1degree
What if I take out a blue? It gets warmer - taking away -1degree
It normally 'clicks' at this point and you hear the penny drop and a smile will be seen!!
Good luck
I don't know why, but "minus" a minus quantity is a positive, so you're right, that 4-(-4) = 8.
when there is only one negative he's lonely and sad. But when there are two negatives they are happy, so they are positive.
Or a other way to see it: negative is equal to reverse. The reverse of 4 is -4. So when you have 4--4; you reverse two times. So actually you're back at the beginning. You just used up your minusses to reverse, so there comes a plus.
(can you follow :D ?)
two negatives only equal a positive in multiplication so the way you wrote it out you would be wrong -4(-4) actually equals 16.
two minus is postive
plus and minus is negative
why? Because maths is that way :|
Negatives are like something you owe. so if you take away something you owe, you are actually gaining something. For example, if you say I don't owe you 4 dollars anymore, then it is like gaining 4 dollars.
Another analogy uses language. If I say, the door is not unlocked, the double negatives cancel to mean, the door *is* locked. Or if you tell me NOT to watch television, but I'm NOT going to do what you say, that means, I will watch television. The two negatives cancel out.
A double negative does equal a positive, so 4--4 would indeed = 8. The reason lies in unary and binary operators. Unary operators take precedence over all binary operators. So in the sum 4--4=8, the two minuses aren't actually the same. The first minus is a binary operator, equalling subtraction, whereas the second minus is a unary operator equalling 'negative 4'. So, the second operator (negative 4) takes precedence over the binary operator (the subtraction sign) and accepts only one operand (since it is unary), the 4 and thus produces -4. Only then can the subtraction sign take an operand, so it will take 4. So in effect we have +4- (-4) = 8.
Hope this helps and is clear enough!
if you have 4 and you take away 4 you have zero.
if you take away a minus this is equivalent to grabbing the 4 on the minus side of the zero and adding to the positive one.
so, if you have 4 and then try to take away -4 you actually end up with 8. It's a good question, hopefully this might help answer it?
i think -4--4=0 because 2 minus's is a positive..what a crap teacher obviously trying to confuse the poor little boy who is brighter than the teacher..personally i would complain to the school governers or the head teacher..my daughter is a primary school teacher and no way should a nine year old get questions like that..could put him off the beauty of maths for life..mb
First off: if you subtract a negative number it is the same as adding the positive number (i.e. 4-(-4)=8, as you think). Your wife is wrong.
To explain it to your child: I would advise using a numberline. Write all the numbers from -10 to +10 in a line. On another piece of paper. Draw 4 arrows in the same direction. Show him that a 4 is the four arrows pointing positive from 0. Show him that 4+4 means starting at 4, with the 4 arrows pointing away from 0, which makes 8. Show him that subtracting a number means turning the arrows around, so that they point the opposite direction (i.e. towards 0). So 4-4=0.
Next step: show him that -4 is the four arrows pointing downwards from zero. Next add this number to 4 by putting it next to 4. It points to zero! So 4+ (-4)=0. Next remind him that to subtract a number you turn it around. So to subtract the -4, you turn it around, and put next to 4 it makes 8!
Hope that makes sense. It was the best way I could think of to explain how it works.
It might help to look at goals for, and goals against an opponent in football.
For example.
Bolton 0 : 4 Man utd.
Man utd 4 : 1 Bolton.
Now do the maths.
Man utd have scored 8 (positive) goals altogether.
Bolton have conceded 8 (negative) and scored 1 (positive).
Boltons goal difference would be -7.
If Bolton score 7 the next match they will have a 0 goal difference.Thats because their goal difference is a negative number, or, less than 0.
in addition the following basic maths rules apply
- - =+
-+ = -
+- = -
++=+
therefore,4 - -4= 4+4=8
the same rules apply for multiplication and division
i hope that this helps
Draw out a numberline. If you take a positive 4, you go left, so do the opposite - i.e. go right
(-) + (-) = (+)
(-) + (+) = (-)
and obviously.
(+) + (+) = (-)
2 negative signs together would cancel each other out or something. I dunno, but it works on a calculator.
Let's try this:
4 + 4 = 8
...-4 = .-4
4.. = 8 - 4
4.. = 8 + (- 4), (-4 = -1*4, or 1*(-4)
.- (-4)...- (-4)
4 - (-4) = 8
another way to look at it is with "times tables"
... 1. .. -1
...┌───┬───┐
..1 │.+1 │.. -1│
.-1 │. -1 │.+1 │
(-1)*(-1) = 1
-(-1) = 1
--1 = 1
1) You are right. Chalk 1 up for thr guys :)
2) Supose you have $8 & you owe someone $4. your worth is $4 ($8-$4=$4)
now supose this debt is cancelled, you subtract the debt so your net worth is now
$4-(-$4)=$8, the $8 you have in your hand.
I dodn't know whether this will work with a nine year old, but here's my explanation.
If you have minus something its like you are holding an IOU for it. So if you have -4 apples it is like you are holding a note saying that you owe somebody 4 apples.
So in 4 - (-4) it is as though you've got 4 of something . apples in my example . and you take away (i.e. you give SOMEBODY ELSE) an IOU for 4 apples.
So you have 4 apples and somebody else owes you 4 apples - so it means you own 8 apples.
Several people have said 'it's because maths is that way'. Whilst this is true, its that way for a reason.
If you start from the other end and say 'what number do you take away from 4 to get 8' you have something that sounds like a riddle, but with a bit a working out it also shows you why maths works this way:
4 - (mystery number) = 8
Call the mystery number X.
4 - X = 8
Now add X to both sides and you have
4 = 8 + X
(you can always add the same number to both sides of an equation and the equality is still true)
So X = 4 -8 = -4
So the mystery number to take away from 4 to get 8 is -4. Basically this is the same as the IOU for 4 items.
I hope that helped more than it confused.
I was taught that positive was to go right across a page and so up a number line. Negative was to go down the number line (left) or change direction.
In mixed commands positive means go in the same direction as the previous command.
Negative is to change direction. Therefore a double negative meant changing direction twice, going left, then right, so becoming positive.
A triple negative is left, right, left and so is negative since you end up pointing left.
Just think that plus (+) is go right in the first instance or stay in the direction you are sent.
Minus (-) is to change direction.
-, - therefore is +
-,-,- therefore is -
-,-,-,- is therfore +
-,+ is -
-.-.-,+ is -
-,+ is -
-.-.+ is +
Hope this helps
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