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secondary 2 | Maths
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Why is 7-(-1) = 8?
Date Posted: 3 years ago
Views: 368
Because, you are subtracting a negative.
When you subtract, it is like going backwards on the number line, i.e proceeding in the reverse direction
Eg.
7 - 4 is like taking 4 steps backwards.
7 - 4 = 3
But we can only go backwards in terms of positive/absolute values.
Since you are asked to subtract (-1), you are asked to move backwards for a negative value. This effectively reverses that reverse direction, bringing you back into the forward direction.
So 7 - (-1) = 7 + 1 = 8
Alternatively,
Let 7 - (-1) = a
Then 7 = a + (-1) = a - 1
7 = 8 - 1
So a = 8
When you subtract, it is like going backwards on the number line, i.e proceeding in the reverse direction
Eg.
7 - 4 is like taking 4 steps backwards.
7 - 4 = 3
But we can only go backwards in terms of positive/absolute values.
Since you are asked to subtract (-1), you are asked to move backwards for a negative value. This effectively reverses that reverse direction, bringing you back into the forward direction.
So 7 - (-1) = 7 + 1 = 8
Alternatively,
Let 7 - (-1) = a
Then 7 = a + (-1) = a - 1
7 = 8 - 1
So a = 8
The same goes for adding a negative number.
7 + (-1) = 7 - 1 = 6
Adding is like moving in the forward direction.
But we can only move forward for a positive/absolute value.
The + in '+ (-1)' is telling us to move forward, but the -1 reverses the direction so effectively we are moving backwards.
7 + (-1) = 7 - 1 = 6
Adding is like moving in the forward direction.
But we can only move forward for a positive/absolute value.
The + in '+ (-1)' is telling us to move forward, but the -1 reverses the direction so effectively we are moving backwards.
See 1 Answer
This is because when you multiply the negative in (-1) , it becomes positive .
There is no multiplication in the above operation.
Actually there is (multiplying the -1 by another -1), but students do not learn it that way
i.e.
7 - (-1)
= 7 - 1 x (-1)
= 7 + (-1) x (-1)
= 7 + 1
= 8
i.e.
7 - (-1)
= 7 - 1 x (-1)
= 7 + (-1) x (-1)
= 7 + 1
= 8
But you do realise that what you've written is the equivalent operation, not the actual.
7 - (-1) = 7 + 1 = 8
This is basically reversing the reverse direction, giving an overall of moving forward on the number line.
7 - (-1) = 7 + 1 = 8
This is basically reversing the reverse direction, giving an overall of moving forward on the number line.
If the multiplication approach was to be explained, then the workings should have been shown by the tutor.
Moreover, the (-1) x (-1) = 1 x 1 is also a cancelling of 2 negatives, which is already achieved by -(-1) = + 1 .
So the multiplication approach, while equivalent, is actually more tedious yet not more intuitive.
Moreover, the (-1) x (-1) = 1 x 1 is also a cancelling of 2 negatives, which is already achieved by -(-1) = + 1 .
So the multiplication approach, while equivalent, is actually more tedious yet not more intuitive.
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