Algebra Tutorials!

 Monday 16th of September

# Calculations with Negative Numbers

## Question: What is the value that satisfies -4 + ? = -10 ?

 Misconception There are several possible misconceptions including ? = 6 and ? = 14 or even ? = - 14 Correct The correct answer is - 6 as this satisfies the sum -4 + (-6) = -10. It can be shown on a number line as given below. Starting at negative 4 and adding negative 6 you get the answer negative 10. Hence -4 + (-6) = -10.

## Further Explanation

It is important to realise that there is no guessing, no doubts but straightforward logic. Here we can associate the meaning owning when the quantity is positive and owing if it negative. Also, as before, we associate the minus sign with opposite.

In this example,

I start by owing 4 ( i.e. the '- 4 ' )

What is this '+?' that must have happened if I ended up 'owing 10' ? ( i.e. the ' - 10 ')

Another debt of 6 must have been added to my plight

We write 'adding a debt of 6' as ' + ( -6) '

So in - 4 + ? = - 10 the ? must be - 6

This is equivalent to the use of a number line as shown above; it does not matter which way you argue as long as you get the logic correct!

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