Addition and Subtraction of Signed Numbers
$$(-11) - (-20) = $$
Incorrect.
If the numbers -11 and -20 were being added, their sum would be -31, but they are being subtracted. Rewrite the subtraction as addition of the opposite first.
Another way to think of this type of problem is that subtracting a negative number is the same as adding a positive number.
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Incorrect.
Be careful rewriting the subtraction as addition of the opposite. The second number (the one _after_ the subtraction symbol) is changed to its opposite, not the first.
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Well done!
The first step when dealing with subtraction of positive and negative numbers is to rewrite the subtraction as addition of the opposite. This means the subtraction symbol should be changed to addition, and simultaneously, the second number (the number _after_ the subtraction symbol) should be changed to its opposite. The opposite of -20 is 20, so
$$\displaystyle (-11) - (-20) = (-11) + (20)$$.
Now the rules for adding signed numbers apply. Looking at the sum -11 + 20, the two numbers have opposite signs, so they will work against each other. Subtract the smaller number from the bigger number to get
$$\displaystyle 20 - 11 = 9$$.
The answer is 9. Since the bigger of the two numbers was positive, the answer is also positive.
$$\displaystyle (11) - (-20) = 9$$
Incorrect.
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Even after rewriting the subtraction as addition of the opposite, the first number will still be negative, so the sum of the two numbers cannot be 31.
$$-31$$
$$-9$$
$$9$$
$$31$$
