# Where Negative Numbers Come From

When you first discovered subtraction, you were probably told that you can't take a small number minus a greater number. For example, if you start with four marbles, you can't subtract six because you can't take away more marbles than you have.

This rule is true for marbles, but in other situations, you *can* subtract a big number from a small one. For example, if you have $4 and you buy something that costs $6, you end up with less than $0 dollars — that is, –$2, which means a *debt* of $2.

A number with a minus sign in front of it, like –2, is called a *negative number.* You call the number –2 either *negative* *two* or *minus two.* Negative numbers appear on the number line to the left of 0.

Subtracting a large number from a small number makes sense on the number line. Just use the rule for subtraction: Start at the first number and count left the second number of places.

When you don't have a number line to work with, here's a simple rule for subtracting a small number minus a big number: Switch the two numbers around and take the big number minus the small one; then attach a negative sign to the result.

## Sample questions

Use the number line to subtract 5 – 8.

**–3.**On the number line, 5 – 8 means*start at 5, left 8.*What is 11 – 19?

**–8.**Because 11 is less than 19, subtract 19 – 11, which equals 8, and attach a minus sign to the result. Therefore, 11 – 19 = –8.

## Practice questions

Using the number line, subtract the following numbers:

**a.****b.****c.****d.**Find the answers to the following subtraction problems:

**a.****b.****c.****d.**

Following are the answers to the practice questions:

Subtraction problems with number line

**a.**1 – 4 =**–3.**Start at 1, down 4.**b.**3 – 7 =**–4.**Start at 3, down 7.**c.**6 – 8 =**–2.**Start at 6, down 8.**d.**7 – 14 =**–7.**Start at 7, down 14.Subtraction problems

**a.**15 – 22 =**–7.**Fifteen is less than 22, so subtract 22 – 15 = 7 and attach a minus sign to the result: –7.**b.**27 – 41**= –14.**Twenty-seven is less than 41, so subtract 41 – 27 = 14 and attach a minus sign to the result: –14.**c.**89 – 133 =**–44.**Eighty-nine is less than 133, so subtract 133 – 89 = 44 and attach a minus sign to the result: –44.**d.**1,000 – 1,234 =**–234.**One thousand is less than 1,234, so subtract 1,234 – 1,000 = 234 and attach a minus sign to the result: –234.