Subtract integers

key notes:

▶️ Subtracting a negative is the same as adding a positive.

Subtracting integers on a number line

You can use a number line to subtract integers, too.

Subtracting a number is the same as adding its opposite. For example, 4–3 is the same as 4+(–3).

So, you can rewrite a subtraction expression as an addition of the opposite. Then, follow the rules for adding integers.

Subtracting a positive integer

Let’s try it. Subtract 3–7.

First, rewrite the subtraction problem as the addition of the opposite. The opposite of 7 is –7.

3–7=3+(–7)

Then, use a number line to add. Find 3 on the number line. Since –7 is negative, move 7 units to the left.

A number line from negative five to five, with a scale of one, is shown. There is a point at 3. There are arrows from 3 to 2, from 2 to 1, from 1 to 0, from 0 to negative 1, from negative 1 to negative 2, from negative 2 to negative 3, and from negative 3 to negative 4. There is also a point at negative 4.

Since you land on –4, the answer is –4.

So, 3–7=–4.

Subtracting a negative integer

Let’s try another one. Subtract –2–(–5).

First, rewrite the subtraction problem as addition of the opposite. The opposite of –5 is 5.

–2–(–5)=–2+5

Then, use a number line to add. Find –2 on the number line. Since 5 is positive, move 5 units to the right.

A number line from negative five to five, with a scale of one, is shown. There is a point at negative 2. There are arrows from negative 2 to negative 1, from negative 1 to 0, from negative 0 to 1, from 1 to 2, and from 2 to 3. There is also a point at 3.

Since you land on 3, the answer is 3.

So, –2–(–5)=3.

Rules for subtracting integers

You can subtract integers without number lines. Rewrite the subtraction problem as addition of the opposite and follow the rules for adding integers.

Subtracting a positive integer

Let’s try it. Subtract –2–3.

First, rewrite the subtraction problem as addition of the opposite.

–2–3=–2+(–3)

Now, follow the rules for adding integers. The signs of the addends are the same, so add their absolute values.

|–2|+|–3|=2+3=5

Since both addends are negative, the sum is also negative.

So, –2–3=–5.

Subtracting a negative integer

Let’s try another one. Subtract –2–(–3).

First, rewrite the subtraction problem as addition of the opposite.

2–(–3)=–2+3

Now, follow the rules for adding integers. The signs of the addends are different, so subtract the lesser absolute value from the greater absolute value.

|3|–|–2|=3–2=1

Since the positive addend, 3, has a greater absolute value, the sum is positive.

So, –2–(–3)=1.

Learn with an example

Subtract:

-7 − 10 =?

  • -3
  • 17
  • 3
  • –17

Change the minus sign to a negative sign:

-7 − 10 = -7 + -10

Since –7 and –10 are both negative, the answer will be negative.

First solve an easier problem:

7 + 10 = 17

Remember that the answer to the problem you’re solving will be negative:

-7 + -10 = -17

So:

-7 − 10 = -17

Subtract:

-9 − 4 = 

Change the minus sign to a negative sign:

-9 − 4 = -9 + -4

Since -9 and -4 are both negative, the answer will be negative.

First solve an easier problem:

9 + 4 = 13

Remember that the answer to the problem you’re solving will be negative:

-9 + -4 = -13

So:

-9 − 4 = -13

Subtract:

-8 − -5 = 

Change the negative sign and the minus sign to a plus sign:

-8 − -5 = -8 + 5

Now you are adding, so you can switch the order of the numbers:

-8 + 5 = 5 + -8

Change the negative sign to a subtraction sign:

5 + -8 = 5 − 8

Since 8 is bigger than 5, the answer will be negative.

First solve an easier problem:

8 − 5 = 3

Remember that the answer to the problem you’re solving will be negative:

5 − 8 =- 3

So:

-8 − -5 = -3

let’s practice: