Content

• To step
• Method 1 of 5: Addition and subtraction of positive integers with a number line
• Method 2 of 5: Add and subtract negative numbers on a number line
• Method 3 of 5: Adding large positive integers
• Method 4 of 5: Subtracting large positive integers
• Method 5 of 5: Addition and subtraction of negative integers
• Tips

You'd whole numbers can think of it as the regular numbers, such as 3, -12, 17, 0, 7000, or -582. Whole numbers are also called that because they are not divided into parts of numbers, such as fractions and decimals. Read this article to learn everything you want to know about integer addition and subtraction, or skip to an area where you need help.

To step

Method 1 of 5: Addition and subtraction of positive integers with a number line

1. What is a number line. A number line turns working with numbers into something real and tangible that you can envision. By using markers and your wits, we can apply them as a kind of calculator for adding and subtracting numbers.
2. Draw a basic number line. Draw a straight line. Place a mark in the middle of the line. Write one 0 or zero next to this mark.
   • Your math book may call this point it point of originbecause this is the point where the numbers matter arises, or start.
3. Draw two marks, 1 on each side of the zero. Write -1 next to the mark on the left and 1 at the right. These are the integers closest to zero.
   • Don't worry too much about perfect spacing - as long as it looks like it, the number line works fine.
4. Add more numbers to the line. Place more markers to the left of -1 and to the right of 1. As follows: -2, -3, and -4 and the markings on the right 2, 3, and 4, etc. as much as you can put on the paper.
5. Understand positive and negative integers. A positive integer, also called one natural number, is an integer greater than zero. 1, 2, 3, 25, 99, and 2007 are all positive integers. A negative integer is an integer less than zero (such as -2, -4, and -88).
   • Fractions such as 1/2 are part of a number, not integers. Likewise with a decimal such as 0.25; decimals are not integers.
6. Solve 1 + 2 by placing your finger on the marker labeled 1.
   • Do you find this a bit too easy? You will not be unfamiliar with adding up and you will know how to solve 1 + 2 by heart.Great: if you already know the answer, it's easier to understand how the number line works. Then you can use a number line for more complicated problems, or to prepare for math and algebra.
7. Do the sum 1 + 2 by sliding your finger 2 marks to the right. Count the number of markers you pass. If you had 2 markers, stop. The number your finger points to is the answer: 3.
8. Another example. Suppose we want to know what 3 + 2 is. Start at 3, move to the right and increase with 2. We end at 5. You write this as 3 + 2 = 5.
9. Subtract positive integers by moving left on the number line. As an example we have the sum 6 - 4. We start at 6, move 4 marks to the left and end at 2. You write this as 6 - 4 = 2.

Method 2 of 5: Add and subtract negative numbers on a number line

1. Learn what a number line is. If you don't know how to make a number line, go back to Adding and subtracting positive numbers and read that again.
2. Understand negative numbers. Positive numbers are to the right of the zero and negative numbers are to the left of the number line. Adding a negative number moves your finger to left on the number line.
   • As an example we take the sum 1 + -4. On a number line we start at 1, move 4 places to the left and end at -3.
3. Use a comparison to understand addition with negative number. Note that -3, our answer, is the same when we work out the sum 1 - 4. 1 + (-4) and 4 - 1 are the same. We can also write this as a comparison, a mathematical way of showing that two things are equal:
   
   1 + (-4) = 1 - 4 = -3
4. Instead of adding a negative number, we can also turn it into a subtraction using only positive numbers. As you could see from our simple equation, we can go two ways - "add a negative number" or "subtract a positive number." You may have had to learn this without being told why - this is the reason.
   • As an example, take -4. If you add -4 to 1, you decrease 1 by 4. Or the mathematical way:
     
     1 + (-4) = 1 - 4
     
     We write this on a number line, and place our finger on the 1, then move 4 places to the left (in other words, add up by -4). Since it's an equation, left equals right - so the converse is also true:
     
     1 - 4 = 1 + (-4)
     
5. Understand how subtracting negative numbers works on a number line. On a number line, subtracting a negative is equivalent to moving to the right. Let's start with 5 - 8.
   • On a number line, we start at 5, decrease it by 8, and end at -3. This is noted as
     
     5 - 8 = -3
     
     
6. Reduce the number you subtract and see what happens. Suppose the sum becomes 5 -7. Now we move 1 space less to the left on the number line. You note this as
   
   5 - 7 = -2
7. Note that a reduction can result in an increase. In this example, we will reduce the number of spaces to the left by 1. As a comparison, this becomes:
   5 - 7 = -2 = 5 - (8 - 1)
8. Convert a minus to a plus when adding negative numbers. Using the step "change the subtraction to addition", we can now write this more briefly as:
   5 - (8 - 1) = 5 - 7 = 5 - 8 + 1 .
   • We already know that 5 - 8 = -3, so let's omit 5 - 8 from our equation and put it in -3:
     5 - (8 - 1) = 5 - 7 = -3 + 1
     
   • We already know what 5 - (8 - 1) is - you move a marker less than 5 - 8. Our equation shows that 5 - 8 = -3, and 1 step less so is -2. Now our equation can be written as:
     
     -3 - (-1) = -3 + 1
     
9. Write the subtraction of negative numbers as an addition. Notice what happened at the end - we proved that:
   
   -3 + 1 = -3 - (-1)
   
   We can express this as a simple, more general mathematical rule:
   
   first number plus second number = first number minus negative second number)
   Or, in simpler terms such as in math class:
   
   Turn two minuses into plus.

Method 3 of 5: Adding large positive integers

1. Write the addition 2503 + 7461 with one number on top of the other. Place the numbers on top of each other, so that the 2 is above the 7, the 5 is above the 4, etc. In this method we learn how to add numbers that are too large to memorize or with a number line.
   • Write a + to the left of the bottom number and a line below it.
2. Start adding the two numbers on the far right. It may seem strange to start on the right, because we are so used to reading numbers from left to right. We will stick to this order because otherwise we will not get the correct answer, as you will see later.
   • Below the two numbers on the right, 3 and 1, you write down the answer of the addition of both numbers: 4 So.
3. Add each number in the same way. Working from left to right, do the following additions: 0+6, 5+4, and 2+7. Write the answers below the pairs of numbers.
   • The answer you will get, if you did it right: 9964. Have you made a mistake, check your elaboration.
4. Now do the sum 857 + 135. Here you see a difference from the previous one, because 7+5 is equal to 12, a 2-digit number. But you cannot put more than 1 digit under a pair of numbers. Keep reading to learn what to do and why you should always start on the right instead of on the left.
5. Do the sum 7 + 5 and learn what to do with the answer. 7 + 5 = 12, but you only place the 2 below the line and the first digit, 1, place you above the second pair of numbers, 5 + 3.
   • If you want to know how this works, think about what dividing the 1 and 2 entails. You actually divide 12 up 10 and 2. You can write the 10 all the way above the numbers if you want, after which you will notice that the 1 aligns with the 5 and the 3, as it should.
6. Do the sum 1 + 5 + 3 to get the next digit of the answer. You now have 3 numbers to add because you added the 1 to it. The answer is 9, so your answer so far is 92.
7. Complete the assignment as usual. Keep doing the sums from right to left until you are done, adding another column in this case. Your final answer is 992.
   • You can try slightly more difficult exercises, such as 974 + 568. Remember that every time you get a two-digit number, you put only the last digit next to the answer and the first digit above the next pair of numbers (the next column). If the last sum has a two-digit answer, you can place both of these with the answer below the line.
   • Look at the Tips for an answer to the problem 974 + 568 to check your own answer.

Method 4 of 5: Subtracting large positive integers

1. Write the sum 4713 - 502 with the first number above the second. Write these so that the 3 is directly above the 2, the 1 above the 0, the 7 above the 5 and the 4 above the empty space.
   • You can put a 0 below 4 if this helps you align both numbers. A zero before a number does not change the value of that number. A zero after it does, so don't put the zero there.
2. Subtract each bottom number from the number immediately above it, starting on the far right. Solve the following sums in sequence: 3-2, 1-0, 7-5 and 4-0. Place the answers directly below the pair of numbers it belongs to.
   • The answer should be: 4211.
3. Now do the problems 924 - 518 in the same way. These numbers are the same length, so you can easily align them. This exercise teaches you something new about subtracting integers (hopefully).
4. The first problem, 4 - 8. This one is tricky, because 4 is less than 8, but we're not going to use negative numbers. Here's how to fix this:
   • Cross out the 2 of the top number and write a 1 there. The 2 is immediately to the left of the 4.
   • Cross out the 4 and make it 14. Do this in a small space, so that it is clear to which pair of numbers 14 belongs, and thus indicates 14 - 8. You can also just write a 1 before 4, if there is enough space.
   • What you just did is "borrow" a 1 from the column containing tens, or also the second column to the right, so that you can add 10 to 4. This gives you 14 in the column with units.
5. Now solve the problem 14 - 8 and write the answer under the right column. You should now see a 6 on the far left below the line.
6. Solve the next column (to the left) with the new number (the 2 was replaced by a 1). So this becomes 1 - 1, which is equal to 0.
   • Your answer belongs so far 06 to be.
7. Complete the problem by solving the last column. 9 - 5 = 4, and so is the answer 406.
8. Now we move on to a problem where we subtract a larger number from a smaller number. Let's say you need to solve 415,990 - 968,772. You write the second number below the first, then you realize that the bottom number is bigger!
   • Make sure the numbers are aligned before you compare them. 912 not greater than 5000, which you can easily see if the numbers are correctly aligned, because the 5 are nowhere above. You can put 1 or more zeros in front of the number, if that helps. For example, write 912 as 0912 so that it is the same length as 5000.
9. Write the smaller number below the larger number and put a minus sign in front of the answer. Anytime you subtract a number from a smaller number, you get a negative number as the answer. It is best to write down the minus sign before solving the problem so that you do not forget it.
10. To find the answer, subtract the small number from the larger number. Don't forget the minus sign. Your answer will be negative, as indicated by the minus sign. Try not to subtract a larger number from a smaller number and then make it negative; because of this you will not get the correct answer.
    • The new problem to solve is: 968.772 - 415.990 = -? Check the Tips to check your answer.

Method 5 of 5: Addition and subtraction of negative integers

1. Learn about adding a negative and a positive number. Adding a negative integer is the same as subtracting a positive number. This is easier to see by testing this out with the number line method described in another section, but you can also think about it in words. A negative number is not a normal amount; it is less than zero, and can represent an amount that is being taken away. If you add this "take away" amount to a regular number, you make it smaller.
   • Example: 10 + -3 = 10 - 3 = 7
   • Example: -12 + 18 = 18 + -12 = 18 - 12 = 6. Remember that you can always switch the order of numbers in an addition, but not when subtracting.
2. Learn what to do if it becomes a subtraction with the smallest number. Sometimes converting from addition to subtraction can give results such as 4 - 7. If this happens, flip the numbers and make the answer negative.
   • Suppose you have 4 + -7.
   • Make this a subtraction: 4 - 7
   • Reverse the order and make the sum negative: - (7 - 4) = - (3) = -3.
   • If you're not used to using parentheses in your sums, think of it like this: 4 - 7 becomes 7 - 4 and add a minus sign. So 7 - 4 = 3 and then you make it -3 to get the correct answer to the sum 4 - 7.
3. Learn how to add two negative integers. Adding two negative numbers always causes the answer to be negative and greater. Nothing positive is added, so you always end up with something even further away from zero. Finding the answer is easy:
   • -3 + -6 = -9
   • -15 + -5 = -20
   • Do you see the pattern? All you have to do is add the numbers together as if they were positive and then add a negative sign to them. -4 + -3 = - (4 + 3) = -7
4. Learn how to subtract a negative integer. As with the addition sums, you can rewrite these so that you only deal with positive numbers. If you subtract a negative number, you are "taking something away" from "something being taken away", which is the same as adding a positive number.
   • Think of a negative number as stolen money. If you "subtract" or take something from the stolen money in order to return it, it is the same as giving money to that person, isn't it?
   • Example: 10 - -5 = 10 + 5 = 10
   • Example: -1 - -2 = -1 + 2. You already learned how to solve this, in a previous step, remember? If you don't remember, reread "Learn how to add a negative and a positive number".
   • Here is the complete solution of the last example: -1 - -2 = -1 + 2 = 2 + -1 = 2 - 1 = 1.

Tips

• You are used to writing long numbers like 2,521,301. In many countries it is common to use a comma instead of a period, or vice versa (with decimals). Don't let that confuse you when looking for information on this topic on the internet. Stick to what you learn about this at school.
• Make different number lines for different numbers. It is not a rule that number lines always go over whole numbers. This can also be over tens or fractions. Except that each space now represents something different, you can still use the number line the same way for addition and subtraction. Just give it a try.
• If you tried the extra problem in the large numbers section, here are the answers: 974 + 568 = 1542. The answer to the sum is 415,990 - 968,772 -552.782.