When you need to do subtraction with a number that goes into the thousands place, remember these important rules. First, line up your two numbers properly. Then, start subtracting each set of digits from the right side. When the number on top is smaller, add 10 and take 1 away from the next number. With a little practice, you’ll get it in no time.
- Line up your two numbers by their places. First, write your starting number (the one before the minus sign). Underneath, write the number you’re subtracting. Line the numbers up so that the ones places are on top of each other, then the tens places, then the hundreds, then the thousands. Put a minus sign to the left and a flat line underneath your two numbers. Now, you’re ready to start!
- Let’s say we want to subtract 5914 – 2346. We would write 5914 on top, then write 2346 so that the 6 is under the 4, the 4 is under the 1, the 3 is under the 9, and the 2 is under the 5.
- Subtract the ones places. These are the two numbers on the far right side of your problem. Write your answer beneath the line.
- If the top number isn’t big enough to subtract the smaller number, cross it out, then add 10 to it and write it again. Take 1 away from the number to the left of it. This is called borrowing.
- We would start to subtract 5914 – 2346 by subtracting 4 – 6. Since 4 is smaller than 6, we add 10 to it to get 14. 14 – 6 is 8, so we write 8 below the line. We also have to take 1 away from the top number in the tens place. 1 – 1 is 0, so now we have a 0 in the tens place.
- Subtract the tens places. Write your answer underneath the line again. It should be next to the number you just wrote. If your top number isn’t big enough, add 10 and subtract 1 from the hundreds place.
- In our example, the tenths place has a 0 over a 4. Since 0 isn’t big enough to subtract 4, we need to add 10. 10 + 0 = 10. 10 – 4 = 6. Write this 6 underneath the line next to the 8. Take 1 away from the 9 in the hundreds place to get 8.
- Subtract the hundreds places. Keep going. Write your answer below the line in the hundreds place. If the number on top isn’t big enough, add 10 to it and subtract 1 from the number in the thousands place.
- In our example, the hundreds place has an 8 over a 3. 8 is bigger than 3, so we don’t need to borrow. 8 – 3 = 5. Write this underneath the line next to the 6 and 8.
- Subtract the thousands place to get your answer. You’re almost done! Subtract the two numbers in the thousands place just like you did with the other places to get your next digit. Write this next to your other answer numbers. The digits below the line make up your answer!
- In our example, the thousands place has a 5 over a 2. 5 – 2 = 3. Write this below the line.
- From left to right, our four answer digits are 3, 5, 6, 8. This means that 5914 – 2346 = 3568.
Problems With Decimal Points
- Line up the decimal points when you write your problem. When you write your problem, line up the decimal points so that they are right on top of one another. Put a decimal point right below them underneath the line. This makes sure that all the numbers in your problem are lined up the right way.
- Let’s subtract 1368.4 – 92.75. Line the decimal point in 1368.4 up with the one in 92.75. This should put the 2 under the first 0, the 9 under the second 0, and the 7 under the 4.
- Fill in blank spaces with zeroes. Fill in any blank spaces in the problem with zeroes. It doesn’t matter which side of the decimal point the spaces are on. This makes sure that every row has two numbers in it.
- In our example problem, there isn’t any number over the 5 right now. We can fix this by putting a 0 above 5. There also aren’t any numbers under the 1 and the 3 in 1368.4. We can fix this by putting a 0 underneath each. This gives us 1368.40 minus 0092.75. Everything is now lined up perfectly.
- Subtract like normal. Now you can use the same rules as before to subtract. Don’t forget to add 10 to each digit that needs it and subtract 1 from the next digit. Ignore the decimal points. They don’t change any of the rules.
- Starting from the far right, we can subtract like this:
- 0 isn’t big enough, so we borrow. 10 – 5 = 5. The next digit is now 3.
- 3 isn’t big enough, so we borrow. 13 – 7 = 6. The next digit is now 7.
- 7 – 2 = 5
- 6 isn’t big enough, so we borrow. 16 – 9 = 7. The next digit is now 2.
- 2 – 0 = 2.
- 1 – 0 = 1.
- Reading from left to right, your final answer for 1368.4 – 92.75 is 1275.65.
- Add a decimal point for numbers that don’t have one. What do you do when you have to subtract two numbers, but only one has a decimal point? Remember that all numbers automatically have one to the right of the ones place. You can add this whenever you need to so that your two numbers line up properly. Don’t forget to fill in blank spaces with zeroes.
- Let’s say we’re subtracting 4750 – 136.2. 4750 doesn’t have a decimal point yet, but we can put one to the right of the 0. After this, we line up the decimal points. Then, we put a 0 below the 4 and a 0 above the 2 so all the spaces are filled in. When we’re done, we have 4750.0 – 0136.2.
- When you have to borrow from a 0, borrow from the next row instead. What do you do when you’re subtracting in the ones row and you have to borrow from the tens column but there’s nothing there? Look in the hundreds row instead. If there’s another 0, look in the thousands row. As soon as you get to a number that’s not a 0, subtract 1 from it and add 10 to the row to the right. Keep borrowing in each row until you have enough to do the first subtraction problem.
- Let’s say that we need to subtract 1003 – 9. 3 isn’t big enough to subtract 9, but we can’t borrow from the 0 in the tens place.
- Instead, let’s look in the hundreds place. There’s a 0 here too, so let’s keep looking.
- Let’s look in the thousands place. Here we have a 1. Subtract 1 and add 10 to the hundreds place. Now we have a 0 in the thousands place and a 10 in the hundreds place.
- Subtract 1 from the hundreds place and add 10 to the tens place. Now we have a 9 in the hundreds place and a 10 in the tens place.
- Finally, subtract 1 from the tens place and add 10 to the ones place. Now we have a 9 in the tens place and an 11 in the ones place. This gives us 11 – 3 = 8. In the tens place, 9 – 0 = 9. In the hundreds place, 9 – 0 = 9 Our final answer is 998.
- If the number on the bottom is bigger, flip the problem and make your answer negative. What do you do when it’s obvious that there isn’t enough in the top row of your problem to finish the subtraction? Just flip the problem over. Move the number in the bottom row to the top and move the number in the top row to the bottom. When you get your answer, write it with a minus sign to the left. This means that it’s a negative number — a number that’s less than zero.
- Let’s say we need to subtract 300 – 1734. Obviously, 300 is less than 1734. If we flip the problem over, we can subtract 1734 – 300 and take the negative version of our answer.
- In the ones place, 4 – 0 = 4. In the tens place, 3 – 0 – 3. In the hundreds place, 7 – 3 = 4. In the thousands place, 1 – 0 = 1. Our first answer is 1434. Adding the negative sign, we get -1434, or 1434 less than zero. This is our true answer.
- If you’re doing a word problem, don’t forget to label your answer. Some teachers will take off points if you forget the label.
- Calculators can help with tricky problems. Here is a handy online subtraction calculator if you get stuck. Try not to use it too much or you might forget how to do the problems by hand.
Sources and Citations
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