3-digit Addition and Subtraction

1Summary 重點摘要

Learn 3-digit addition and subtraction, with carrying and borrowing.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Align the placesWhen writing a vertical sum, line the two numbers up first: ones under ones, tens under tens, hundreds under hundreds, then draw a line below, with the plus or minus sign at the left. With the places aligned, we can add or subtract matching units directly. For example, in 365 + 478, the 5 must sit over the 8, the 6 over the 7 and the 3 over the 4. A common mistake is to put the last digit of 478 under the hundreds of 365, making a slanted sum that cannot come out right. Before calculating, check every place is directly above its partner; never rush this step.
2. Step 2: Add from the rightWhen adding, start from the ones place on the far right: ones first, then tens, then hundreds. For 365 + 478: the ones give 5 + 8 = 13, the tens 6 + 7 = 13, the hundreds 3 + 4 = 7, recording each result in turn. Keeping the same order means we never miss a place, and the working is quick and steady. A common mistake is to add from the hundreds on the left; as soon as the ones need a carry, the written answer must be rubbed out and done again, which wastes time and invites errors. Build the right-to-left habit and bigger numbers will not confuse you later.
3. Step 3: CarryIf the digits in a place add up to more than 9, we carry. In 365 + 478, the ones give 5 + 8 = 13: write 3 in the ones place and carry 1 to the tens. The tens give 6 + 7 = 13, and with the carried 1 that is 14, so write 4 and carry 1 to the hundreds. The hundreds give 3 + 4 = 7, plus the carried 1 makes 8, so the answer is 843. A common mistake is to forget the carried 1 and work out the tens as 3 instead of 4. In a vertical sum you may jot a small 1 above the next column to help yourself remember, then check the whole sum once more at the end.
4. Step 4: Subtract from the rightSubtraction works like addition: start from the ones on the far right, then tens, then hundreds, subtracting the bottom number from the top number in each place. For 512 − 276: the ones 2 − 6 and the tens 1 − 7 both cannot be done directly, so regroup first and then subtract place by place; at the hundreds, 5 − 2 must also account for what was lent away. Keeping the same order keeps the working tidy. A common mistake is to jump between places, doing the hundreds first and coming back, which easily confuses the borrowing; fix the order from right to left, one step at a time, and errors fall away.
5. Step 5: BorrowIf a place is too small to subtract, for example the ones in 512 − 276, where 2 − 6 is impossible, borrow 1 from the tens. The borrowed 1 works as 10 in the ones place: 12 − 6 = 6. The tens digit was 1; after lending 1 it becomes 0, and 0 − 7 still cannot be done, so borrow 1 from the hundreds: 10 − 7 = 3. The hundreds digit 5, having lent 1, is now 4, and 4 − 2 = 2, so the answer is 236. A common mistake is to forget to reduce the digit that lent, and subtract with the original 1 or 5. Each time you borrow, mark the digit that lent, to remind yourself it is 1 less.
6. Step 6: CheckAfter working, check by using addition and subtraction on each other. After subtracting, add the answer to the number subtracted and see whether it equals the starting number. For 512 − 276 = 236, check with 236 + 276 = 512, which returns to the original, so the calculation is correct. After adding, subtract one addend from the sum and see whether the other addend remains. A common mistake is only to glance over the working without really calculating again, or to trust the first answer when the check disagrees. If the two results differ, you must go through the places again and find where the error is.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Add-subtract must align places
• Start from right (units)
• Addition over 10 must carry
• Subtraction not enough must borrow
• Can check answer with add-subtract