Subtraction feels harder than addition for most people, and borrowing is the reason. Every borrow is one more thing to hold in your head, and a single slip changes the whole answer. The good news is that you rarely need to borrow at all when you subtract mentally. The methods below go around the borrowing instead of through it.
Each one comes with worked examples, and every answer is checked by adding back. There is a practice set at the end.
Subtraction asks for the difference between two numbers, so you can find it by counting up from the smaller number to the bigger one. Jump to a round number first, then make the bigger jumps.
For 800 − 573: from 573, jump to the next hundred, 573 + 27 = 600. Then jump to the target, 600 + 200 = 800. The two jumps add up to the answer, 27 + 200 = 227. So 800 − 573 = 227.
For 503 − 268: 268 + 2 = 270, then 270 + 30 = 300, then 300 + 203 = 503. Add the jumps: 2 + 30 + 203 = 235. So 503 − 268 = 235.
Counting up shines when the bigger number is round, like 500, 800 or 1,000. It is also how people check change: if something costs 6.35 and you pay with 10, count up 6.35 + 0.65 = 7.00, then 7.00 + 3.00 = 10.00, so the change is 3.65.
Keep the first number whole and subtract the second one in pieces, biggest first.
As with adding from the left, you hold one running total at each step, and you know roughly how big the answer is from the start.
If the number you subtract is close to a round number, subtract the round number, then give back the extra.
For 652 − 298: subtract 300 instead, 652 − 300 = 352. But you took away 2 more than you should have, so give it back: 352 + 2 = 354. So 652 − 298 = 354.
The rule: if you took away too much, add the difference back. If you rounded the number you subtract down, you took away too little, so take a bit more away afterwards.
Sometimes both numbers are near round ones. For 978 − 624, round 978 up to 1,000 and 624 down to 600. The rounded subtraction is 1,000 − 600 = 400.
Now undo both changes, one at a time. Raising 978 by 22 made the answer 22 too big. Lowering 624 by 24 made the answer 24 too big as well, because you are now taking away less. So take both off: 400 − 22 − 24 = 354. Therefore 978 − 624 = 354. Check: 354 + 624 = 978.
This works, but two adjustments are two chances for a slip. If one number is far from round, Method 3 or counting up is usually safer.
The gap between two numbers stays the same if you move both of them by the same amount. So shift both to make the number you take away round.
The second example is why subtracting from 1,000 is so fast. Once it is 999 minus something, no digit ever needs a borrow: 9 − 3 is 6, 9 − 8 is 1, and 9 − 6 is 3, which gives 613. A Vedic Maths sutra uses the same idea, and you can read about it in Vedic Maths subtraction tricks.
For long numbers, the written method is still the right tool. Here is 632 − 419, one column at a time.
So 632 − 419 = 213. The classic mistake is to take the smaller digit from the bigger one in every column ("9 take away 2 is 7"), which gives 227. Counting up avoids this: 419 + 1 = 420, then 420 + 200 = 620, then 620 + 12 = 632, and 1 + 200 + 12 = 213.
Subtraction and addition undo each other, so add your answer to the number you took away. You should land on the number you started with.
This is the same fact family idea children learn with small numbers: one addition fact gives two subtraction facts. Our guide to fact families explains it, and quick addition tricks will make the checking step fast.
Answers:
Then put it to work against the clock. In Math Monster Battle you answer quickly to beat the monster, and in practice mode you can choose subtraction only and raise the difficulty when you are ready.
Count up from the smaller number to the bigger one, jumping to a round number first. It avoids borrowing completely, and the jumps are additions, which most people find easier.
Take 1 from both numbers so the sum becomes 999 minus something. Then take each digit from 9; no digit needs a borrow. For 1,000 − 456, that gives 999 − 455, which is 544.
Subtraction measures the gap between two numbers. If both move up by 3, the gap doesn't change, just as two people stay the same distance apart when they both take three steps forward.