Three-Digit Addition & Subtraction
A three-digit number is made of hundreds, tens, and ones, so 256 is 200 and 50 and 6 put together. In addition, when a column adds up to 10 or more you carry 1 to the next place, and in subtraction, when you cannot take away enough you borrow 10 from the place above. When you handle big numbers, like saving your allowance or counting items, you line up the places and work through them step by step in a vertical calculation. Choose addition or subtraction, change the two numbers, and watch the process with place-value blocks and the vertical form.
To add or subtract two numbers at once, you have to gather only the same place together. If a slot piles up 10 or more, that 10 has to leave as 1 in the slot to the left. If a slot is too small to subtract, you bring 10 from the slot to the left before the next slot will match. That is why you start at the ones, then the tens, and the hundreds last. Writing the numbers in columns pins that order down on the page.
Pick the addition or subtraction button and change the two sliders between 100 and 499, and the first picture writes the full equation and the answer in one line at the top. Below that are three columns for hundreds, tens, and ones: darker blocks for the first number, lighter blocks for the second, and the result digit for that column under a line. A red carry label and a dashed curve from ones to tens appear only when the ones sum is 10 or more. A borrow label from tens to ones appears only when subtraction cannot take the ones. There is no mark from tens to hundreds on this picture. If you chose subtraction and the first number is smaller, the two numbers swap on the drawing. The second picture is the same work written in columns. The digits and the answer are already written; they do not fill in one place at a time. When a carry happens, a small 1 sits above that column.
If you think you must add or subtract from the hundreds on the left, it is easy to lose where the extra 1 from a full slot went. Column work starts at the ones on the right. When a slot sums to 10 or more, you leave only the ones digit in that slot and send 1 to the slot on the left, or the next sum will be wrong. When a slot cannot subtract, you bring 10 from the left first and only then finish that slot. Starting at the high slot makes it hard to fit a 1 that arrives later.