Showing the Working

Lining Up the Columns #

Stack by place value, then work rightwards first.

Stacking numbers by place value is what lets you add one column at a time

Place value lines them up: ones under ones, tens under tens. Start: 6 + 1 = 7.

Similarly, add the digits in the tens' place to get 7.

Now the hundreds. Add 4 and 3, write the 7. The answer is 777.

Carrying #

A column that makes ten passes it along.

When a column makes ten or more, that ten moves across to the next column

Add the units: 7 and 8 make 15. A column holds one digit, so 15 will not fit.

So write the 5 underneath, and the carried 1 sits on top of the tens.

Add the tens: the carried 1, then 4 and 2. Write 7. The answer is 75.

Carrying in More Than One Column #

Every column carries the same way.

A carry can happen in any column, and every one of them works the same way

Add the units: 8 and 5 make 13. Write the 3, and carry the 1 ten.

Add the tens: 1 carried, 6 and 7 make 14. Write 4, and carry 1 hundred.

Add the hundreds: 1 carried, 1 and 2 make 4. Read the answer: 443.

Borrowing #

Take a ten from next door when you run short.

When the top digit is too small, take one from the column to its left

2 is smaller than 7, so we cannot subtract yet. Borrow from the tens place.

Take one ten from the 5 tens: they drop to 4, and the units become 12.

Now subtract both columns: 12 − 7 = 5, and 4 − 2 = 2. The answer is 25.

Borrowing Past a Zero #

A zero has nothing to lend, so keep going left.

A zero has nothing to lend, so the borrow travels one more column along

4 is smaller than 7, so we must borrow. But the tens place is a 0. What now?

Borrow from the hundreds. The 3 drops to 2, and the zero becomes 10 tens.

Now the tens have something to lend: 10 drops to 9, and units become 14.

Now subtract each column to get the answer: 177.

Two-Step Word Problems #

The first answer feeds the second step.

The first answer is the number the second step works on

The fair takes $345, then $187 more. First find the total: 345 + 187 = 532.

Paying $268 for the tent is the second step, and it acts on 532: 532 − 268 = 264.

Two steps, one chain: each step works on the answer the last one made.