Math Core

You already know how to add and subtract numbers up to 1,000. The same steps work for numbers in the thousands and hundred thousands. You just have more places to work through.

Adding with the standard algorithm

To add big numbers, stack them so the places line up: ones under ones, tens under tens, and so on. Then add one place at a time, starting with the ones.

Adding multi-digit numbers

Line up the numbers by place value.
Add each place, starting from the ones and moving left.
If a place adds up to 10 or more, write the ones digit and regroup 1 to the next place on the left.

Worked example: Adding with regrouping

Find $36{,}478 + 27{,}965$ .

\begin{array}{r} 36{,}478 \\ +\;27{,}965 \\ \hline 64{,}443 \end{array}

Ones: $8 + 5 = 13$ . Write 3, regroup 1 ten.
Tens: $1 + 7 + 6 = 14$ . Write 4, regroup 1 hundred.
Hundreds: $1 + 4 + 9 = 14$ . Write 4, regroup 1 thousand.
Thousands: $1 + 6 + 7 = 14$ . Write 4, regroup 1 ten thousand.
Ten thousands: $1 + 3 + 2 = 6$ . Write 6.

The sum is 64,443.

Subtracting with the standard algorithm

Subtraction works the same way, from the ones place to the left. When the top digit is smaller than the bottom digit, regroup: take 1 from the next place on the left and turn it into 10 in the place you are working on.

Worked example: Subtracting with regrouping

Find $52{,}314 - 18{,}672$ .

\begin{array}{r} 52{,}314 \\ -\;18{,}672 \\ \hline 33{,}642 \end{array}

Ones: $4 - 2 = 2$ .
Tens: 1 is less than 7. Regroup 1 hundred as 10 tens: $11 - 7 = 4$ . Now there are 2 hundreds left.
Hundreds: 2 is less than 6. Regroup 1 thousand as 10 hundreds: $12 - 6 = 6$ . Now there is 1 thousand left.
Thousands: 1 is less than 8. Regroup 1 ten thousand as 10 thousands: $11 - 8 = 3$ . Now there are 4 ten thousands left.
Ten thousands: $4 - 1 = 3$ .

The difference is 33,642.

Subtracting across zeros

When the top number has zeros, you may need to regroup from a place farther to the left.

Worked example: Regrouping across zeros

Find $60{,}003 - 28{,}457$ .

The ones place needs regrouping (3 is less than 7), but the tens, hundreds and thousands are all 0. Go all the way to the 6 ten thousands.

Think of 60,003 as 6,000 tens and 3 ones. Take 1 ten: now it is 5,999 tens and 13 ones. So the top number becomes 5 ten thousands, 9 thousands, 9 hundreds, 9 tens and 13 ones.

\begin{array}{r} 60{,}003 \\ -\;28{,}457 \\ \hline 31{,}546 \end{array}

Ones: $13 - 7 = 6$
Tens: $9 - 5 = 4$
Hundreds: $9 - 4 = 5$
Thousands: $9 - 8 = 1$
Ten thousands: $5 - 2 = 3$

The difference is 31,546. Check by adding: $31{,}546 + 28{,}457 = 60{,}003$ . ✅

Common mistake

Always subtract the bottom digit from the top digit. A common mistake is to "flip" a place, like doing $7 - 3$ instead of regrouping for $3 - 7$ . If the top digit is smaller, you must regroup.

Checking with estimation

Rounding helps you check whether an answer is reasonable. Round each number, then add or subtract the rounded numbers.

Worked example: Is the answer reasonable?

A stadium sold 48,215 tickets on Saturday and 39,870 tickets on Sunday. How many tickets did it sell in all?

Estimate: Round to the nearest ten thousand: $50{,}000 + 40{,}000 = 90{,}000$ .

Exact: $48{,}215 + 39{,}870 = 88{,}085$ .

The exact answer, 88,085, is close to 90,000, so it makes sense.

Tip

Check a subtraction problem by adding. If $a - b = c$ , then $c + b$ should give you back $a$ .

Practice

Practice 1

Find $4{,}582 + 3{,}219$ .

Type a number.

Practice 2

Find $23{,}506 + 48{,}795$ .

Type a number.

Practice 3

Find $9{,}436 - 2{,}718$ .

Type a number.

Practice 4

Find $70{,}000 - 34{,}286$ .

Type a number.

Practice 5

Find $305{,}418 - 127{,}659$ .

Type a number.

Practice 6

A library has 12,845 books. It buys 3,976 new books. Then it gives away 1,450 old books. How many books does the library have now?

Type a number.

Practice 7

What number goes in the box? $\square + 48{,}250 = 93{,}000$

Type a number.

Practice 8

Maya added $489{,}212 + 305{,}977$ and got 695,189. Use estimation to decide: is her answer reasonable?