Line the numbers up so like units sit in the same column.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Regroup wherever a column fills
Ten ones become a ten. Ten tens become a hundred. Ten hundreds become a thousand.
It is still one ten
The digit you write above the next column is one of that unit, not one of anything else.
Estimate first
Round both numbers before you start, so a wrong answer stands out.
Step 2: Try It Yourself
Tap and try it out.
First number
and Second number
Altogether
Hundreds
5
Tens
13
Ones
13
368 + 275 = 643
There are 13 loose ones. Ten of them can become one more ten.
Hundreds
3
Tens
6
Ones
8
3 hundreds, 6 tens and 8 ones is 368.
4867+2459
4,867 and 2,459 as pieces
Step 0 of 4
4,867 + 2,459 = …
Step 3: In Real Life
A charity’s year
A charity raised 24,586 dollars in spring and 18,749 in fall. Column by column, carrying where needed: 43,335. The algorithm is place value, written fast.
Step 4: Watch an Example
One step at a time.
Watch Ana Add 4,867 and 2,459
Ana adds two four-digit numbers.
- Step 1
She estimates first: about 5,000 and about 2,500, so around 7,500.
Step 5: Your Turn
Practice makes it stick.
Two Crowds
Problem 1 of 2
3,486 people came on Saturday and 2,795 on Sunday. How many in all?
people
Two Journeys
Problem 2 of 2
A trip of 1,258 km, then 2,647 km. How far in total?
km
Add the Columns
1 of 3
2,486 + 1,375 = ?
2 of 3
5,092 + 3,918 = ?
3 of 3
4,679 + 2,845 = ?
Build the Answer
Build it, then check.
What is 368 and 275? Build the answer.
Nothing.
You need ten ones before you can bundle.
Hundreds
0
Tens
0
Ones
0
0 hundreds, 0 tens and 0 ones is 0.
Step 6: Quick Check
Show what you know.
Question 1 of 2
3,758 + 2,496 = ?
Question 2 of 2
When a column of tens fills, what do you make?
What You Learned
- Line up like units in columns.
- Ten of any unit becomes one of the next unit up.
- Estimate first so a wrong answer stands out.
For the grown-up
This lesson is where the child adds multi-digit whole numbers fluently using the standard algorithm. Each place is ten times the one to its right, and that single rule generates the whole system all the way to a million and, later, all the way down past the decimal point.
Watch for large numbers read digit by digit. "Four hundred and seven thousand" is a structure; "four zero seven" is a phone number.
Have them say the number aloud before working with it. Most errors with big numbers are reading errors that the arithmetic then faithfully preserves.
Why the standard algorithm is allowed — Column addition works because each column holds a different unit and like units can be combined. Adding the ones, then the tens, then the hundreds is just adding the expanded forms in pieces. The algorithm is a compact record of that, not a separate magic procedure.
What the little carried digit is — When a column totals ten or more, ten of that unit bundle into one of the next unit up. The small 1 you write above the next column is that bundle. It is not a mark to remember — it is a real quantity that has moved to the column where it belongs.
Alignment is not neatness, it is correctness — A digit written one column out is added to the wrong unit and changes the answer by a factor of ten. With five- and six-digit numbers, use squared paper or draw the columns. This is the most common error in multi-digit addition and it is entirely avoidable.
Estimate before, check after — Round both numbers to the leading place and add: 4,382 + 2,715 is roughly 4,000 + 3,000 = 7,000. The exact answer, 7,097, sits close. An estimate cannot confirm a small slip, but it catches every misalignment, which is the error that matters.
Same bundling, more columns — 45,678 + 27,845. Ones: 8 + 5 = 13. Keep 3, bundle a ten. Tens: 7 + 4 + 1 = 12 tens. Keep 2, bundle a hundred. Carry on through every column the same way. 73,523. Nothing new since you first started bundling, except the number of columns.