Early Math · Grade 2
Adding and Subtracting Within 1,000
Quick answer
Three-digit numbers add and subtract by place value, the same way two-digit numbers do, with one more place. Sometimes ten ones make a new ten or ten tens make a new hundred, as in 368 + 457 = 825. Sometimes a hundred must be broken into ten tens, or a ten into ten ones, as in 503 − 268 = 235. These trades change how a number is split up but never how much it is, which is why they give the right answer.
What you'll learn
- Add and subtract three-digit numbers by adding or subtracting like places
- Make a new ten or hundred, or break one apart, when needed
- Write the work in columns and explain why each step keeps the value
Add like places
To add , add each place on its own.
- Hundreds: hundreds
- Tens: tens
- Ones: ones
So .
Make a new ten and a new hundred
Now try .
- Ones: . That is ten and ones.
- Tens: , plus the new ten, is tens. That is hundred and tens.
- Hundreds: , plus the new hundred, is hundreds.
The answer is . In columns, each new ten or hundred is written above its place:
Break a hundred to subtract
For , the ones and tens are too small: ones and tens.
Break one hundred into ten tens. Then break one of those tens into ten ones. Now is hundreds, tens and ones.
- Ones:
- Tens:
- Hundreds:
So .
Why the trades are allowed
A hundred is ten tens, and a ten is ten ones. Trading one for the other changes how the number is split up. It never changes how much there is.
and ” hundreds, tens and ones” are the same amount: . Since the amount stays the same, the answer does too.
Worked examples
Common mistakes
Practice problems
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Find .
Answer
Full solution
Hundreds: . Tens: . Ones: .
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Find .
Answer
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Ones: . Tens: . Hundreds: .
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Find .
Answer
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Ones: , so ten and ones. Tens: , so hundred and tens. Hundreds: . The answer is .
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Find .
Answer
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Break a hundred: is hundreds and tens. Tens: . Hundreds: . So .
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Find by counting up.
Answer
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From , gets to , and more gets to . .
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Find .
Answer
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Ones: , a new ten. Tens: , a new hundred. Hundreds: . So .
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Find .
Answer
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Ones: . Tens: tens, and must go, so break a hundred: hundreds and tens. . Hundreds: . So .
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Find .
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. Then .
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Why is the same as hundreds, tens and ones?
Answer
. One hundred was traded for ten tens, and one ten for ten ones.
Full solution
Trading a hundred for ten tens, and a ten for ten ones, keeps the amount. Adding the parts back gives .
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Leo says . What went wrong?
Hint
Can you take ones from ones?
Answer
He took each smaller digit from the bigger one. The answer is .
Full solution
has ones and tens. Break a hundred and a ten: hundreds, tens and ones.
Ones: . Tens: . Hundreds: . So . Check: .
Frequently asked questions
How do I add 368 + 457?
Hundreds: 300 + 400 = 700. Tens: 60 + 50 = 110. Ones: 8 + 7 = 15. Then 700 + 110 + 15 = 825.
What does it mean to make a new hundred?
When the tens add up to ten or more, ten of them trade for one hundred. 12 tens is 1 hundred and 2 tens.
How do I subtract 503 − 268 when there are no tens?
Break a hundred into ten tens, then a ten into ten ones: 503 is 4 hundreds, 9 tens and 13 ones. Then subtract place by place to get 235.
Is there another way to subtract?
Count up from the smaller number: 268 to 300 is 32, and 300 to 503 is 203. 32 + 203 = 235.
Why does breaking a hundred not change the answer?
A hundred and ten tens are the same amount. The number is only split up another way.
Standards alignment
This lesson covers the following Common Core State Standards for Mathematics.
- CCSS.MATH.CONTENT.2.NBT.B.7Number and Operations in Base TenAdd and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
- CCSS.MATH.CONTENT.2.NBT.B.9Number and Operations in Base TenExplain why addition and subtraction strategies work, using place value and the properties of operations.