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 243+152243 + 152, add each place on its own.

Two hundred forty-three and one hundred fifty-two Base-ten blocks for 243 on top: two flats, four rods, three cubes. Below, blocks for 152: one flat, five rods, two cubes.
Two hundred forty-three and one hundred fifty-two
  • Hundreds: 2+1=32 + 1 = 3 hundreds
  • Tens: 4+5=94 + 5 = 9 tens
  • Ones: 3+2=53 + 2 = 5 ones

So 243+152=395243 + 152 = 395.

Make a new ten and a new hundred

Now try 368+457368 + 457.

  • Ones: 8+7=158 + 7 = 15. That is 11 ten and 55 ones.
  • Tens: 6+5=116 + 5 = 11, plus the new ten, is 1212 tens. That is 11 hundred and 22 tens.
  • Hundreds: 3+4=73 + 4 = 7, plus the new hundred, is 88 hundreds.

The answer is 825825. In columns, each new ten or hundred is written above its place:

10100368+  457825\begin{array}{r} \rlap{\scriptsize 1}\phantom{0}\rlap{\scriptsize 1}\phantom{0}\phantom{0} \\ 368 \\ +\; 457 \\ \hline 825 \end{array}

Break a hundred to subtract

For 503−268503 - 268, the ones and tens are too small: 33 ones and 00 tens.

Break one hundred into ten tens. Then break one of those tens into ten ones. Now 503503 is 44 hundreds, 99 tens and 1313 ones.

  • Ones: 13−8=513 - 8 = 5
  • Tens: 9−6=39 - 6 = 3
  • Hundreds: 4−2=24 - 2 = 2

So 503−268=235503 - 268 = 235.

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.

503503 and ”44 hundreds, 99 tens and 1313 ones” are the same amount: 400+90+13=503400 + 90 + 13 = 503. Since the amount stays the same, the answer does too.

Worked examples

Common mistakes

Practice problems

  1. Find 321+456321 + 456.

    Answer

    777777

    Full solution

    Hundreds: 3+4=73 + 4 = 7. Tens: 2+5=72 + 5 = 7. Ones: 1+6=71 + 6 = 7.

  2. Find 584−263584 - 263.

    Answer

    321321

    Full solution

    Ones: 4−3=14 - 3 = 1. Tens: 8−6=28 - 6 = 2. Hundreds: 5−2=35 - 2 = 3.

  3. Find 278+145278 + 145.

    Answer

    423423

    Full solution

    Ones: 8+5=138 + 5 = 13, so 11 ten and 33 ones. Tens: 7+4+1=127 + 4 + 1 = 12, so 11 hundred and 22 tens. Hundreds: 2+1+1=42 + 1 + 1 = 4. The answer is 423423.

  4. Find 630−240630 - 240.

    Answer

    390390

    Full solution

    Break a hundred: 630630 is 55 hundreds and 1313 tens. Tens: 13−4=913 - 4 = 9. Hundreds: 5−2=35 - 2 = 3. So 390390.

  5. Find 400−125400 - 125 by counting up.

    Answer

    275275

    Full solution

    From 125125, 7575 gets to 200200, and 200200 more gets to 400400. 75+200=27575 + 200 = 275.

  6. Find 509+391509 + 391.

    Answer

    900900

    Full solution

    Ones: 9+1=109 + 1 = 10, a new ten. Tens: 0+9+1=100 + 9 + 1 = 10, a new hundred. Hundreds: 5+3+1=95 + 3 + 1 = 9. So 900900.

  7. Find 745−382745 - 382.

    Answer

    363363

    Full solution

    Ones: 5−2=35 - 2 = 3. Tens: 44 tens, and 88 must go, so break a hundred: 66 hundreds and 1414 tens. 14−8=614 - 8 = 6. Hundreds: 6−3=36 - 3 = 3. So 363363.

  8. Find 250+250+125250 + 250 + 125.

    Answer

    625625

    Full solution

    250+250=500250 + 250 = 500. Then 500+125=625500 + 125 = 625.

  9. Why is 503503 the same as 44 hundreds, 99 tens and 1313 ones?

    Answer

    400+90+13=503400 + 90 + 13 = 503. 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 503503.

  10. Leo says 602−175=573602 - 175 = 573. What went wrong?

    Hint

    Can you take 55 ones from 22 ones?

    Answer

    He took each smaller digit from the bigger one. The answer is 427427.

    Full solution

    602602 has 22 ones and 00 tens. Break a hundred and a ten: 55 hundreds, 99 tens and 1212 ones.

    Ones: 12−5=712 - 5 = 7. Tens: 9−7=29 - 7 = 2. Hundreds: 5−1=45 - 1 = 4. So 427427. Check: 427+175=602427 + 175 = 602.

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.

What to learn next

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.