Adding and Subtracting Within 1,000: practice solutions, Grade 2 – download the PDF

1 Adding blocks ★★★

Maria has \(300 + 60 + 4 = 364\). Jonah has \(200 + 10 + 5 = 215\).

Ones: \(4 + 5 = 9\). Tens: \(6 + 1 = 7\). Hundreds: \(3 + 2 = 5\).

\(364 + 215 = 579\). Together they have 579.

2 Add column by column ★★★

1. \(421 + 356 = 777\)
2. \(534 + 245 = 779\)
3. \(612 + 176 = 788\)
4. \(203 + 405 = 608\)

In each one I added the ones, then the tens, then the hundreds. No column reached 10, so I did not need to regroup.

3 Subtract column by column ★★★

1. \(758 - 324 = 434\)
2. \(689 - 453 = 236\)
3. \(947 - 713 = 234\)
4. \(805 - 304 = 501\)

Every top digit was big enough, so no trading was needed.

4 Do I need to regroup? ★★★

1. \(6 + 5 = 11\) cubes. Yes: 10 cubes make 1 more rod, and 1 cube is left.
2. Ones: 1. Tens: \(2 + 3 + 1 = 6\). Hundreds: \(1 + 1 = 2\). So \(126 + 135 = 261\).

5 Mystery digit ★★★

1. Tens: \(\square + 1 = 7\), so \(\square = 6\). Check: \(465 + 213 = 678\).
2. Tens: \(\square - 1 = 3\), so \(\square = 4\). Check: \(742 - 310 = 432\).

6 Library shelves ★★★

\(342 + 125 = 467\).

The library has 467 books in all.

7 True or false? ★★★

1. True: 3 hundreds + 4 hundreds = 7 hundreds.
2. False: 8 hundreds \(-\) 3 hundreds = 5 hundreds, so \(800 - 300 = 500\).
3. True: 25 tens + 25 tens = 50 tens = 500.
4. False: \(750 - 250 = 500\), because \(250 + 500 = 750\).

8 Regroup the ones ★★★

Ones: \(8 + 7 = 15\), which is 1 ten and 5 ones. I regrouped the ones.

Tens: \(3 + 5 + 1 = 9\). Hundreds: \(2 + 1 = 3\).

\(238 + 157 = 395\).

9 Regroup the tens ★★★

Ones: \(4 + 3 = 7\). Tens: \(7 + 8 = 15\) tens, which is 1 hundred and 5 tens. I regrouped the tens.

Hundreds: \(3 + 2 + 1 = 6\).

\(374 + 283 = 657\).

10 Regroup twice ★★★

Ones: \(6 + 9 = 15\), so 5 ones and 1 ten regrouped.

Tens: \(8 + 4 + 1 = 13\), so 3 tens and 1 hundred regrouped.

Hundreds: \(4 + 3 + 1 = 8\).

\(486 + 349 = 835\).

11 Trade once ★★★

1. Ones: \(4 < 9\), so trade: \(14 - 9 = 5\). Tens: \(5 - 2 = 3\) (the 6 became 5). Hundreds: \(7 - 3 = 4\). \(764 - 329 = 435\). Check: \(435 + 329 = 764\).
2. Ones: \(13 - 7 = 6\). Tens: \(4 - 1 = 3\) (the 5 became 4). Hundreds: \(8 - 2 = 6\). \(853 - 217 = 636\). Check: \(636 + 217 = 853\).

12 Trade twice ★★★

Ones: \(1 < 4\). Trade 1 ten for 10 ones: \(11 - 4 = 7\). The 2 tens become 1 ten.

Tens: \(1 < 7\). Trade 1 hundred for 10 tens: \(11 - 7 = 4\). The 6 hundreds become 5.

Hundreds: \(5 - 3 = 2\).

\(621 - 374 = 247\). Check: \(247 + 374 = 621\).

13 Ticket sale ★★★

1. \(275 + 168 = 443\) tickets.
2. \(500 - 443 = 57\). They must sell 57 more tickets. Check: \(443 + 57 = 500\).

14 Find the mistake ★★★

No. Ones: \(2 + 9 = 11\), so 1 one and 1 ten. Tens: \(5 + 8 + 1 = 14\), so 4 tens and 1 hundred. Hundreds: \(3 + 1 + 1 = 5\).

Mia forgot to add the regrouped hundred. The correct sum is \(352 + 189 = 541\).

15 Quick estimates ★★★

1. Estimate: \(400 + 200 = 600\). Exact: \(389 + 212 = 601\).
2. Estimate: \(700 - 300 = 400\). Exact: \(703 - 296 = 407\).

Both exact answers are close to the estimates, so they make sense.

16 Subtracting across zeros ★★★

1. Trade 1 hundred for 10 tens, then 1 ten for 10 ones: 5 hundreds, 9 tens, 10 ones. \(10 - 7 = 3\), \(9 - 5 = 4\), \(5 - 3 = 2\). \(600 - 357 = 243\). Check: \(357 + 243 = 600\).
2. \(400 - 168 = 232\). Check: \(168 + 232 = 400\).
3. 805 is 7 hundreds, 9 tens and 15 ones. \(15 - 9 = 6\), \(9 - 4 = 5\), \(7 - 4 = 3\). \(805 - 449 = 356\). Check: \(449 + 356 = 805\).

17 Counting up ★★★

Start at 268. Jump to 300: \(+32\). Jump to 500: \(+200\). Jump to 531: \(+31\).

\(32 + 200 + 31 = 263\). So \(531 - 268 = 263\). Check: \(268 + 263 = 531\).

18 Friendly hundreds ★★★

Change the order (commutative property) and group \(275 + 25\) (associative property):

\(275 + 25 = 300\), and \(300 + 138 = 438\).

So \(275 + 138 + 25 = 438\).

19 Which is greater? ★★★

\(468 + 275 = 743\) and \(812 - 90 = 722\).

743 is greater. \(743 - 722 = 21\), so it is greater by 21.

20 Missing number ★★★

1. \(\square = 561 - 278 = 283\). Check: \(283 + 278 = 561\).
2. \(\square = 904 - 547 = 357\). Check: \(904 - 357 = 547\).

21 Fruit stand ★★★

Step 1: \(356 + 278 = 634\) pieces picked.

Step 2: \(634 - 415 = 219\).

There are 219 pieces of fruit left. Estimate check: \(600 - 400 = 200\), which is close to 219.

22 Explain Sam’s strategy ★★★

Sam subtracted 400, but he only needed to subtract 389. That is 11 too many, so the answer must be 11 bigger.

\(300 + 11 = 311\), so \(700 - 389 = 311\). Check: \(311 + 389 = 700\).