Adding and Subtracting Within 1,000: practice solutions, Grade 3 – download the PDF

1 Breaking apart ★★★

Hundreds: \(100 + 200 = 300\). Tens: \(20 + 30 = 50\). Ones: \(4 + 5 = 9\). Then \(300 + 50 + 9 = 359\).

So \(124 + 235 = 359\).

2 Friendly numbers ★★★

1. \(250 + 150 = 400\) because \(50 + 50 = 100\) and \(200 + 100 = 300\), so the total is 400.
2. \(430 + 270 = 700\) because \(400 + 200 = 600\) and \(30 + 70 = 100\).
3. \(360 + 390 = 750\) because \(300 + 300 = 600\) and \(60 + 90 = 150\).

3 Subtracting round numbers ★★★

1. \(8 \text{ hundreds} - 3 \text{ hundreds} = 5 \text{ hundreds}\), so \(800 - 300 = 500\).
2. \(750 - 200 = 550\).
3. \(640 - 100 = 540\), then \(540 - 30 = 510\). So \(640 - 130 = 510\).

4 Adding without regrouping ★★★

Ones: \(2 + 6 = 8\). Tens: \(4 + 1 = 5\). Hundreds: \(3 + 5 = 8\).

\[\begin{array}{r} 342 \\ +\;516 \\ \hline 858 \end{array}\]

So \(342 + 516 = 858\).

5 Regrouping ones and tens ★★★

Ones: \(4 + 8 = 12\), write 2 and regroup 1 ten. Tens: \(6 + 3 + 1 = 10\), write 0 and regroup 1 hundred. Hundreds: \(2 + 1 + 1 = 4\).

\[\begin{array}{r} 264 \\ +\;138 \\ \hline 402 \end{array}\]

So \(264 + 138 = 402\).

6 Subtracting without regrouping ★★★

Ones: \(9 - 5 = 4\). Tens: \(7 - 4 = 3\). Hundreds: \(8 - 3 = 5\).

\[\begin{array}{r} 879 \\ -\;345 \\ \hline 534 \end{array}\]

So \(879 - 345 = 534\).

7 True or false? ★★★

Ones: \(5 + 8 = 13\), write 3 and regroup 1 ten. Tens: \(4 + 7 + 1 = 12\), write 2 and regroup 1 hundred. Hundreds: \(3 + 2 + 1 = 6\). So \(345 + 278 = 623\).

Ben is wrong. He forgot to add the regrouped ten.

8 The mystery number ★★★

Let \(n\) be the mystery number: \(285 + n = 632\). Addition and subtraction are inverse operations, so \(n = 632 - 285\).

\[\begin{array}{r} 632 \\ -\;285 \\ \hline 347 \end{array}\]

Check: \(285 + 347 = 632\). The mystery number is 347.

9 Regrouping twice ★★★

Ones: \(2 < 5\), so trade 1 ten for 10 ones: \(12 - 5 = 7\). Tens: now 2 tens, and \(2 < 8\), so trade 1 hundred for 10 tens: \(12 - 8 = 4\). Hundreds: \(6 - 4 = 2\).

\[\begin{array}{r} 732 \\ -\;485 \\ \hline 247 \end{array}\]

So \(732 - 485 = 247\). Check: \(247 + 485 = 732\).

10 Subtracting across a zero ★★★

There are no tens and no ones to trade, so trade 1 hundred for 10 tens (7 hundreds and 10 tens), then 1 ten for 10 ones (9 tens and 10 ones). Ones: \(10 - 7 = 3\). Tens: \(9 - 6 = 3\). Hundreds: \(7 - 3 = 4\).

\[\begin{array}{r} 800 \\ -\;367 \\ \hline 433 \end{array}\]

So \(800 - 367 = 433\).

11 Is it reasonable? ★★★

1. \(618 \approx 600\) and \(283 \approx 300\), so the estimate is \(600 + 300 = 900\). The exact sum is \(618 + 283 = 901\), very close to 900.
2. \(742 \approx 700\) and \(389 \approx 400\), so the estimate is \(700 - 400 = 300\). The exact difference is \(742 - 389 = 353\). It is near 300, so it is reasonable.

12 Tickets at the stadium ★★★

Parts are put together, so add: \(438 + 479 = t\).

\[\begin{array}{r} 438 \\ +\;479 \\ \hline 917 \end{array}\]

Check: \(917 - 479 = 438\). The stadium sold 917 tickets in all.

13 Walking the trail ★★★

The whole is 750 feet and one part is 468 feet, so subtract: \(750 - 468 = f\).

\[\begin{array}{r} 750 \\ -\;468 \\ \hline 282 \end{array}\]

Check: \(282 + 468 = 750\). Mia has 282 feet left to walk.

14 Fact family ★★★

First check that \(296 + 458 = 754\): \(6 + 8 = 14\), \(9 + 5 + 1 = 15\), \(2 + 4 + 1 = 7\), so it is true. The other equations are:

• \(458 + 296 = 754\)
• \(754 - 296 = 458\)
• \(754 - 458 = 296\)

15 Find the error ★★★

Leo subtracted the smaller digit from the larger one in every column (\(8 - 4 = 4\), \(7 - 3 = 4\), \(5 - 2 = 3\)). In the ones column, \(4 - 8\) is not possible without regrouping.

\[\begin{array}{r} 534 \\ -\;278 \\ \hline 256 \end{array}\]

The correct answer is 256. Check: \(256 + 278 = 534\).

16 Books read in class ★★★

1. Class A read 245 books and class B read 318, so \(245 + 318 = 563\). They read 563 books together.
2. \(318 - 190 = 128\). Class B read 128 more books than class D.

17 Greater or not? ★★★

\(468 + 397 = 865\) (ones \(8 + 7 = 15\), tens \(6 + 9 + 1 = 16\), hundreds \(4 + 3 + 1 = 8\)). \(912 - 48 = 864\) (\(912 - 50 = 862\), then add 2).

\(468 + 397\) is greater, by \(865 - 864 = 1\).

18 Digit cards ★★★

To get the greatest difference, make the greatest possible number and the least possible number. The greatest number uses the three biggest cards: 765. The least number uses the three smallest cards: 234.

\[\begin{array}{r} 765 \\ -\;234 \\ \hline 531 \end{array}\]

The greatest difference is 531.

19 Missing digits ★★★

Ones: \(4 + 8 = 12\), write 2 and regroup 1 ten. Tens: \(\blacksquare + 3 + 1\) must end in 0, so it equals 10 and \(\blacksquare = 6\); regroup 1 hundred. Hundreds: \(3 + \blacktriangle + 1 = 6\), so \(\blacktriangle = 2\).

\[\begin{array}{r} 364 \\ +\;238 \\ \hline 602 \end{array}\]

The missing digits are 6 and 2.

20 Will it fit? ★★★

Estimate: \(468 \approx 500\) and \(349 \approx 300\), so \(500 + 300 = 800\).

Exact:

\[\begin{array}{r} 468 \\ +\;349 \\ \hline 817 \end{array}\]

The total is 817 pounds, which is less than 1,000 pounds. Yes, the truck can carry both crates.

21 Check the answer ★★★

Check: \(355 + 458 = 813\), which is not 703. Eli is wrong.

Correct subtraction: trade 1 hundred, then 1 ten: 6 hundreds, 9 tens, 13 ones. \(13 - 8 = 5\), \(9 - 5 = 4\), \(6 - 4 = 2\).

\[\begin{array}{r} 703 \\ -\;458 \\ \hline 245 \end{array}\]

The correct answer is 245. Check: \(245 + 458 = 703\).

22 Museum visitors ★★★

Let \(m\) be the morning visitors: \(m + 276 = 641\). So \(m = 641 - 276\).

\[\begin{array}{r} 641 \\ -\;276 \\ \hline 365 \end{array}\]

Check: \(365 + 276 = 641\). In the morning 365 people visited the museum.

23 Filling the tank ★★★

Subtract the amount already in the tank from the total: \(900 - 478 = l\).

\[\begin{array}{r} 900 \\ -\;478 \\ \hline 422 \end{array}\]

Check: \(422 + 478 = 900\). It needs 422 more liters.