Adding and Subtracting Whole Numbers: practice solutions, Grade 4 – download the PDF

1 Add four-digit numbers ★★★

1. No carrying is needed: \(5 + 3 = 8\), \(2 + 6 = 8\), \(4 + 1 = 5\), \(3 + 2 = 5\). The sum is 5,588.
2. Ones: \(8 + 5 = 13\), write 3, carry 1. Tens: \(3 + 8 + 1 = 12\), write 2, carry 1. Hundreds: \(7 + 6 + 1 = 14\), write 4, carry 1. Thousands: \(4 + 2 + 1 = 7\). The sum is 7,423.
3. Ones: \(6 + 7 = 13\), write 3, carry 1. Tens: \(9 + 0 + 1 = 10\), write 0, carry 1. Hundreds: \(0 + 9 + 1 = 10\), write 0, carry 1. Thousands: \(8 + 1 + 1 = 10\). The sum is 10,003.

2 Subtract four-digit numbers ★★★

1. No borrowing is needed: \(4 - 1 = 3\), \(6 - 2 = 4\), \(7 - 5 = 2\), \(8 - 3 = 5\). The difference is 5,243.
2. Ones: \(5 - 8\) is not possible, so borrow from the tens (0), which means borrowing from the hundreds first: 3 hundreds become 2 hundreds and 10 tens, then 9 tens and 15 ones. \(15 - 8 = 7\). Tens: \(9 - 4 = 5\). Hundreds: \(2 - 1 = 1\). Thousands: \(6 - 2 = 4\). The difference is 4,157.
3. Ones: \(2 < 7\), borrow: 12 − 7 = 5, tens become 0. Tens: \(0 < 8\), borrow: 10 − 8 = 2, hundreds become 3. Hundreds: \(3 < 6\), borrow: 13 − 6 = 7, thousands become 8. Thousands: \(8 - 5 = 3\). The difference is 3,725.

3 Trading places ★★★

1. 1 thousand = 10 hundreds.
2. 15 ones = 1 ten and 5 ones, so the tens become \(3 + 1 = 4\). The number is 4 hundreds, 4 tens, 5 ones (445).
3. 6,040 = 6 thousands and 4 tens. Trading 1 thousand for 10 hundreds gives 5 thousands, 10 hundreds, 4 tens. Check: \(5{,}000 + 1{,}000 + 40 = 6{,}040\).

4 Round and estimate ★★★

A. 3,462 has a 6 in the tens place, so it rounds up to 3,500. 7,849 has a 4 in the tens place, so it rounds down to 7,800. 2,950 has a 5 in the tens place, so it rounds up to 3,000. 9,951 has a 5 in the tens place, so it rounds up to 10,000.

B. \(3{,}462 \approx 3{,}500\) and \(2{,}538 \approx 2{,}500\). The estimate is \(3{,}500 + 2{,}500 = \) 6,000.

5 Fans at the stadium ★★★

Add the two days: \(12{,}450 + 8{,}375\). Ones: \(0 + 5 = 5\). Tens: \(5 + 7 = 12\), write 2, carry 1. Hundreds: \(4 + 3 + 1 = 8\). Thousands: \(2 + 8 = 10\), write 0, carry 1. Ten thousands: \(1 + 1 = 2\).

\(12{,}450 + 8{,}375 = 20{,}825\). 20,825 fans came during the weekend.

6 True or false? ★★★

1. False. Check by adding: \(3{,}866 + 1{,}234 = 5{,}100\), not 5,000. Borrowing across zeros gives \(5{,}000 - 1{,}234 = 3{,}766\).
2. True. Ones: \(6 + 4 = 10\). Tens: \(5 + 4 + 1 = 10\). Hundreds: \(4 + 5 + 1 = 10\). Thousands: \(3 + 2 + 1 = 6\). The sum is 6,000.

7 Check with the inverse ★★★

1. Add the answer to the number subtracted: \(4{,}623 + 4{,}578 = 9{,}201\). It matches, so Jana is correct.
2. \(4{,}755 + 2{,}345 = 7{,}100\), which is not 7,000. Leo is wrong. The correct difference is \(7{,}000 - 2{,}345 = 4{,}655\). Check: \(4{,}655 + 2{,}345 = 7{,}000\).

8 Subtract across zeros ★★★

1. Rewrite 6,000 as 5 thousands, 9 hundreds, 9 tens, 10 ones. Subtract: \(10 - 7 = 3\), \(9 - 8 = 1\), \(9 - 4 = 5\), \(5 - 2 = 3\). The answer is 3,513. Check: \(3{,}513 + 2{,}487 = 6{,}000\).
2. Rewrite 30,007 as 2 ten thousands, 9 thousands, 9 hundreds, 10 tens, 7 ones. Ones: \(7 < 9\), so take 1 ten: 17 ones and 9 tens. \(17 - 9 = 8\), \(9 - 2 = 7\), \(9 - 4 = 5\), \(9 - 8 = 1\), \(2 - 1 = 1\). The answer is 11,578. Check: \(11{,}578 + 18{,}429 = 30{,}007\).
3. Regroup 80,400: take 1 hundred to make 10 tens, then 1 ten to make 10 ones, so the number has 3 hundreds, 9 tens, and 10 ones. The hundreds are still too small (\(3 < 9\)), and the thousands are 0, so take 1 ten thousand to make 10 thousands, then 1 thousand to make 10 more hundreds. Now the number is 7 ten thousands, 9 thousands, 13 hundreds, 9 tens, 10 ones. Ones: \(10 - 2 = 8\). Tens: \(9 - 6 = 3\). Hundreds: \(13 - 9 = 4\). Thousands: \(9 - 5 = 4\). Ten thousands: \(7 - 3 = 4\). The answer is 44,438. Check: \(44{,}438 + 35{,}962 = 80{,}400\).

9 Is the answer reasonable? ★★★

\(48{,}725 \approx 50{,}000\) and \(31{,}284 \approx 30{,}000\). The estimate is \(50{,}000 + 30{,}000 = 80{,}000\).

70,009 is far from 80,000, so it is not reasonable (a key was probably mistyped). Exact sum: \(48{,}725 + 31{,}284 = 80{,}009\), which is very close to the estimate.

10 Road trip ★★★

Miles driven in two days: \(328 + 457 = 785\).

Miles left: \(1{,}205 - 785 = 420\).

Check: \(785 + 420 = 1{,}205\). They must drive 420 miles on day 3.

11 Missing digits ★★★

Ones: \(A + 9\) must end in 3, so \(A + 9 = 13\) and \(A = 4\), carry 1.

Tens: \(8 + B + 1\) must end in 0, so \(8 + B + 1 = 10\) and \(B = 1\), carry 1.

Hundreds: \(5 + 2 + 1 = 8\). It works. A = 4 and B = 1, and \(584 + 219 = 803\).

12 Library shelves ★★★

Total before removing: \(15{,}230 + 9{,}875 = 25{,}105\), then \(25{,}105 + 4{,}360 = 29{,}465\).

After removing: \(29{,}465 - 3{,}750 = 25{,}715\).

Check: \(25{,}715 + 3{,}750 = 29{,}465\). 25,715 books are left.

13 Savings model ★★★

1. Lena’s bar is Sam’s bar plus 1,275: \(2{,}350 + 1{,}275 = 3{,}625\). Lena saved 3,625 dollars.
2. Together: \(2{,}350 + 3{,}625 = 5{,}975\). They saved 5,975 dollars. Estimate: \(2{,}000 + 4{,}000 = 6{,}000\), so the answer is reasonable.

14 Find the mistake ★★★

The student subtracted the smaller digit from the larger digit in every column (\(7 - 5 = 2\), \(6 - 0 = 6\), \(8 - 2 = 6\), \(4 - 1 = 3\)) instead of borrowing.

Correct work: regroup 4,205 as 3 thousands, 11 hundreds, 9 tens, 15 ones (the 0 tens must borrow from the hundreds, and then the hundreds borrow from the thousands). Ones: \(15 - 7 = 8\). Tens: \(9 - 6 = 3\). Hundreds: \(11 - 8 = 3\). Thousands: \(3 - 1 = 2\).

\(4{,}205 - 1{,}867 = 2{,}338\). Check: \(2{,}338 + 1{,}867 = 4{,}205\). The correct answer is 2,338.

15 Ribbon in centimeters ★★★

Ribbon used: \(348 + 275 = 623\) cm.

Ribbon left: \(1{,}000 - 623 = 377\) cm. Check: \(377 + 623 = 1{,}000\).

Since 1 inch is about 2.5 cm, 377 cm is about 150 inches (\(2.5 \times 150 = 375\)). 377 cm of ribbon are left.

16 Mountain climber ★★★

After the first climb: \(3{,}200 + 1{,}250 = 4{,}450\) ft.

At the lake: \(4{,}450 - 475 = 3{,}975\) ft.

At the ridge: \(3{,}975 + 890 = 4{,}865\) ft.

Check by estimate (nearest hundred): \(3{,}200 + 1{,}300 - 500 + 900 = 4{,}900\), close to the exact answer. Her elevation is 4,865 feet.

17 Concert tickets ★★★

1. Nights 1 and 2: \(6{,}925 + 7{,}380 = 14{,}305\). Night 3: \(18{,}640 - 14{,}305 = 4{,}335\). 4,335 tickets. Check: \(14{,}305 + 4{,}335 = 18{,}640\).
2. \(7{,}380 - 4{,}335 = 3{,}045\). 3,045 more tickets were sold on night 2.

18 Think of a number ★★★

Work backward using inverse operations. Undo “add 1,250” by subtracting: \(8{,}000 - 1{,}250 = 6{,}750\). Undo “subtract 3,785” by adding: \(6{,}750 + 3{,}785 = 10{,}535\).

Check: \(10{,}535 - 3{,}785 = 6{,}750\) and \(6{,}750 + 1{,}250 = 8{,}000\). The number is 10,535.

19 Digit cards ★★★

1. Put the greatest digits in the tens place: tens 9 and 6, ones 4 and 2. For example \(94 + 62 = 156\). Swapping the ones digits gives \(92 + 64 = 156\) too. The greatest sum is 156.
2. Put the least digits in the tens place: tens 2 and 4, ones 6 and 9. For example \(26 + 49 = 75\) (and \(29 + 46 = 75\)). The least sum is 75.

20 Three towns ★★★

A and B together: \(48{,}306 + 37{,}589 = 85{,}895\).

Difference with Town C: \(85{,}895 - 52{,}014 = 33{,}881\).

Estimate: \(48{,}000 + 38{,}000 - 52{,}000 = 34{,}000\), close to the exact answer. 33,881 more people live in Towns A and B together.

21 Is the budget enough? ★★★

1. \(4{,}875 \approx 5{,}000\) and \(3{,}260 \approx 3{,}000\). The estimate is 8,000, exactly the budget. The estimate cannot decide because the exact total could be a little above or a little below 8,000.
2. \(4{,}875 + 3{,}260 = 8{,}135\). Since 8,135 is more than 8,000, the budget is not enough. The school is short by \(8{,}135 - 8{,}000 = 135\) dollars.

22 Video game rounds ★★★

Round 2: \(24{,}560 - 3{,}875 = 20{,}685\).

Round 3: \(20{,}685 + 5{,}430 = 26{,}115\).

Total: \(24{,}560 + 20{,}685 = 45{,}245\), then \(45{,}245 + 26{,}115 = 71{,}360\).

Estimate: \(25{,}000 + 21{,}000 + 26{,}000 = 72{,}000\). Kira’s total score was 71,360 points.