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Complete Chapter 3 answer key

Full answers and reasoning for every chapter lesson and assessment.

Print this separately when students work on assessment pages. These are publicly available explanatory solutions, not secure school answers.

Lesson 1: Addition with Regrouping

Entry

  1. 438 — 253 is 200 + 53; add the two parts to 185. The sum is 438.
  2. 320 — 290 is 200 + 90; add the two parts to 30. The sum is 320.

Worked checks

  1. 3085 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,848 + 1,237 = 3,085.
  2. 3395 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,018 + 1,377 = 3,395.
  3. 3715 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,198 + 1,517 = 3,715.

Guided

  1. 2715 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,718 + 997 = 2,715.
  2. 3015 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,888 + 1,127 = 3,015.
  3. 3325 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,058 + 1,267 = 3,325.
  4. 3635 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,228 + 1,407 = 3,635.

Independent

  1. 2215 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 918 + 1,297 = 2,215.
  2. 2515 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,088 + 1,427 = 2,515.
  3. 2825 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,258 + 1,567 = 2,825.
  4. 3135 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,428 + 1,707 = 3,135.
  5. 3445 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,608 + 1,837 = 3,445.
  6. 3755 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,778 + 1,977 = 3,755.
  7. 4065 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 1,948 + 2,117 = 4,065.
  8. 4375 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,128 + 2,247 = 4,375.

Challenge

  1. 1 ten and 4 ones — 14 ones = 10 ones + 4 ones. Exchange ten ones for one ten; the quantity does not change.
  2. 834 — 4+3=7 hundreds; 7+5=12 tens; 8+6=14 ones. Trade 14 ones for 1 ten and 4 ones; then 13 tens for 1 hundred and 3 tens; total 834.

Exit

  1. 4615 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,718 + 1,897 = 4,615.
  2. 4915 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,888 + 2,027 = 4,915.
  3. 5225 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 3,058 + 2,167 = 5,225.

Lesson 2: Subtraction with Regrouping — Part 1

Entry

  1. 4115 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,118 + 1,997 = 4,115.
  2. 4415 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,288 + 2,127 = 4,415.

Worked checks

  1. 1084 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,084; add 958 to check.
  2. 1974 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,974; add 228 to check.
  3. 2074 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,074; add 288 to check.

Guided

  1. 1504 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,504; add 508 to check.
  2. 1594 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,594; add 568 to check.
  3. 1684 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,684; add 638 to check.
  4. 1774 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,774; add 708 to check.

Independent

  1. 2704 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,704; add 908 to check.
  2. 2794 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,794; add 968 to check.
  3. 884 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 884; add 238 to check.
  4. 974 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 974; add 308 to check.
  5. 1074 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,074; add 368 to check.
  6. 1164 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,164; add 438 to check.
  7. 1254 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,254; add 508 to check.
  8. 1354 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,354; add 568 to check.

Challenge

  1. 5 tens and 12 ones — Exchange one of the 6 tens for 10 ones: 6 tens + 2 ones equals 5 tens + 12 ones.
  2. 5 hundreds, 11 tens, 11 ones — 621 = 5 hundreds + 12 tens + 1 one = 5 hundreds + 11 tens + 11 ones. Now 35 can be subtracted from ones/tens.

Exit

  1. 304 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 304; add 908 to check.
  2. 394 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 394; add 968 to check.
  3. 1284 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,284; add 238 to check.

Lesson 3: Subtraction with Regrouping — Part 2

Entry

  1. 184 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 184; add 838 to check.
  2. 274 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 274; add 898 to check.

Worked checks

  1. 2617 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 423 = 2,617.
  2. 3509 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 496 = 3,509.
  3. 431 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 569 = 431.

Guided

  1. 2633 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 407 = 2,633.
  2. 3525 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 480 = 3,525.
  3. 447 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 553 = 447.
  4. 1394 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 2,020 − 626 = 1,394.

Independent

  1. 2213 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 827 = 2,213.
  2. 3685 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 320 = 3,685.
  3. 607 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 393 = 607.
  4. 1554 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 2,020 − 466 = 1,554.
  5. 2501 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 539 = 2,501.
  6. 3393 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 612 = 3,393.
  7. 315 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 685 = 315.
  8. 1262 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 2,020 − 758 = 1,262.

Challenge

  1. 2,999 — Exchange one thousand into 10 hundreds, one hundred into 10 tens, and one ten into 10 ones. Then remove one one.
  2. 3,815 — Rename 4,002 as 3 thousands, 9 hundreds, 9 tens, 12 ones; subtract 0 thousands, 1 hundred, 8 tens, 7 ones, obtaining 3,815.

Exit

  1. 2533 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 507 = 2,533.
  2. 3425 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 580 = 3,425.
  3. 347 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 653 = 347.

Lesson 4: Estimating Sums and Differences — Part 1

Entry

  1. 5,510 — Find the neighboring multiples of 10; compare with their midpoint. This is a Chapter 1 rounding skill.
  2. 5,500 — Find the neighboring multiples of 100; compare with their midpoint. This is a Chapter 1 rounding skill.

Worked checks

  1. 5,600 — Round 4,302 to 4,300 and 1,330 to 1,300. Estimate 4,300 + 1,300 = 5,600; it need not equal the exact answer.
  2. 6,150 — Round 4,633 to 4,630 and 1,521 to 1,520. Estimate 4,630 + 1,520 = 6,150; it need not equal the exact answer.
  3. 6,700 — Round 4,964 to 5,000 and 1,712 to 1,700. Estimate 5,000 + 1,700 = 6,700; it need not equal the exact answer.

Guided

  1. 8,890 — Round 7,753 to 7,750 and 1,141 to 1,140. Estimate 7,750 + 1,140 = 8,890; it need not equal the exact answer.
  2. 2,500 — Round 1,184 to 1,200 and 1,332 to 1,300. Estimate 1,200 + 1,300 = 2,500; it need not equal the exact answer.
  3. 3,040 — Round 1,515 to 1,520 and 1,523 to 1,520. Estimate 1,520 + 1,520 = 3,040; it need not equal the exact answer.
  4. 3,500 — Round 1,846 to 1,800 and 1,714 to 1,700. Estimate 1,800 + 1,700 = 3,500; it need not equal the exact answer.

Independent

  1. 7,990 — Round 7,353 to 7,350 and 641 to 640. Estimate 7,350 + 640 = 7,990; it need not equal the exact answer.
  2. 8,500 — Round 7,684 to 7,700 and 832 to 800. Estimate 7,700 + 800 = 8,500; it need not equal the exact answer.
  3. 2,140 — Round 1,115 to 1,120 and 1,023 to 1,020. Estimate 1,120 + 1,020 = 2,140; it need not equal the exact answer.
  4. 2,600 — Round 1,446 to 1,400 and 1,214 to 1,200. Estimate 1,400 + 1,200 = 2,600; it need not equal the exact answer.
  5. 3,190 — Round 1,777 to 1,780 and 1,405 to 1,410. Estimate 1,780 + 1,410 = 3,190; it need not equal the exact answer.
  6. 3,700 — Round 2,108 to 2,100 and 1,596 to 1,600. Estimate 2,100 + 1,600 = 3,700; it need not equal the exact answer.
  7. 4,230 — Round 2,439 to 2,440 and 1,787 to 1,790. Estimate 2,440 + 1,790 = 4,230; it need not equal the exact answer.
  8. 3,100 — Round 2,770 to 2,800 and 278 to 300. Estimate 2,800 + 300 = 3,100; it need not equal the exact answer.

Challenge

  1. No — When both addends are replaced by numbers at least as large, their combined total cannot decrease.
  2. About 210; yes — 96≈100 and 112≈110 so approximately 210. Exact total is 208, also enough.

Exit

  1. 7,890 — Round 6,553 to 6,550 and 1,341 to 1,340. Estimate 6,550 + 1,340 = 7,890; it need not equal the exact answer.
  2. 8,400 — Round 6,884 to 6,900 and 1,532 to 1,500. Estimate 6,900 + 1,500 = 8,400; it need not equal the exact answer.
  3. 8,940 — Round 7,215 to 7,220 and 1,723 to 1,720. Estimate 7,220 + 1,720 = 8,940; it need not equal the exact answer.

Lesson 5: Estimating Sums and Differences — Part 2

Entry

  1. 6,530 — Round 4,923 to 4,920 and 1,611 to 1,610. Estimate 4,920 + 1,610 = 6,530; it need not equal the exact answer.
  2. 7,100 — Round 5,254 to 5,300 and 1,802 to 1,800. Estimate 5,300 + 1,800 = 7,100; it need not equal the exact answer.

Worked checks

  1. 4,950 — Round 6,339 to 6,340 and 1,387 to 1,390. Estimate 6,340 − 1,390 = 4,950; it need not equal the exact answer.
  2. 5,100 — Round 6,670 to 6,700 and 1,578 to 1,600. Estimate 6,700 − 1,600 = 5,100; it need not equal the exact answer.
  3. 5,230 — Round 7,001 to 7,000 and 1,769 to 1,770. Estimate 7,000 − 1,770 = 5,230; it need not equal the exact answer.

Guided

  1. 5,910 — Round 7,473 to 7,470 and 1,561 to 1,560. Estimate 7,470 − 1,560 = 5,910; it need not equal the exact answer.
  2. 6,000 — Round 7,804 to 7,800 and 1,752 to 1,800. Estimate 7,800 − 1,800 = 6,000; it need not equal the exact answer.
  3. 1,000 — Round 1,235 to 1,240 and 243 to 240. Estimate 1,240 − 240 = 1,000; it need not equal the exact answer.
  4. 1,200 — Round 1,566 to 1,600 and 434 to 400. Estimate 1,600 − 400 = 1,200; it need not equal the exact answer.

Independent

  1. 6,010 — Round 7,073 to 7,070 and 1,061 to 1,060. Estimate 7,070 − 1,060 = 6,010; it need not equal the exact answer.
  2. 6,100 — Round 7,404 to 7,400 and 1,252 to 1,300. Estimate 7,400 − 1,300 = 6,100; it need not equal the exact answer.
  3. 6,300 — Round 7,735 to 7,740 and 1,443 to 1,440. Estimate 7,740 − 1,440 = 6,300; it need not equal the exact answer.
  4. -400 — Round 1,166 to 1,200 and 1,634 to 1,600. Estimate 1,200 − 1,600 = -400; it need not equal the exact answer.
  5. -330 — Round 1,497 to 1,500 and 1,825 to 1,830. Estimate 1,500 − 1,830 = -330; it need not equal the exact answer.
  6. 1,500 — Round 1,828 to 1,800 and 316 to 300. Estimate 1,800 − 300 = 1,500; it need not equal the exact answer.
  7. 1,650 — Round 2,159 to 2,160 and 507 to 510. Estimate 2,160 − 510 = 1,650; it need not equal the exact answer.
  8. 1,800 — Round 2,490 to 2,500 and 698 to 700. Estimate 2,500 − 700 = 1,800; it need not equal the exact answer.

Challenge

  1. The errors occur in opposite subtraction positions — Rounding the first number changes the minuend; rounding the second changes the amount subtracted. Their errors can have different effects.
  2. 400 (exactly 413) — 700−300≈400; exact difference 702−289=413, which is 13 from 400.

Exit

  1. 4,510 — Round 6,273 to 6,270 and 1,761 to 1,760. Estimate 6,270 − 1,760 = 4,510; it need not equal the exact answer.
  2. 6,300 — Round 6,604 to 6,600 and 252 to 300. Estimate 6,600 − 300 = 6,300; it need not equal the exact answer.
  3. 6,500 — Round 6,935 to 6,940 and 443 to 440. Estimate 6,940 − 440 = 6,500; it need not equal the exact answer.

Lesson 6: Word Problems

Entry

  1. 2544 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,544; add 448 to check.
  2. 2634 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,634; add 508 to check.

Worked checks

  1. 4861 — Identify the whole and its parts, then compute 4,373 + 488 = 4,861. Estimate to hundreds to check size.
  2. 4037 — Identify the whole and its parts, then compute 4,596 − 559 = 4,037. Estimate to hundreds to check size.
  3. 5449 — Identify the whole and its parts, then compute 4,819 + 630 = 5,449. Estimate to hundreds to check size.

Guided

  1. 2249 — Identify the whole and its parts, then compute 2,534 − 285 = 2,249. Estimate to hundreds to check size.
  2. 3113 — Identify the whole and its parts, then compute 2,757 + 356 = 3,113. Estimate to hundreds to check size.
  3. 2553 — Identify the whole and its parts, then compute 2,980 − 427 = 2,553. Estimate to hundreds to check size.
  4. 3701 — Identify the whole and its parts, then compute 3,203 + 498 = 3,701. Estimate to hundreds to check size.

Independent

  1. 2549 — Identify the whole and its parts, then compute 3,534 − 985 = 2,549. Estimate to hundreds to check size.
  2. 4813 — Identify the whole and its parts, then compute 3,757 + 1,056 = 4,813. Estimate to hundreds to check size.
  3. 3753 — Identify the whole and its parts, then compute 3,980 − 227 = 3,753. Estimate to hundreds to check size.
  4. 4501 — Identify the whole and its parts, then compute 4,203 + 298 = 4,501. Estimate to hundreds to check size.
  5. 4057 — Identify the whole and its parts, then compute 4,426 − 369 = 4,057. Estimate to hundreds to check size.
  6. 5089 — Identify the whole and its parts, then compute 4,649 + 440 = 5,089. Estimate to hundreds to check size.
  7. 4361 — Identify the whole and its parts, then compute 4,872 − 511 = 4,361. Estimate to hundreds to check size.
  8. 5677 — Identify the whole and its parts, then compute 5,095 + 582 = 5,677. Estimate to hundreds to check size.

Challenge

  1. It is an estimate, not an exact count — Find the exact difference for the required answer; use 1,200 only as a reasonableness check.
  2. 2,114 tickets — Add sold: 1,275+986=2,261. Remove refunds: 2,261−147=2,114. Check estimate ≈2,300−150≈2,150.

Exit

  1. 4949 — Identify the whole and its parts, then compute 5,534 − 585 = 4,949. Estimate to hundreds to check size.
  2. 6413 — Identify the whole and its parts, then compute 5,757 + 656 = 6,413. Estimate to hundreds to check size.
  3. 5253 — Identify the whole and its parts, then compute 5,980 − 727 = 5,253. Estimate to hundreds to check size.

Practice

Solutions

  1. 4715 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 3,668 + 1,047 = 4,715.
  2. 1615 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 438 + 1,177 = 1,615.
  3. 1925 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 608 + 1,317 = 1,925.
  4. 2904 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 2,904; add 758 to check.
  5. 194 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 194; add 818 to check.
  6. 284 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 284; add 888 to check.
  7. 223 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 777 = 223.
  8. 1170 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 2,020 − 850 = 1,170.
  9. 2697 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 343 = 2,697.
  10. 8,490 — Round 7,303 to 7,300 and 1,191 to 1,190. Estimate 7,300 + 1,190 = 8,490; it need not equal the exact answer.
  11. 9,000 — Round 7,634 to 7,600 and 1,382 to 1,400. Estimate 7,600 + 1,400 = 9,000; it need not equal the exact answer.
  12. 2,640 — Round 1,065 to 1,070 and 1,573 to 1,570. Estimate 1,070 + 1,570 = 2,640; it need not equal the exact answer.
  13. 5,410 — Round 7,023 to 7,020 and 1,611 to 1,610. Estimate 7,020 − 1,610 = 5,410; it need not equal the exact answer.
  14. 5,600 — Round 7,354 to 7,400 and 1,802 to 1,800. Estimate 7,400 − 1,800 = 5,600; it need not equal the exact answer.
  15. 7,400 — Round 7,685 to 7,690 and 293 to 290. Estimate 7,690 − 290 = 7,400; it need not equal the exact answer.
  16. 1949 — Identify the whole and its parts, then compute 2,984 − 1,035 = 1,949. Estimate to hundreds to check size.
  17. 4313 — Identify the whole and its parts, then compute 3,207 + 1,106 = 4,313. Estimate to hundreds to check size.
  18. 3153 — Identify the whole and its parts, then compute 3,430 − 277 = 3,153. Estimate to hundreds to check size.

Chapter Review

Solutions

  1. 1234 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,234; add 558 to check.
  2. 3605 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 400 = 3,605.
  3. 7,500 — Round 6,274 to 6,300 and 1,222 to 1,200. Estimate 6,300 + 1,200 = 7,500; it need not equal the exact answer.
  4. 2969 — Identify the whole and its parts, then compute 3,364 − 395 = 2,969. Estimate to hundreds to check size.
  5. 8,500 — Round 6,936 to 6,900 and 1,604 to 1,600. Estimate 6,900 + 1,600 = 8,500; it need not equal the exact answer.
  6. 1474 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 2,020 − 546 = 1,474.
  7. Both sums reach at least 10 units — 9+4=13 ones carries 1 ten; 7+5+1=13 tens carries 1 hundred.
  8. 2,600 — Round 3,066 to 3,100 and 534 to 500. Estimate 3,100 − 500 = 2,600; it need not equal the exact answer.
  9. 1414 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,414; add 698 to check.
  10. About 1,600; exactly 1,653 — 2,600−1,000≈1,600; 2,640−987=1,653.
  11. 1324 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,324; add 628 to check.
  12. 527 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 1,000 − 473 = 527.
  13. 1415 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 568 + 847 = 1,415.
  14. 2,524 — Regroup thousands through hundreds and tens to obtain sufficient ones. 3,000−476=2,524.
  15. 1144 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,144; add 498 to check.
  16. 2,400 — Round 2,735 to 2,740 and 343 to 340. Estimate 2,740 − 340 = 2,400; it need not equal the exact answer.
  17. 2713 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 327 = 2,713.
  18. 4053 — Identify the whole and its parts, then compute 3,587 + 466 = 4,053. Estimate to hundreds to check size.
  19. 410 — Round 2,073 to 2,070 and 1,661 to 1,660. Estimate 2,070 − 1,660 = 410; it need not equal the exact answer.
  20. 2,381 — A difference of 403 means the larger is 1,978+403=2,381.
  21. 8,020 — Round 6,605 to 6,610 and 1,413 to 1,410. Estimate 6,610 + 1,410 = 8,020; it need not equal the exact answer.
  22. 6,970 — Round 5,943 to 5,940 and 1,031 to 1,030. Estimate 5,940 + 1,030 = 6,970; it need not equal the exact answer.
  23. 1115 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 398 + 717 = 1,115.
  24. 2035 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 908 + 1,127 = 2,035.
  25. 500 — Round 2,404 to 2,400 and 1,852 to 1,900. Estimate 2,400 − 1,900 = 500; it need not equal the exact answer.
  26. 3273 — Identify the whole and its parts, then compute 3,810 − 537 = 3,273. Estimate to hundreds to check size.
  27. 1725 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 738 + 987 = 1,725.
  28. 4641 — Identify the whole and its parts, then compute 4,033 + 608 = 4,641. Estimate to hundreds to check size.

Practice Exam

Solutions

  1. 6,870 — Round 5,143 to 5,140 and 1,731 to 1,730. Estimate 5,140 + 1,730 = 6,870; it need not equal the exact answer.
  2. 610 — Round 1,273 to 1,270 and 661 to 660. Estimate 1,270 − 660 = 610; it need not equal the exact answer.
  3. 2453 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 3,040 − 587 = 2,453.
  4. 3515 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,198 + 1,317 = 3,515.
  5. 15 ones = 1 ten + 5 ones — Ten ones have the same value as one ten, leaving five ones.
  6. 3,500 — 5,749 rounds to 5,700; 2,151 rounds to 2,200; difference 5,700−2,200=3,500.
  7. 4,002 — Subtract 1,000 then add 2 back: 5,000−1,000+2=4,002.
  8. 6553 — Identify the whole and its parts, then compute 5,587 + 966 = 6,553. Estimate to hundreds to check size.
  9. 3345 — Rename a nonzero higher-place unit to supply ten of the next smaller units; continue exchanging across zeros. 4,005 − 660 = 3,345.
  10. Estimate 4,000; exact 4,004 — 1,489≈1,500 and 2,515≈2,500; exact sum 4,004.
  11. 3815 — Combine ones, tens, hundreds, and thousands. Exchange 10 units for 1 in the next column whenever needed; 2,368 + 1,447 = 3,815.
  12. 700 — Round 1,604 to 1,600 and 852 to 900. Estimate 1,600 − 900 = 700; it need not equal the exact answer.
  13. 4469 — Identify the whole and its parts, then compute 5,364 − 895 = 4,469. Estimate to hundreds to check size.
  14. It ignores place value and exchanges — A minuend column with too few units must exchange from a higher place; digit-by-digit absolute differences do not preserve the whole.
  15. 1,262 — 2,005−968=1,037; plus 225 gives 1,262.
  16. 1,765 — 3,240−1,475=1,765; 1,765+1,475=3,240.
  17. 1,401 — 798+603=1,401.
  18. 1,250 + 1,750 = 3,000 — 50+50 creates 100 and the other digits combine to a whole hundred/thousand.
  19. 1544 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,544; add 498 to check.
  20. 5,700 — Round 5,474 to 5,500 and 222 to 200. Estimate 5,500 + 200 = 5,700; it need not equal the exact answer.
  21. 206 — 702−500=202, plus 4 back =206; 214 differs from the correct compensation.
  22. 3,817 — Rename 4,002 as 3 thousands, 9 hundreds, 9 tens, 12 ones. Subtract 185 to get 3,817.
  23. 1634 — Exchange a larger unit into 10 smaller units when needed. Preserve the total and subtract. Difference = 1,634; add 558 to check.
  24. About 1,000 — 1,876≈1,900 and 945≈900; difference ≈1,000.