Long Division — Grade 4 Math 练习题

Grade 4 中等难度 10 道题

Long division is a written method for dividing larger numbers one place value at a time. In Grade 4, students divide dividends with up to four digits by a one-digit divisor, repeating the cycle of divide, multiply, subtract, and bring down until every digit has been used.

Estimating first keeps answers reasonable. Before computing 573÷4573 \div 4, notice the answer should be a bit more than 100100, because 4×100=4004 \times 100 = 400. Place-value sense helps students predict how many digits the quotient should have.

A remainder is what is left after the divisor goes in as many whole times as possible. The remainder must always be less than the divisor — if it is not, the quotient digit is too small and needs to be raised.

Every division can be checked with multiplication: multiply the quotient by the divisor, then add the remainder. The result should equal the dividend, because dividend == divisor ×\times quotient ++ remainder.

练习的技能

  • Dividing 2-, 3-, and 4-digit numbers by a 1-digit divisor
  • Using the divide, multiply, subtract, bring down cycle
  • Estimating quotients before computing
  • Interpreting and writing remainders
  • Checking quotients with multiplication
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练习题：Long Division

说明： 仔细解答每一道题。清晰地展示所有解题过程。在指定位置或按指示在另一张纸上写出最终答案。

  1. 1.5{,}832 \div 6 = _____

Long Division — 练习题（续）

  1. 2.7{,}455 \div 5 = _____
  2. 3.9{,}408 \div 7 = _____

Long Division — 练习题（续）

  1. 4.8{,}244 \div 9 = _____
  2. 5.6{,}390 \div 8 = _____

Long Division — 练习题（续）

  1. 6.A bakery packs 4{,}872 cookies into boxes. Each box holds 6 cookies. How many boxes are needed?
  2. 7.A farmer has 3{,}654 apples. He puts them into crates that hold 9 apples each. How many crates does he need?

Long Division — 练习题（续）

  1. 8.A school orders 5{,}280 pencils. The pencils are divided equally among 8 classrooms. How many pencils does each classroom receive?
  2. 9.A truck carries 7{,}392 pounds of sand. The sand is divided equally into 7 piles. How many pounds of sand are in each pile?

Long Division — 练习题（续）

  1. 10.A factory produces 4{,}905 toy cars. The cars are packed into boxes of 5. How many boxes are filled?

参考答案

  1. 1.
    6×900=5,4006 \times 900 = 5{,}400; 5,832−5,400=4325{,}832 - 5{,}400 = 432; 6×72=4326 \times 72 = 432; 900+72=972900 + 72 = 972
    最终答案： 972972
  2. 2.
    5×1,000=5,0005 \times 1{,}000 = 5{,}000; 7,455−5,000=2,4557{,}455 - 5{,}000 = 2{,}455; 5×400=2,0005 \times 400 = 2{,}000; 2,455−2,000=4552{,}455 - 2{,}000 = 455; 5×90=4505 \times 90 = 450; 455−450=5455 - 450 = 5; 5×1=55 \times 1 = 5; 1,000+400+90+1=1,4911{,}000 + 400 + 90 + 1 = 1{,}491
    最终答案： 1,4911{,}491
  3. 3.
    7×1,000=7,0007 \times 1{,}000 = 7{,}000; 9,408−7,000=2,4089{,}408 - 7{,}000 = 2{,}408; 7×300=2,1007 \times 300 = 2{,}100; 2,408−2,100=3082{,}408 - 2{,}100 = 308; 7×40=2807 \times 40 = 280; 308−280=28308 - 280 = 28; 7×4=287 \times 4 = 28; 1,000+300+40+4=1,3441{,}000 + 300 + 40 + 4 = 1{,}344
    最终答案： 1,3441{,}344
  4. 4.
    9×900=8,1009 \times 900 = 8{,}100; 8,244−8,100=1448{,}244 - 8{,}100 = 144; 9×16=1449 \times 16 = 144; 900+16=916900 + 16 = 916
    最终答案： 916916

参考答案（续）

  1. 5.
    8×700=5,6008 \times 700 = 5{,}600; 6,390−5,600=7906{,}390 - 5{,}600 = 790; 8×90=7208 \times 90 = 720; 790−720=70790 - 720 = 70; 8×8=648 \times 8 = 64; 70−64=670 - 64 = 6; 700+90+8=798700 + 90 + 8 = 798 remainder 66
    最终答案： 798798 R 66 (or 798.75798.75)
  2. 6.
    6×800=4,8006 \times 800 = 4{,}800; 4,872−4,800=724{,}872 - 4{,}800 = 72; 6×12=726 \times 12 = 72; 800+12=812800 + 12 = 812
    最终答案： 812812 boxes
  3. 7.
    9×400=3,6009 \times 400 = 3{,}600; 3,654−3,600=543{,}654 - 3{,}600 = 54; 9×6=549 \times 6 = 54; 400+6=406400 + 6 = 406
    最终答案： 406406 crates
  4. 8.
    8×600=4,8008 \times 600 = 4{,}800; 5,280−4,800=4805{,}280 - 4{,}800 = 480; 8×60=4808 \times 60 = 480; 600+60=660600 + 60 = 660
    最终答案： 660660 pencils
  5. 9.
    7×1,000=7,0007 \times 1{,}000 = 7{,}000; 7,392−7,000=3927{,}392 - 7{,}000 = 392; 7×50=3507 \times 50 = 350; 392−350=42392 - 350 = 42; 7×6=427 \times 6 = 42; 1,000+50+6=1,0561{,}000 + 50 + 6 = 1{,}056
    最终答案： 1,0561{,}056 pounds

参考答案（续）

  1. 10.
    5×900=4,5005 \times 900 = 4{,}500; 4,905−4,500=4054{,}905 - 4{,}500 = 405; 5×80=4005 \times 80 = 400; 405−400=5405 - 400 = 5; 5×1=55 \times 1 = 5; 900+80+1=981900 + 80 + 1 = 981
    最终答案： 981981 boxes
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需要避免的常见错误

  • Forgetting to bring down the next digit
  • Writing a remainder that is larger than the divisor
  • Misaligning quotient digits above the wrong place value
  • Skipping the check with multiplication
  • Omitting a zero in the quotient when the divisor does not go into a digit

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