Reference / Curriculum / 3B / Chapter 11

3B · Chapter 11 · Lesson 4

Subtracting from Kilometers

Regroup one kilometer as 1,000 meters and subtract correctly.

MATH-3B-C11-L04Independent and tutor-supported

Today's mathematical question

Subtract 405 m from 8 km 65 m. Give mixed units.

Learning target

Regroup one kilometer as 1,000 meters and subtract correctly.

Before starting: Prior lesson: Kilometers. Try the warm-up independently.

Prerequisite · 3 questions

Check earlier skills first

These are earlier ideas you need for today; revisit them if they are difficult.

  1. P1

    Convert 2 km 375 m into m.

    Reveal explanation

    Answer: 2,375 m

    2 km = 2,000 m; add 375 to make 2,375 m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. P2

    Express 2,875 m as km and m.

    Reveal explanation

    Answer: 2 km 875 m

    Partition 2,875 into 2 full groups of 1,000 plus 875.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. P3

    Convert 6 km 480 m into m.

    Reveal explanation

    Answer: 6,480 m

    6 km = 6,000 m; add 480 to make 6,480 m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Learn and understand

A mixed kilometers-and-meters subtraction may need regrouping. One kilometer is 1,000 meters. For 5 km 140 m minus 380 m, rename the starting distance as 4 km 1,140 m. Subtract to obtain 4 km 760 m. To subtract 600 m from 2 km 150 m, exchange one kilometer: 1 km 1,150 m − 600 m = 1 km 550 m. Check by adding back 600 m.

Represent it three ways

  1. Concrete: Build equal pieces, measures, counters or shapes with real objects when useful.
  2. Pictorial: Use two aligned place-value columns labeled km and m. Trade exactly 1 km for 1,000 m when the small column is too small.
  3. Abstract: Write the matching number sentence, calculation, comparison or mathematical description. Explain each number's unit.

Important vocabulary

regroup
exchange one larger unit for equivalent smaller units
difference
what remains after subtraction
kilometer
1,000 meters

Fully worked examples and checks

Try each new understanding check before revealing the explanation.

Worked example 1

Explore, calculate, verify

Subtract 405 m from 8 km 65 m. Give mixed units.

1 km1000 m each=1,000 m
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. Exchange one km for 1000 m, then subtract: 8065 − 405 = 7660 m. Regroup the result into km and m.
  3. Check that the answer uses the right units and makes sense.

Answer: 7 km 660 m

Check your understanding 1

Subtract 105 m from 4 km 55 m. Give mixed units.

Reveal answer and explanation

3 km 950 m — Exchange one km for 1000 m, then subtract: 4055 − 105 = 3950 m. Regroup the result into km and m.

1 km1000 m each=1,000 m
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Worked example 2

Explore, calculate, verify

Subtract 928 m from 7 km 20 m. Give mixed units.

1 km1000 m each=1,000 m
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. Exchange one km for 1000 m, then subtract: 7020 − 928 = 6092 m. Regroup the result into km and m.
  3. Check that the answer uses the right units and makes sense.

Answer: 6 km 92 m

Check your understanding 2

Subtract 177 m from 3 km 55 m. Give mixed units.

Reveal answer and explanation

2 km 878 m — Exchange one km for 1000 m, then subtract: 3055 − 177 = 2878 m. Regroup the result into km and m.

1 km1000 m each=1,000 m
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Worked example 3

Explore, calculate, verify

Subtract 531 m from 3 km 20 m. Give mixed units.

1 km1000 m each=1,000 m
One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  1. Identify the whole, the units, and what the question asks.
  2. Exchange one km for 1000 m, then subtract: 3020 − 531 = 2489 m. Regroup the result into km and m.
  3. Check that the answer uses the right units and makes sense.

Answer: 2 km 489 m

Check your understanding 3

Subtract 652 m from 3 km 650 m. Give mixed units.

Reveal answer and explanation

2 km 998 m — Exchange one km for 1000 m, then subtract: 3650 − 652 = 2998 m. Regroup the result into km and m.

1 km1000 m each=1,000 m
One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Guided · 5 questions

Guided practice

Keep the model and earlier examples visible while practising.

  1. G1

    Subtract 930 m from 3 km 375 m. Give mixed units.

    Reveal explanation

    Answer: 2 km 445 m

    Exchange one km for 1000 m, then subtract: 3375 − 930 = 2445 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. G2

    Subtract 846 m from 3 km 125 m. Give mixed units.

    Reveal explanation

    Answer: 2 km 279 m

    Exchange one km for 1000 m, then subtract: 3125 − 846 = 2279 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. G3

    Subtract 546 m from 8 km 20 m. Give mixed units.

    Reveal explanation

    Answer: 7 km 474 m

    Exchange one km for 1000 m, then subtract: 8020 − 546 = 7474 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. G4

    Subtract 650 m from 2 km 65 m. Give mixed units.

    Reveal explanation

    Answer: 1 km 415 m

    Exchange one km for 1000 m, then subtract: 2065 − 650 = 1415 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. G5

    Subtract 587 m from 5 km 375 m. Give mixed units.

    Reveal explanation

    Answer: 4 km 788 m

    Exchange one km for 1000 m, then subtract: 5375 − 587 = 4788 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Independent · 8 questions

Independent practice

Work these without hints and explain the method used. Write answers on paper.

  1. I1

    Subtract 165 m from 3 km 125 m. Give mixed units.

    Reveal explanation

    Answer: 2 km 960 m

    Exchange one km for 1000 m, then subtract: 3125 − 165 = 2960 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. I2

    Subtract 636 m from 2 km 125 m. Give mixed units.

    Reveal explanation

    Answer: 1 km 489 m

    Exchange one km for 1000 m, then subtract: 2125 − 636 = 1489 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. I3

    Subtract 895 m from 2 km 875 m. Give mixed units.

    Reveal explanation

    Answer: 1 km 980 m

    Exchange one km for 1000 m, then subtract: 2875 − 895 = 1980 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  4. I4

    Subtract 863 m from 5 km 55 m. Give mixed units.

    Reveal explanation

    Answer: 4 km 192 m

    Exchange one km for 1000 m, then subtract: 5055 − 863 = 4192 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  5. I5

    Subtract 910 m from 5 km 650 m. Give mixed units.

    Reveal explanation

    Answer: 4 km 740 m

    Exchange one km for 1000 m, then subtract: 5650 − 910 = 4740 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  6. I6

    Subtract 170 m from 5 km 40 m. Give mixed units.

    Reveal explanation

    Answer: 4 km 870 m

    Exchange one km for 1000 m, then subtract: 5040 − 170 = 4870 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  7. I7

    Subtract 391 m from 2 km 20 m. Give mixed units.

    Reveal explanation

    Answer: 1 km 629 m

    Exchange one km for 1000 m, then subtract: 2020 − 391 = 1629 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  8. I8

    Subtract 992 m from 4 km 650 m. Give mixed units.

    Reveal explanation

    Answer: 3 km 658 m

    Exchange one km for 1000 m, then subtract: 4650 − 992 = 3658 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.

Challenge · 2 questions

Challenge and error analysis

Go beyond arithmetic: justify a claim, correct reasoning, or connect two representations.

  1. C1

    Why is 4 km exactly the same length as 4,000 m?

    Reveal explanation

    Answer: 1 km = 1,000 m

    Each of the 4 kilometers contains 1,000 meters. The unit changes, not the distance.

  2. C2

    A path is 4 km 200 m. After walking 450 m, what remains? Explain the exchange.

    Reveal explanation

    Answer: 3 km 750 m

    Rename as 3 km 1,200 m, then subtract 450 m to get 3 km 750 m.

Exit · 3 questions

Exit check

Solve independently, then return on another day to check retention.

  1. E1

    Subtract 999 m from 4 km 40 m. Give mixed units.

    Reveal explanation

    Answer: 3 km 41 m

    Exchange one km for 1000 m, then subtract: 4040 − 999 = 3041 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  2. E2

    Subtract 683 m from 3 km 250 m. Give mixed units.

    Reveal explanation

    Answer: 2 km 567 m

    Exchange one km for 1000 m, then subtract: 3250 − 683 = 2567 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
  3. E3

    Subtract 509 m from 2 km 375 m. Give mixed units.

    Reveal explanation

    Answer: 1 km 866 m

    Exchange one km for 1000 m, then subtract: 2375 − 509 = 1866 m. Regroup the result into km and m.

    1 km1000 m each=1,000 m
    One larger unit is exchanged into an equal number of smaller units without changing the quantity.
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