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Ratios and Data 6-8 / Week 05 / Monday
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Week 05 · Decimals, Factors and Multiples

Monday

Long division
// Long division, decimal points, and what two numbers share
⏱ about 20 min

Monday: Long Division

The Numbers Desk has moved to the garage workshop. A tape measure runs the length of a long board.

"The relay course is 1,500 meters in all," Rocket says. "Twelve equal laps. One lap is, um, 150 meters?"

"Check it," says Raven. "What do you notice when you multiply back?"

"12 × 150 is 1,800. Too big." Rocket scratches his head. "The numbers are too large to guess."

Nova hovers over the tape measure. "Then do not guess," she says. "Divide one place at a time, left to right."

"Long division," Raven says, pulling a pencil from her hair. "Twelve into fifteen, then bring down the zeros."

Rocket grabs the clipboard. "Divide, multiply, subtract, bring down. I can do that."

Rocket holds a tape measure along a long board in the workshop while Raven reads a note and Nova hovers above.

The standard algorithm

Long division works one place at a time, from the biggest place to the smallest. Four steps repeat: divide, multiply, subtract, bring down.

Here is 1,500 ÷ 12. Read the layout from the top.

      125
   -------
12 | 1500
    -12
    ----
      30
     -24
     ---
       60
      -60
      ---
        0
  1. Divide: 12 goes into 15 one time. Write 1 above the 5.
  2. Multiply: 1 × 12 = 12. Subtract: 15 - 12 = 3.
  3. Bring down the 0 to make 30. Divide: 12 goes into 30 two times. Write 2.
  4. Multiply: 2 × 12 = 24. Subtract: 30 - 24 = 6. Bring down the last 0 to make 60.
  5. Divide: 12 goes into 60 five times. Write 5. Multiply and subtract: 60 - 60 = 0. Done.

So 1,500 ÷ 12 = 125. One lap is 125 meters. Check: 12 × 125 = 1,500.

When the last subtraction is not 0, what is left is the remainder. 1,000 ÷ 24 is 41 with 16 left over.

DIVIDE IT
  • Read the question.
  • Tap your answer.
1,500 ÷ 12 = ?
2,448 ÷ 16 = ?
3,456 ÷ 24 = ?
9,720 ÷ 45 = ?
THE FOUR STEPS, IN ORDER
  • Think about how Rocket works through 1,500 ÷ 12.
  • Tap the steps in order.
1First
2Second
3Third
4Fourth
WASHERS IN BAGS
  • Read the question.
  • Tap your answer.
The crew has 1,000 washers for the ring toss. Bags hold 24. How many full bags?
The crew has 1,000 washers. Bags hold 24. How many washers are left over?
A 2,500 centimeter rope is marked every 36 centimeters. How many full marks?
SentenceTrue or false?
1,500 ÷ 12 = 125?
2,448 ÷ 16 = 153?
12 × 150 = 1,500?
9,720 ÷ 45 = 216?
WHY THIS EXERCISEMultiplying back is the check that catches a slipped digit in long division.
How many meters long is one lap of the relay course? Type the number.
WHY THIS EXERCISEThe lap length sets every distance the crew measures this week.
Try it
Write 2,448 ÷ 16 in the long division layout on paper. Say each step out loud as you do it.
Then check by multiplying your answer by 16.
Draw the long division layout for 1,500 ÷ 12, with every subtraction shown.

Solid dividing. Tomorrow the tape measure gives decimals, and the decimal point needs a careful home.