Neft Teacher · Learn It

Unit 2 · Standard 6.NOS.2

Divide Multi-Digit Numbers Using an Algorithm

Lesson 2-6 · Learn It — how the math works

Why we're learning this

The space station has 1,344 nutrition bars that must be divided equally among 12 crew sections for a 4-week rotation. How many bars does each section receive?

✱ Math Workbench

Learn It

How do you divide big numbers?

Dividing means splitting a total into equal groups. Long division finds the quotient one digit at a time by repeating the same four steps: divide, multiply, subtract, bring down.

Picture itSee what the math looks like before you read about it

A school district has 13,275 elementary-age students. The district plans to redistrict and divide the students equally among its 15 elementary schools.
Where you see this in real lifeA school district has 13,275 elementary-age students. The district plans to redistrict and divide the students equally among its 15 elementary schools.

Watch me solve itI do — read one step at a time

  1. I want 1,344 ÷ 12. The is 1,344 and the is 12, so 12 goes outside the bracket and 1,344 goes inside.1,344 ÷ 12
  2. DIVIDE: 12 does not fit into 1, so I look at 13. How many 12s fit into 13? One. I write 1 above the 3.
  3. MULTIPLY: 1 × 12 = 12. I write 12 underneath the 13.1 × 12 = 12
  4. SUBTRACT: 13 − 12 = 1. That is what is left so far.
  5. : I bring the next digit, 4, down next to the 1 to make 14. Now I repeat the cycle.
  6. REPEAT: 14 ÷ 12 → 1 (written above the 4), 1 × 12 = 12, 14 − 12 = 2, and I the last 4 to make 24.4), 1 × 12 = 12, 14
  7. REPEAT: 24 ÷ 12 → 2 (written above the last 4), 2 × 12 = 24, 24 − 24 = 0. Nothing is left to , so the is 0.4), 2 × 12 = 24, 24
  8. The digits I wrote are 1, 1, 2, so 1,344 ÷ 12 = 112. I check by multiplying: 12 × 112 = 1,344.1,344 ÷ 12 = 112

Watch out — mistakes students make here

  • Multiply your answer back: 16 × 137 = 2,192, which falls short of 2,352. The quotient needs to be a little larger.
  • Re-multiply your answer by 16; does it return to 2,352?
  • 146 boxes × 14 = 2,044 items, which leaves 140 items unpacked. Multiply your answer by 14 and check that it rebuilds exactly 2,184.

Try it with meWe do — you answer first, then check

Same steps, new numbers.

  1. Let's do 384 ÷ 8. DIVIDE: 8 does not fit into 3, so we look at 38. How many 8s fit into 38?384 ÷ 8
    Check this step
    (4 — write it above the 8.)
  2. MULTIPLY: what is 4 × 8?4 × 8
    Check this step
    (32 — write it under the 38.)
  3. SUBTRACT: what is 38 − 32?
    Check this step
    (6.)
  4. : bring the 4 down next to the 6. What number do you have now?
    Check this step
    (64.)
  5. DIVIDE: how many 8s fit into 64?
    Check this step
    (8 — write it above the 4.)
  6. MULTIPLY: what is 8 × 8?8 × 8
    Check this step
    (64 — write it under the 64.)
  7. SUBTRACT: what is 64 − 64?
    Check this step
    (0.)
  8. : is there another digit left to bring down?
    Check this step
    (No — the is 0, so 384 ÷ 8 = 48. Check: 8 × 48 = 384.)384 ÷ 8 = 48

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember the cycle: divide, multiply, subtract, — and repeat it until no digits are left.

Solve: A warehouse has 2,184 items to pack into boxes of 14. How many boxes are needed?

My answer

Stuck? Open one hint at a time.

Hint 1

The question asks how many groups of 14 fit into 2,184 — that phrase 'how many boxes' signals division.

Hint 2

Estimate to anchor yourself: 14 × 150 = 2,100 is close to 2,184. Then set it up as long division and run the cycle.

Hint 3

DIVIDE: 21 ÷ 14 → 1. MULTIPLY: 1 × 14 = 14. SUBTRACT: 21 − 14 = 7. BRING DOWN the 8 to make 78, then repeat the cycle.

Check my answer
✅ Answer: 156 boxes
2,184 ÷ 14 = 156. Check: 14 × 156 = 14 × 150 + 14 × 6 = 2,100 + 84 = 2,184.

Turn & TalkSay it out loud with a partner

The station must divide 1,344 nutrition bars equally among 12 crew sections. Before dividing, about how many bars should each section get, and how do you know?

Try starting with:

  • Each section gets about ___ bars because 1,344 is close to ___.Cada sección recibe unas ___ barras porque 1,344 está cerca de ___.
  • I estimated by ___.Estimé usando ___.
Use these wordsdividenddivisorquotientestimatebring down