Neft Teacher · Learn It

Unit 2 · Standard 6.NOS.3

Divide Decimals Using an Algorithm

Lesson 2-7 · Learn It — how the math works

Why we're learning this

A school bought new math workbooks as shown in the order form. What is the cost of each workbook?

✱ Math Workbench

Learn It

How do you divide with decimals?

Dividing splits a total into equal groups. When you divide by a decimal, first move the point to make the divisor a whole number — then run the same long-division cycle: divide, multiply, subtract, bring down.

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

A school paid for math workbooks with the money shown. There are three identical stacks, and each stack holds one $5 bill, one $1 bill, and a single quarter.
Where you see this in real lifeA school paid for math workbooks with the money shown. There are three identical stacks, and each stack holds one $5 bill, one $1 bill, and a single quarter.

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

  1. I want 18.9 ÷ 6.3. The is 6.3, and long division needs a whole-number divisor.18.9 ÷ 6.3
  2. STEP 0 — MOVE THE POINT: I move the decimal point 1 place right in the , so 6.3 becomes 63.
  3. I slide the decimal point 1 place to the right in the too, so 18.9 becomes 189. Both points slid the same 1 place, so the answer does not change. The problem is now 189 ÷ 63.189 ÷ 63
  4. Now I write it the tall way — 63 into 189 — with the answer going on top of the bar and the answer's decimal point in the column directly above the 's point. Then I repeat the same four steps I always use: DIVIDE, MULTIPLY, SUBTRACT, BRING DOWN.
  5. DIVIDE: 63 does not fit into 1 or 18, so my first working number is 189. How many 63s fit into 189? Three. I write 3 above the 9.
  6. MULTIPLY: 3 × 63 = 189. I write it underneath.3 × 63 = 189
  7. SUBTRACT: 189 − 189 = 0.
  8. BRING DOWN: there are no digits left to bring down, so the cycle is finished and the remainder is 0. 18.9 ÷ 6.3 = 3.0. 18.9 ÷ 6.3 = 3
  9. I check by multiplying: 6.3 × 3 = 18.9. Correct — 18.9 ÷ 6.3 = 3.6.3 × 3 = 18.9

Watch out — mistakes students make here

  • Dividing by less than 1 makes the answer larger, not smaller.
  • Move both decimals so you divide by a whole number, then divide.
  • Check your decimal placement — you shifted one place too many.

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

Same steps, new numbers.

  1. Let's do 8.4 ÷ 2.1. STEP 0 — MOVE THE POINT: how many places make 2.1 a whole number?8.4 ÷ 2.1
    Check this step
    (1 place, so 2.1 becomes 21.)
  2. Now slide the decimal point 1 place to the right in the too. What does 8.4 become?
    Check this step
    (84, so the new problem is 84 ÷ 21.)
  3. DIVIDE: how many 21s fit into 84?
    Check this step
    (Four. I write 4 on top, above the 4 in 84.)
  4. MULTIPLY: what is 4 × 21?4 × 21
    Check this step
    (84. I write it underneath the 84.)
  5. SUBTRACT: what is 84 − 84?
    Check this step
    (0.)
  6. BRING DOWN: is there another digit left to bring down?
    Check this step
    (No — nothing is left, so 8.4 ÷ 2.1 = 4. Check: 2.1 × 4 = 8.4.)8.4 ÷ 2.1 = 4

On your ownYou do — solve this one by yourself

Before you start, remember:

  • Remember: move the point in both numbers, put the point in the , then divide, multiply, subtract, bring down.

Solve: A water tank holds 19.2 liters. It is poured into bottles that each hold 1.6 liters. How many bottles can be filled?

My answer

Stuck? Open one hint at a time.

Hint 1

You're asking how many 1.6s fit into 19.2 — that's division, and the divisor 1.6 needs to become whole first.

Hint 2

Multiply both amounts by 10 to build an equivalent whole-number division, then divide.

Hint 3

19.2 × 10 = 192 and 1.6 × 10 = 16. Now run the cycle on 192 ÷ 16: DIVIDE 19 ÷ 16 → 1, MULTIPLY 1 × 16 = 16, SUBTRACT 19 − 16 = 3, BRING DOWN the 2.

Check my answer
✅ Answer: 12 bottles
19.2 ÷ 1.6: multiply both by 10 → 192 ÷ 16 = 12 bottles.

Turn & TalkSay it out loud with a partner

The order form shows the school paid $394.50 in total for 75 workbooks. What division would tell you the cost of one workbook, and why is it division and not multiplication?

Try starting with:

  • I think ___ because ___.Pienso que ___ porque ___.
  • I agree / disagree with you because ___.Estoy / no estoy de acuerdo contigo porque ___.
Use these wordsDivide DecimalsDividendDivisorQuotientDecimal Division Algorithm