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Lesson 7: Divide Decimals Using an Algorithm6.NOS.3

Stuck? Start here. Read the steps, try the problem, then check your answer.

I can…

I can divide with decimals by making the divisor a whole number first.

Key words

  • Divide Decimals — Slide both decimal points right, then divide.
  • Dividend — The number you split up.
  • Divisor — The number you divide by.
  • Quotient — The answer when you divide.
  • Decimal Division Algorithm — Slide both decimal points right the same amount. Then divide.
  • Equivalent division — Multiply both numbers by 10 or 100. The answer is the same.
  • Annex a zero — Put a zero at the end of a decimal. The value stays.
  • Algorithm — A set of steps you follow the same way every time.
  • Power of ten — Ten, one hundred, one thousand, and so on.

Steps

  1. I want 18.9 ÷ 6.3. The divisor is 6.3, and long division needs a whole-number divisor.
  2. STEP 0 — MOVE THE POINT: I move the decimal point 1 place right in the divisor, so 6.3 becomes 63.
  3. I slide the decimal point 1 place to the right in the dividend 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.
  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 dividend'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.
  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.
  9. I check by multiplying: 6.3 × 3 = 18.9. Correct — 18.9 ÷ 6.3 = 3.

Try it

Next, you will move the point so the divisor is a whole number, then run the divide, multiply, subtract, bring down cycle on your own.

Check your answer

Check with your guided notes.

Sentence starter

I know ___ because ___.

Goal: I can explain my work using the words dividend, divisor, quotient, and equivalent division.