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

I can…

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

Key words

• Divide Decimals — Find a quotient with decimals by sliding both decimal points right until the divisor is a whole number.
• Dividend — The total number being divided into equal groups (the number inside the division bracket).
• Divisor — The number of equal groups you are dividing into (the number outside the division bracket).
• Quotient — The answer when you divide.
• Decimal Division Algorithm — The steps for dividing decimals: slide the divisor's decimal point right until the divisor is a whole number, slide the dividend's point right the same number of places, then divide.
• Equivalent division — Multiplying both numbers by 10 or 100 gives the same answer.

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

What is 19.2 ÷ 0.8?

Check your answer

24

Multiply both by 10: 192 ÷ 8 = 24.

Sentence starter

I know ___ because ___.

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