Lesson 2.7Divide Decimals Using an Algorithm
Start hereWords, worked example, and sentence starters
Learning target I can divide with decimals by making the divisor a whole number first.
Why This Matters A school bought new math workbooks as shown in the order form. What is the cost of each workbook?
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| DividendSpanish: Dividendo | The total number being divided into equal groups (the number inside the division bracket). | In 84.6 ÷ 6, it is 84.6 |
| DivisorSpanish: Divisor | The number of equal groups you are dividing into (the number outside the division bracket). | In 84.6 ÷ 6, it is 6 |
| QuotientSpanish: Cociente | The answer when you divide. | 84.6 ÷ 6 = 14.1 |
| Decimal Division AlgorithmSpanish: Algoritmo de división decimal | 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. | 8.4 ÷ 2.1 → move the point in both → 84 ÷ 21 → divide, multiply, subtract, bring down → 4 |
| Equivalent divisionSpanish: División equivalente | Multiplying both numbers by 10 or 100 gives the same answer. | 7.56 ÷ 0.12 = 756 ÷ 12 = 63 (both multiplied by 100) |
| Annex a zeroSpanish: Agregar un cero | Write a zero after the last decimal digit without changing the value. | 7.2 → 7.20 |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A rope 25.2 meters long is cut into 6 equal pieces. How long is each piece?
- Write 25.2 ÷ 6. Put the quotient’s point above the point in 25.2.
- 6 goes into 25 four times, 1 left over. Bring down the 2 to make 12.
- 12 ÷ 6 = 2. Check: 4.2 × 6 = 25.2.
Answer: 4.2 meters for each piece
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
Let's do 8.4 ÷ 2.1. STEP 0 — MOVE THE POINT: how many places make 2.1 a whole number? (1 place, so 2.1 becomes 21.)
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The dividend is and the divisor is .
- I placed the decimal point because .
- When a remainder appeared I .
- I checked my quotient by .
Word bank dividenddivisorquotientdecimal pointalgorithmannexbring downplace valueestimatecheckmultiplysubtract
Watch out!A common mistake
A common mistake in Divide Decimals is moving the decimal point in the divisor but forgetting to move it the same number of places in the dividend. For example, in 6.4 ÷ 0.8 a student changes 0.8 to 8 but leaves the dividend as 6.4, then divides 6.4 ÷ 8 = 0.8 instead of moving both points to get 64 ÷ 8 = 8. A second version of this mistake happens when the divisor has two decimal places, like 0.12: students move both points only 1 place instead of 2, turning 9.6 ÷ 0.12 into 96 ÷ 1.2 instead of the correct 960 ÷ 12. Count the divisor's decimal places first, then move BOTH points that same number of places.
Lesson 2.7Divide Decimals Using an Algorithm
Level 0Most support · every hint printed
Learning target I can divide with decimals by making the divisor a whole number first.
Why This Matters A school bought new math workbooks as shown in the order form. What is the cost of each workbook?
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A rope 25.2 meters long is cut into 6 equal pieces. How long is each piece?
- Write 25.2 ÷ 6. Put the quotient’s point above the point in 25.2.
- 6 goes into 25 four times, 1 left over. Bring down the 2 to make 12.
- 12 ÷ 6 = 2. Check: 4.2 × 6 = 25.2.
Answer: 4.2 meters for each piece
-
1Complete the table. Show how you found each value.
Rewrite each problem by making the divisor a whole number, then solve.
Original Multiply Both By New Problem Quotient 4.5 ÷ 0.9 10 3.6 ÷ 0.4 10 Steps to try- The 'Multiply Both By' column is the key move: choose 10 or 100 based on how many decimal places the DIVISOR has.
- One decimal place in the divisor means multiply both numbers by 10; then rewrite and divide whole numbers.
- Row 1: 0.9 has one decimal place, so multiply 4.5 and 0.9 each by 10 and write the new whole-number problem in the row.
Show your work
-
2Circle the letter of the best answer. Show how you know.
What is 14.4 ÷ 1.2?
- A0.12
- B1.2
- C12
- D120
Steps to try- Dividing by a decimal is awkward — notice the divisor 1.2 has one decimal place. There's a move that makes it whole.
- Multiply BOTH numbers by 10: scaling dividend and divisor the same way keeps the quotient exactly the same.
- Compute 14.4 × 10 = 144 and 1.2 × 10 = 12. Now solve 144 ÷ 12 — a whole-number division you already know how to do.
Show your work -
3Circle the letter of the best answer. Show how you know.
What is 3.78 ÷ 0.6?
- A0.063
- B0.63
- C6.3
- D63
Steps to try- The divisor 0.6 has one decimal place — shifting both numbers one place makes the divisor a whole number.
- Multiply both numbers by 10 to build an equivalent problem, then divide, keeping the decimal point in the dividend.
- 3.78 × 10 = 37.8 and 0.6 × 10 = 6. Now compute 37.8 ÷ 6, keeping the decimal point lined up in your answer.
Show your work -
4Circle the letter of the best answer. Show how you know.
What is 8.4 ÷ 0.7?
- A0.12
- B1.2
- C12
- D120
Steps to try- Ask yourself: how many groups of 0.7 fit inside 8.4? Since 0.7 is less than 1, expect MORE groups than 8.
- Scale both numbers by 10 so you're dividing by a whole number instead of a decimal.
- 8.4 becomes 84 and 0.7 becomes 7. Solve 84 ÷ 7 — your 7s times-table facts will carry you there.
Show your work
Explain your thinkingWhy does moving the point the same number of places in both numbers give you the same quotient — and why is it worth doing before you start the divide, multiply, subtract, bring down cycle?
Sentence starter Multiplying both numbers by ___ doesn't change the quotient because ___.