Dividing Decimals

Why Divide Decimals?

We divide decimals in many real-world situations:

• Splitting a bill: $45.75 ÷ 3 people
• Finding unit price: $6.75 for 5 items
• Sharing measurements: 12.5 feet ÷ 5 sections

Dividing Decimal by Whole Number

Example: 12.6 ÷ 3

Steps:

1. Set up division normally
2. Bring the decimal point straight up into the answer
3. Divide as usual

    4.2
  ------
3 | 12.6
    12
    --
     06
      6
     --
      0 ✓

Answer: 4.2

The Key Rule: Make the Divisor a Whole Number

When dividing by a decimal, move the decimal point to make the divisor (outside number) a whole number.

Then move the decimal the SAME number of places in the dividend (inside number)!

Dividing by a Decimal

Example: 7.2 ÷ 0.4

Step 1: Make divisor a whole number

• Move decimal in 0.4 one place right → 4
• Move decimal in 7.2 one place right too → 72

Step 2: Divide

• 72 ÷ 4 = 18 ✓

Answer: 18

Longer Example with Steps

Example: 4.68 ÷ 0.6

Step 1: Move decimals to make 0.6 a whole number

• 0.6 → 6 (moved 1 place)
• 4.68 → 46.8 (moved 1 place)

Step 2: Divide

    7.8
  ------
6 | 46.8
    42
    --
     4 8
     4 8
     ---
       0 ✓

Answer: 7.8

Adding Zeros When Needed

Sometimes you need to add zeros to keep dividing!

Example: 15 ÷ 0.4

Step 1: Move decimals

• 0.4 → 4
• 15 → 150 (moved 1, can write as 150.0)

Step 2: Divide

    37.5
  ------
4 | 150.0
    12
    --
     30
     28
     --
      20
      20
      --
       0 ✓

Answer: 37.5

Dividing by 10, 100, 1,000

Quick rule: Move the decimal point to the LEFT!

Divide by 10: Move decimal 1 place left

• 34.5 ÷ 10 = 3.45

Divide by 100: Move decimal 2 places left

• 34.5 ÷ 100 = 0.345

Divide by 1,000: Move decimal 3 places left

• 34.5 ÷ 1,000 = 0.0345

Money Problems

Example: Three friends split a $47.85 bill evenly. How much does each person pay?

Solve: $47.85 ÷ 3

    15.95
  -------
3 | 47.85
     3
    --
    17
    15
    --
     28
     27
     --
      15
      15
      --
       0 ✓

Answer: $15.95 each

Finding Unit Price

Example: 4 apples cost $3.96. How much is one apple?

Solve: $3.96 ÷ 4 =$0.99 per apple ✓

This helps compare prices in stores!

Estimation

Always estimate first!

Example: 47.6 ÷ 7.8 ≈ ?

• Round: 48 ÷ 8 = 6
• So answer should be close to 6

Actual: 47.6 ÷ 7.8 ≈ 6.1 ✓ (Close!)

Repeating Decimals

Sometimes decimals repeat forever!

Example: 10 ÷ 3 = 3.333...

Options:

1. Round to a specific place
2. Write with a bar: 3.3̄ (means 3 repeats)
3. Use a fraction instead: 10/3

Real-World Applications

Gas mileage: You drove 345.6 miles on 12.8 gallons

• 345.6 ÷ 12.8 = 27 miles per gallon ✓

Rate of pay: Earned $156.25 for 12.5 hours of work

• $156.25 ÷ 12.5 =$12.50 per hour ✓

Practice Strategy

Steps for dividing decimals:

1. Move decimal in divisor to make it a whole number
2. Move decimal in dividend the same number of places
3. Place decimal point in answer directly above
4. Divide normally
5. Add zeros if needed to continue dividing

Check your work:

• Multiply your answer by the divisor
• Should get the dividend back!
• Example: If 12.6 ÷ 3 = 4.2, then 4.2 × 3 should equal 12.6 ✓

Visual Model: Sharing Equally

Think of division as sharing!

$4.50 ÷ 3 means sharing$4.50 among 3 people

Person 1: $1.50
Person 2: $1.50
Person 3: $1.50
Total: $4.50 ✓

Common Mistakes

❌ Forgetting to move the decimal point in both numbers ❌ Moving the decimals different amounts ❌ Not bringing the decimal straight up in the answer ❌ Stopping too soon and not adding zeros to continue

✅ Move decimal same number of places in BOTH numbers ✅ Divisor (outside) must become a whole number ✅ Bring decimal straight up before you start dividing ✅ Add zeros as needed to finish division or round

Rounding Decimal Quotients

Sometimes answers go on forever!

Example: 22 ÷ 7 = 3.142857142857...

Round to nearest tenth: 3.1 Round to nearest hundredth: 3.14 Round to nearest thousandth: 3.143

For money: Always round to the nearest cent (hundredth)

• $5.678 →$5.68 ✓

Division Vocabulary

• Dividend: The number being divided (inside)
• Divisor: The number you're dividing by (outside)
• Quotient: The answer
• Remainder: What's left over (with decimals, we can keep dividing!)

Remember: Dividend ÷ Divisor = Quotient