Dividing Decimals

Why Do We Divide Decimals? 🍕

Division means splitting something into equal groups or sharing it fairly. We do this with decimals all the time in real life:

• Splitting a bill: $45.75 ÷ 3 friends
• Finding the unit price: $6.75 for $5$ snacks → how much is one?
• Sharing a measurement: $12.5$ feet of rope $\div\ 5$ pieces

A decimal is just a number with a point in it, like $12.6$ or $0.4$. Dividing decimals uses the same long division you already know — we just have to take good care of that little decimal point.

Dividing a Decimal by a Whole Number ➗

The easiest case is when the number you are dividing by (the divisor) is a whole number.

Example: $12.6 \div 3$

The big trick: bring the decimal point straight up into your answer, then divide like normal!

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

Step by step:

1. The decimal point in $12.6$ is between the $2$ and the $6$. Bring it straight up to that same spot in the answer.
2. $12 \div 3 = 4$ → write the $4$.
3. $6 \div 3 = 2$ → write the $2$.

Answer: $12.6 \div 3 = 4.2$ ✓

⭐ The Key Rule for Dividing BY a Decimal

What if you divide by a decimal, like $7.2 \div 0.4$? We don't like dividing by a decimal, so we change it!

Make the divisor (the outside number) a whole number by moving its decimal point to the right.

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

Moving the decimal the same number of places in both numbers keeps the answer exactly the same. It's like making both numbers $10$ times (or $100$ times) bigger — the division result doesn't change!

Quick Concept Check ✅

Let's make sure the big idea is clear.

Worked Example: Dividing by a Decimal 🧮

Let's fully solve $4.68 \div 0.6$, one step at a time.

Step 1 — Make the divisor a whole number. Move the decimal in $0.6$ one place right → it becomes $6$.

Step 2 — Move the dividend the SAME number of places. Move the decimal in $4.68$ one place right → it becomes $46.8$.

So now we solve the easier problem: $46.8 \div 6$.

Step 3 — Divide, bringing the point straight up.

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

• $46 \div 6 = 7$ (since $6 \times 7 = 42$), remainder $4$.
• Bring down the $8$ → $48$. The decimal point comes straight up here.
• $48 \div 6 = 8$.

Answer: $4.68 \div 0.6 = 7.8$ ✓

Worked Example: Adding Zeros When Needed ➕0️⃣

Sometimes the division doesn't end neatly, so we add zeros after the decimal point to keep going. Adding a zero on the end never changes the value ($15 = 15.0 = 15.00$).

Example: $15 \div 0.4$

Step 1 — Make $0.4$ a whole number: move 1 place right → $4$. Step 2 — Move $15$ the same 1 place right: $15 \to 150$ (you can write it as $150.0$).

Step 3 — Divide $150 \div 4$, adding a zero to finish:

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

• $15 \div 4 = 3$, remainder $3$ → bring down $0$ to make $30$.
• $30 \div 4 = 7$, remainder $2$ → bring down a $0$ (added!) to make $20$.
• $20 \div 4 = 5$.

Answer: $15 \div 0.4 = 37.5$ ✓

Your Turn: Divide These ✍️

Use the steps you just learned. Type each answer as a decimal number, like 4.2.

1. $8.4 \div 4 = \;?$
2. $9.6 \div 0.8 = \;?$ (make $0.8$ into $8$ first!)
3. $6 \div 0.5 = \;?$ (make $0.5$ into $5$, and $6$ into $60$)

Multiple Choice 🎯

Work through each one carefully. Move the decimals first if you are dividing by a decimal!

Dividing by 10, 100, and 1,000 🔽

Quick rule: dividing by $10$, $100$, or $1{,}000$ just moves the decimal point to the LEFT!

• $\div\ 10$ → move 1 place left
• $\div\ 100$ → move 2 places left
• $\div\ 1{,}000$ → move 3 places left

Choose the correct answer for each.

Dividing Decimals in the Real World 🌎

Dividing decimals helps us share money fairly and find the price of one item.

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

Solve $47.85 ÷ 3:

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

Each friend pays $15.95.

Finding the unit price: $4$ apples cost $3.96. How much is one apple?

Solve $3.96 ÷ 4 = $0.99 per apple. Knowing the unit price lets you compare deals at the store. Now try a few yourself!

Word Problem Practice 💵

Type each answer as a decimal number (no dollar sign needed), like 0.99.

1. A $12.5$-foot rope is cut into $5$ equal pieces. How long is each piece (in feet)?
2. Five granola bars cost $6.75. What is the price of one bar?
3. A $4.8$-liter jug of juice is poured equally into $8$ cups. How many liters are in each cup?

One More Word Problem 🧠

Review: Everything You Learned 📋

You can now divide decimals like a pro! Here is a quick summary.

Estimate first! Round the numbers to check your answer is reasonable. For example, $47.6 \div 7.8 \approx 48 \div 8 = 6$, so the real answer ($\approx 6.1$) makes sense.

Ready for the final challenge? Let's go! 🚀

Final Challenge 🏆