Master Long Division With Multi-Digit Numbers

In this lesson:

• Read each quotient digit as a place-value amount
• Run the four-move cycle: divide, multiply, subtract, bring down
• Estimate two-digit-divisor quotients and adjust by one

What You Will Be Able to Do

By the end, you will:

1. Run the four moves: divide, multiply, subtract, bring down
2. Read each quotient digit in place-value language
3. Predict the quotient's digit count first
4. Estimate two-digit-divisor digits and adjust
5. Place a zero in the quotient when the divisor doesn't fit

A Familiar Case to Read Aloud

Read the quotient digits in place-value language:

• The 2 above the 8 means 2 tens
• The 1 above the 4 means 1 one
• Together:

Each Quotient Digit Names a Place Value

Each digit's column tells you its place value.

The Four Moves of Long Division

Each cycle has four steps that repeat:

1. Divide — how many divisors fit into the partial dividend?
2. Multiply — that many times the divisor
3. Subtract — from the partial dividend
4. Bring down — the next digit of the dividend

The cycle repeats until the dividend is exhausted.

Walking Through 1,536 Divided by 4

How many 4s in 15 hundreds? 3 hundreds, leftover 3 hundreds.

Bring down 3 tens → 33 tens. How many 4s? 8 tens, leftover 1 ten.

Bring down 6 ones → 16 ones. How many 4s? 4 ones, exactly.

When the Divisor Doesn't Fit Yet

In , the leftmost digit is 1, but 4 doesn't fit into 1.

• Look at the first two digits together: 15
• The first quotient digit lands above the hundreds column, not thousands

This is normal — not an error.

Worked Example: 2,940 Divided by 5

How many 5s in 29 hundreds? 5 hundreds, leftover 4 hundreds.

Bring down 4 tens → 44 tens. How many 5s? 8 tens, leftover 4 tens.

Bring down 0 ones → 40 ones. How many 5s? 8 ones.

Watch Out: Place a Zero, Don't Skip

Every position contributes a digit — write the 0 when the divisor doesn't fit.

Worked Example: 6,003 Divided by 3

How many 3s in 6 thousands? 2 thousands, exactly.

How many 3s in 0 hundreds? 0 hundreds — write the zero.

How many 3s in 0 tens? 0 tens — write the zero.

How many 3s in 3 ones? 1 one.

Two-Digit Divisors Need an Estimate

For one-digit divisors, multiplication facts give the answer.

For two-digit divisors, no fact applies — you must estimate.

Predict the Quotient's Digit Count First

Before dividing :

• Dividend has 4 digits; divisor has 2 digits
• Quotient has either 2 or 3 digits

This catches missing-zero errors before they happen.

Round the Divisor to Estimate

To estimate "how many 24s in 187":

Round to a friendlier number, multiply, see how close.

Worked Example: 1,872 Divided by 24

24 doesn't fit into 1 or 18 — look at 187.

Estimate: , try 7. . .

Bring down 2 → 192. exactly. Write 8.

When the Estimate Is Too High: Adjust Down

Product bigger than partial dividend? Reduce the estimate by 1.

When the Estimate Is Too Low: Adjust Up

Suppose you tried 6:

But — leftover is too big. Increase by 1.

Try, Multiply, Check, Adjust

The loop:

1. Try a digit (rounded-divisor estimate)
2. Multiply divisor × digit
3. Check — fits under the partial dividend? Leftover < divisor?
4. Adjust by ±1 if needed

Expect to miss sometimes. The loop handles it.

Worked Example: 7,488 Divided by 36

Predict: 4-digit ÷ 2-digit → quotient has 3 or 4 digits.

36 fits into 74 → 2 times (, leftover 2).

Bring down 8 → 28. 36 doesn't fit → write 0.

Bring down 8 → 288. → write 8.

Check-In: Compute and Predict First

Before dividing, predict the quotient's digit count, then compute:

Show your prediction, then your work.

Answers and Common Errors to Avoid

1. (3 digits ✓)
2. (3 digits ✓)

Wrong answer 65 on Q1 → dropped a digit somewhere.

Wrong answer 26 on Q2 → missing-zero or alignment error.

Key Takeaways for Long Division

• Every quotient digit names a place-value amount
• The four moves cycle: divide, multiply, subtract, bring down
• Predict the quotient's digit count first
• Two-digit divisors need an estimate; adjust by ±1
• Place a zero when the divisor doesn't fit — don't skip

Coming Up: Three Forms for the Remainder

You can now run the algorithm cleanly.

In Lesson 2, you will:

• Express a remainder in three equivalent forms
• Choose the form a real-world question demands
• Apply long division to bus-loading, money, sharing problems