1/15
00:00

Learn more about this topic →

I.8 Multiply 4-digit numbers by 1-digit numbers: word problems

Loading questions...

Go to the practice →

Multiply a 4-digit number by a 1-digit number

When we multiply a 4-digit number by a 1-digit number, we are finding the total of a large group repeated a certain number of times. The 4-digit number has a thousands place, hundreds place, tens place, and ones place. The 1-digit number tells us how many groups we have.

Example meaning: 3,124 × 2 means "two groups of three thousand one hundred twenty-four."

Place value review:
  • In 3,746: 3 is in the thousands place → 3,000
  • 7 is in the hundreds place → 700
  • 4 is in the tens place → 40
  • 6 is in the ones place → 6
Note

Understanding place value is the key to multiplying larger numbers correctly. Each digit has its own value.

The standard multiplication algorithm (step-by-step)

The standard algorithm is a step-by-step way to multiply. We multiply the 1-digit number by each digit of the 4-digit number, starting from the ones place and moving left. If a product is ten or more, we regroup (carry) to the next place.

Example 1: no regrouping

Multiply 2,103 × 3

2,103
× 3
6,309

  • Step 1: Multiply the ones: 3 × 3 = 9. Write 9 in the ones place.
  • Step 2: Multiply the tens: 3 × 0 = 0. Write 0 in the tens place.
  • Step 3: Multiply the hundreds: 3 × 1 = 3. Write 3 in the hundreds place.
  • Step 4: Multiply the thousands: 3 × 2 = 6. Write 6 in the thousands place.
Note

Always start with the ones place. Even if a digit is zero, you must multiply it. 3 × 0 = 0.

When regrouping (carrying) is needed

Sometimes when you multiply a digit, the product is 10 or greater. You keep the ones digit in the current place and move the tens digit to the next place. This is called regrouping or carrying.

Example 2: with regrouping

Multiply 1,478 × 4

1,478
× 4
5,912

  1. Ones: 4 × 8 = 32. Write 2 in the ones place. Regroup 3 tens to the tens place.
  2. Tens: 4 × 7 = 28, plus the regrouped 3 = 31. Write 1 in the tens place. Regroup 3 hundreds to the hundreds place.
  3. Hundreds: 4 × 4 = 16, plus the regrouped 3 = 19. Write 9 in the hundreds place. Regroup 1 thousand to the thousands place.
  4. Thousands: 4 × 1 = 4, plus the regrouped 1 = 5. Write 5 in the thousands place.

Final product: 5,912

Note

After multiplying each place, always add the regrouped number right away. Double-check your regrouping by estimating: 1,478 is close to 1,500, and 4 × 1,500 = 6,000. Our answer 5,912 is reasonable.

Multiplying with a larger 4-digit number and more regrouping

Sometimes you will have to regroup more than once, and the regrouped numbers can be larger. The same steps work every time.

Example 3: multiple regroupings

Multiply 3,659 × 6

3,659
× 6
21,954

  1. 6 × 9 = 54. Write 4, regroup 5 to tens.
  2. 6 × 5 = 30, plus 5 = 35. Write 5, regroup 3 to hundreds.
  3. 6 × 6 = 36, plus 3 = 39. Write 9, regroup 3 to thousands.
  4. 6 × 3 = 18, plus 3 = 21. Write 21. (Since there are no more places, we write the whole 21.)

Final product: 21,954

Note

In the thousands step, we had 21. That means 21 thousands = 2 ten-thousands and 1 thousand. So we write 1 in the thousands place and 2 in the ten-thousands place. That's why the answer has five digits.

Multiplying when the 4-digit number has zeros inside

Zeros are placeholders. When you multiply by zero, the product is zero. But you must still account for any numbers that were regrouped from the previous step.

Example 4: zero in tens place

Multiply 4,206 × 5

4,206
× 5
21,030

  1. 5 × 6 = 30. Write 0, regroup 3 to tens.
  2. Tens place: digit is 0. 5 × 0 = 0, plus regrouped 3 = 3. Write 3. No regrouping.
  3. Hundreds place: digit is 2. 5 × 2 = 10. Write 0, regroup 1 to thousands.
  4. Thousands place: 5 × 4 = 20, plus regrouped 1 = 21. Write 21.

Final product: 21,030

Example 5: zero in hundreds place

Multiply 3,089 × 7

3,089
× 7
21,623

  1. 7 × 9 = 63. Write 3, regroup 6.
  2. Tens: 7 × 8 = 56, plus 6 = 62. Write 2, regroup 6.
  3. Hundreds: 7 × 0 = 0, plus 6 = 6. Write 6. No regroup.
  4. Thousands: 7 × 3 = 21. Write 21.
Note

Don't skip the zero! Even though it's zero, you still have to add any regrouped number to it.

Estimating to check for reasonableness

Before or after you multiply, you can estimate the answer by rounding the 4-digit number to the nearest thousand. This helps you see if your exact answer makes sense.

Estimation example:

Multiply 2,785 × 4

  • Exact multiplication (using algorithm):
    2,785
    × 4
    11,140

  • Round 2,785 to the nearest thousand → 3,000.
  • Estimate: 3,000 × 4 = 12,000.
  • Our exact answer is 11,140, which is close to 12,000. It's reasonable.
Note

If your exact answer is very different from the estimate (like 6,000 vs 12,000), check your regrouping and multiplication again.

Word problems with 4-digit by 1-digit multiplication

Many real-world situations use this multiplication. Look for keywords like "each," "total," "every," or "times."

Example problem:

A warehouse has 1,248 boxes on each shelf. There are 6 shelves. How many boxes are there in total?

Multiply: 1,248 × 6

1,248
× 6
7,488

There are 7,488 boxes in total.

Note

Always include the unit (boxes, miles, people, etc.) in your final answer.

Common mistakes to avoid

Even fourth graders who understand the steps can make small errors. Watch out for these common pitfalls.

Mistakes and fixes:
  • Forgetting to add the regrouped number: After you multiply, immediately add the number you carried.
  • Multiplying by the wrong place: Remember, the 1-digit number multiplies each entire digit value, not the whole number at once.
  • Not writing the regrouped number clearly: Write it small above the next column so you don't lose it.
  • Incorrect zero multiplication: 6 × 0 = 0, not 6. But don't forget to add any carried number to that zero.
Note

Practice with graph paper to keep your columns straight. Neatness prevents most errors.

Extra practice examples (with answers)

Try these on your own, then check your work.

Practice set:
  1. 3,217 × 4 = ?
    3,217
    × 4
    12,868
  2. 5,082 × 6 = ?
    5,082
    × 6
    30,492
  3. 9,401 × 3 = ?
    9,401
    × 3
    28,203
  4. 2,999 × 5 = ?
    2,999
    × 5
    14,995
Note

Check your regrouping carefully, especially when many 9's are involved.

Why the algorithm works: expanded form connection

The standard algorithm is just a shortcut for breaking the number into its place values and using the distributive property.

Expanded form method:

Take 3,659 × 6 from earlier.

3,659 = 3,000 + 600 + 50 + 9

Multiply each part by 6:

  • 6 × 3,000 = 18,000
  • 6 × 600 = 3,600
  • 6 × 50 = 300
  • 6 × 9 = 54

Add them: 18,000 + 3,600 = 21,600; +300 = 21,900; +54 = 21,954. Same answer!

Note

Understanding the expanded form helps you see why we "carry" numbers — it's just combining like place values.

Go to the practice →

Common Core alignment: CCSS.MATH.CONTENT.4.NBT.B.5 – Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Notes for teachers

This lesson is aligned with CCSS.MATH.CONTENT.4.NBT.B.5. All content is 100% free, use it for whole-class instruction, independent study and practice, or homework. Emphasize place value and regrouping. The math-stack format helps students visualize the alignment of digits.