3-Digit and 4-Digit by 1-Digit Multiplication Worksheets

3 and 4-digit by 1-digit multiplication uses the same steps as 2-digit problems, repeated for each column, with a carry from one column to the next. The five PDFs on this page have 3-digit problems, 4-digit problems, grid paper and story problems, and every sheet has an answer key. They follow standard 4.NBT.B.5 of the Common Core standards for grade 4 number and operations in base ten, and the notes below show worked examples, how often carries happen and how to estimate.

About these worksheets

Multiplying a 3-digit or 4-digit number by one digit uses the same steps as 2-digit numbers, repeated for each column: multiply, write the ones, carry the tens. Grade 4 children do this with up to four digits (Common Core 4.NBT.B.5).

Worked example: 658 × 7

1. 8 × 7 = 56. Write 6, carry 5.
2. 5 × 7 = 35, plus 5 = 40. Write 0, carry 4.
3. 6 × 7 = 42, plus 4 = 46. Write 46.
4. The answer is 4,606.

Estimate first to catch mistakes: 658 is close to 700, and 700 × 7 = 4,900, so 4,606 makes sense.

3 and 4-digit by 1-digit multiplication worksheets: what is in the set

There are 5 3 and 4-digit by 1-digit multiplication worksheets on this page, and every one has an answer key except for any cut-out games. Two sheets are 3-digit problems, one is on grid paper, one has 4-digit problems, and one has story problems.

3 and 4-digit by 1-digit multiplication: four worked examples

3 and 4-digit by 1-digit multiplication goes one column at a time, from the right. In each column, multiply the digit by the multiplier, add the carry from the column before, write the ones digit, and carry the tens digit. Wikipedia’s article on multiplication algorithms describes this as the oldest method. These tables show four problems. First, 324 × 3, where only one column carries:

324 × 3 = 972

Second, 658 × 7, which has a carry in every column:

658 × 7 = 4,606

Third, a 4-digit number, 2,413 × 4:

2,413 × 4 = 9,652

Fourth, a number with a zero in it, 4,056 × 3:

4,056 × 3 = 12,168

3 digit by 1 digit multiplication worksheets: how many carries?

The 3 digit by 1 digit multiplication worksheets have problems with up to three carries. How many carries a problem has depends on the multiplier. This table counts the 900 three-digit numbers, from 100 to 999, by the number of columns that carry, for four multipliers:

With a multiplier of 3, only 48 (5%) of the problems have no carry, but with a multiplier of 9, 648 (72%) of the problems have three carries. This is why the practice sets mix the multipliers, so that children meet every case. The 2-digit by 1-digit multiplication page has the same count for 2-digit numbers.

4 digit by 1 digit multiplication: how big can the product be?

For 4 digit by 1 digit multiplication, the product has four or five digits. A four-digit number gives a five-digit product when it is at least 10,000 divided by the multiplier. This table shows the smallest and biggest products, and how many four-digit numbers have a five-digit product, for each multiplier:

With a multiplier of 9, 99% of the four-digit numbers have a five-digit product, and with a multiplier of 2, 56% do. An estimate tells a child how many digits to expect before they start.

Multi digit multiplication worksheets: zeros in the number

A zero in the number needs care in multi digit multiplication worksheets. The product of a zero digit is zero, but a carry from the column before is added, so the digit written is the carry. This table shows five problems with zeros:

For 4,056 × 3, the hundreds digit is 0, and 0 × 3 = 0, plus the carry 1, so the digit written is 1. A child who skips the zero loses a digit and gets 1,268 instead of 12,168. The place value worksheets pages show why each digit has its own column.

4th grade multiplication worksheets: estimating and the area model

For 4th grade multiplication worksheets, the standard asks children to illustrate the calculation with equations, rectangular arrays or area models. The area model splits the number into hundreds, tens and ones, multiplies each part, and adds. This table shows four problems:

Each part is an easy multiplication with zeros. To estimate, round the number to the nearest hundred and multiply. This table shows six problems, with the estimate and the exact product:

The estimating with rounding and rounding worksheets pages have more practice with rounding. A check is to divide the product by the multiplier, and this table checks five answers:

Common mistakes with 3 and 4-digit by 1-digit multiplication

The most common mistake is to forget a carry. This table shows five mistakes, what went wrong and the fix:

3 and 4-digit by 1-digit multiplication word problems

Story problems use large numbers from stadiums, farms and factories. Ask children to estimate first, and then to multiply column by column:

Games and activities for 3 and 4-digit by 1-digit multiplication

Children learn 3 and 4-digit by 1-digit multiplication best when they play with it. These games use things that are found at home or in a classroom:

• Estimate and check: estimate each product by rounding to the nearest hundred, and then multiply
• Digit cards: draw three or four digit cards and a multiplier card, and multiply
• Carry detective: find the missing carry in a worked example
• Zero hunt: find the problems in a list that have a zero in the number, and solve them
• Area model race: split each number into hundreds, tens and ones and add the four products
• Multiplication bingo: a bingo card with products, and calling cards with problems

Extra support and extra challenge with 3 and 4-digit by 1-digit multiplication

For children who need more support: make sure that 2-digit by 1-digit multiplication is secure. Use grid paper, one digit to a box, and write each carry above the next digit. Say each step: “8 times 7 is 56, write 6 and carry 5”. Do the 3-digit sheets with multipliers of 2, 3 and 4 first, and use the answer key to find the column of a mistake.

For children who need more challenge: ask for the biggest 4-digit number that gives a 5-digit product with a multiplier of 3, for a product with a zero in the middle, and for the missing digit in 4☐6 × 7 = 3,262. A story problem that needs two steps, such as finding the cost of 7 boxes of 658 and then the change, is a good challenge.

How to tell that a child is ready to move on from 3 and 4-digit by 1-digit multiplication

Before moving on from 3 and 4-digit by 1-digit multiplication, check that the child can do all four of these things:

1. The child multiplies each column and adds the carry.
2. The child writes a digit for a zero in the number.
3. The child estimates by rounding to the nearest hundred.
4. The child multiplies 4-digit numbers by one digit.

When all four are true, move on to the 2-digit by 2-digit multiplication page, or to the long division 3-digit by 1-digit page.

A 20-minute lesson on 3 and 4-digit by 1-digit multiplication

A short lesson is the best way to introduce 3 and 4-digit by 1-digit multiplication. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where 3 and 4-digit by 1-digit multiplication fits across the grades

No skill stands alone. This table shows what children learn before and after 3 and 4-digit by 1-digit multiplication, with the standard that goes with each step:

This page is the middle of the multi-digit multiplication pages. The whole sequence is on the multiplication worksheets page.

Helping at home with 3 and 4-digit by 1-digit multiplication

Parents do not need to be experts to help with 3 and 4-digit by 1-digit multiplication. These suggestions work well, and each takes only a few minutes:

• Ask the child to estimate before multiplying.
• Use real large numbers: “4 sections of 2,413 seats”.
• Look for the carries when checking the homework.
• Use grid paper, one digit to a box.
• Check each answer by dividing by the multiplier.

How to check progress in 3 and 4-digit by 1-digit multiplication

A teacher or parent can check progress in 3 and 4-digit by 1-digit multiplication with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for 3 and 4-digit by 1-digit multiplication

Most children need about a week of short sessions for 3 and 4-digit by 1-digit multiplication. This plan follows the order of the worksheets on this page:

When the plan for 3 and 4-digit by 1-digit multiplication is complete, move on to the 2-digit by 2-digit multiplication page. The whole sequence is on the multiplication worksheets page.