Browse

Multi-Digit Multiplication Worksheets

31 free PDFsUS Letter PDFsAnswer key includedNo login

Multiply by 10, 100 and 1,000, then 2-, 3- and 4-digit numbers by 1 digit and 2-digit by 2-digit, with area models, partial products and estimates.

Download the multi-digit multiplication worksheets

Multiply by 10, 100 and 1,000

Use a basic fact and place value: 7 × 6,000 is 7 × 6 thousands, 42 thousands.

Multiply by a 1-digit number

2-, 3- and 4-digit numbers times a 1-digit number in columns, with a small box for each regrouped digit.

Multiply 2-digit by 2-digit numbers

Multiply by the ones, then by the tens with a grey 0 holding the ones place, then add the two rows.

Area model and partial products

See the place value parts of a product: a rectangle split by tens and ones, and the same parts written as partial products.

Estimate and check

Round to estimate a product, and find the mistake in worked problems.

Print at 100% (actual size) for the cleanest tracing lines.

About these multi-digit multiplication worksheets

In 4th grade, multiplication grows from facts to big numbers: up to four digits times one digit (4,286 × 7) and two digits times two digits (46 × 38). Every method rests on place value. 46 × 38 is really 40 × 30, 40 × 8, 6 × 30 and 6 × 8 added together, and once a child sees that, the written method stops being a list of rules.

These pages build the skill in the order it makes sense. First multiply by 10, 100 and 1,000 and by multiples of them (6 × 300 = 1,800). Then show the place value parts with an area model, write them as partial products, and finally use the column method, with small boxes for the regrouped digits and a grey 0 to hold the ones place in the second row of 2-digit by 2-digit problems.

Most pages come as Sheet A, B and C with new problems at the same level. Every page has an answer key on page 2 that shows the regrouped digits and both rows of the work, so you can see exactly where a mistake happened. The estimate and find-the-mistake pages teach children to check their own answers.

Standards

  • CCSS.MATH.CONTENT.4.NBT.B.5Multiply 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.
  • CCSS.MATH.CONTENT.4.NBT.A.1Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

How to use them

  1. Start with Multiply by 10, 100 and 1,000 so the zeros make sense before the long problems.
  2. Use the area model pages next. Drawing the rectangle shows why 23 × 6 is 20 × 6 plus 3 × 6.
  3. Move to partial products, then the column method. Children who know where each partial product comes from make far fewer slips.
  4. Give 2-digit by 1-digit before 3- and 4-digit by 1-digit, and those before 2-digit by 2-digit.
  5. Finish a unit with Estimate, Then Multiply and the find-the-mistake pages, and ask children to explain each mistake out loud.

Teaching tips

  • Say the place value out loud: in 46 × 38, the 4 is 40 and the 3 is 30.
  • In the second row of 2-digit by 2-digit, the 0 in the ones place is not optional. Leaving it out is the most common mistake.
  • Add a regrouped digit after multiplying, not before. The find-the-mistake pages show both errors.
  • Estimate first. 487 × 6 is about 500 × 6 = 3,000, so 2,922 is reasonable and 29,220 is not.
  • If facts are slow, practice them alongside. Long multiplication uses the same facts again and again.

Questions teachers and parents ask

What multiplication do 4th graders learn?

Fourth graders multiply up to a 4-digit number by a 1-digit number and multiply two 2-digit numbers, using place value strategies such as area models and partial products, and explain their work.

What is the area model for multiplication?

It is a rectangle split into parts by place value. For 23 × 6, one part is 20 × 6 = 120 and the other is 3 × 6 = 18, and the product is 120 + 18 = 138.

What are partial products?

Partial products are the products of each place value part. For 34 × 12 they are 4 × 2, 30 × 2, 4 × 10 and 30 × 10, which add up to 408.

Why is there a 0 in the second row?

In 2-digit by 2-digit multiplication, the second row multiplies by the tens digit, so its answer is tens. The 0 keeps the ones place empty.