How do you multiply two digit numbers?

Split each number into tens and ones, multiply every part by every part, and add. For 23 × 15: 20 × 10 = 200, 3 × 10 = 30, 20 × 5 = 100 and 3 × 5 = 15, so 23 × 15 = 345.

How do you multiply a 2 digit number by a 1 digit number?

Multiply the tens and the ones separately, then add. For 74 × 6: 70 × 6 = 420 and 4 × 6 = 24, so 74 × 6 = 444.

What is the area model for two digit multiplication?

A rectangle split into four boxes by place value. For 52 × 36, the boxes are 50 × 30 = 1500, 2 × 30 = 60, 50 × 6 = 300 and 2 × 6 = 12, which add up to 1872.

What is the difference between partial products and the standard algorithm?

Partial products writes all four pieces separately. The standard algorithm combines them into two rows, one for the ones digit and one for the tens digit. Both give the same answer.

What grade learns 2 digit by 2 digit multiplication?

In the US Common Core, grade 4, usually with area models and partial products (4.NBT.B.5), then the standard algorithm in grade 5 (5.NBT.B.5). In England, long multiplication by a two-digit number begins in Year 5.

Is there a free two digit multiplication worksheet with answers?

Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Grades 3 to 5 (Years 3 to 5 in England)

Two digit multiplication: 2 digit by 1 digit and 2 digit by 2 digit

Here is how to multiply two digit numbers, starting with 2 digit by 1 digit and building up to 2 digit by 2 digit with the area model, partial products and the standard algorithm. Try the free practice below, then print a fresh two digit multiplication worksheet with an answer key.

The method, step by step

Split each two digit number into tens and ones, such as 37 = 30 + 7.
Multiply every part of one number by every part of the other.
Keep the zeros: 30 × 20 is 3 × 2 = 6 with two zeros on the end, so 600.
Add the partial products to get the answer.
Check with an estimate, rounding each number to the nearest ten.

CCSS 3.NBT.A.3CCSS 4.NBT.B.5England: Y3 Multiplication and divisionEngland: Y4 Multiplication and divisionEngland: Y5 Multiplication and division

Worked example

37 × 24 = ?

Split the numbers: 37 = 30 + 7 and 24 = 20 + 4.
Multiply by the 20: 30 × 20 = 600 and 7 × 20 = 140.
Multiply by the 4: 30 × 4 = 120 and 7 × 4 = 28.
Add the four partial products: 600 + 140 + 120 + 28 = 888.
Estimate: 40 × 20 = 800, so 888 is sensible. 37 × 24 = 888.

Practice now

Question 1 of 100 correct

Use long multiplication: 88 × 46

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Start with 2 digit by 1 digit

Multiplying a two digit number by a one digit number uses one idea: split the two digit number into tens and ones, multiply each part, then add. For 58 × 6, work out 50 × 6 = 300 and 8 × 6 = 48, so 58 × 6 = 348. This works because six lots of 58 is the same as six lots of 50 plus six lots of 8.

The tens part is a times table fact with a zero on the end. 50 × 6 is 5 × 6 = 30 tens, which is 300. If that step feels shaky, practice multiplying tens first: 40 × 7 = 280, 90 × 3 = 270 and 60 × 8 = 480.

23 × 4 = 80 + 12 = 92.
67 × 5 = 300 + 35 = 335.
89 × 7 = 560 + 63 = 623.

2 digit by 2 digit with the area model

For 2 digit by 2 digit multiplication, split both numbers. For 52 × 36, draw a rectangle and label one side 50 and 2, the other 30 and 6. That cuts it into four boxes, and each box holds one partial product: 50 × 30 = 1500, 2 × 30 = 60, 50 × 6 = 300 and 2 × 6 = 12. Add the four boxes: 1500 + 60 + 300 + 12 = 1872.

The picture shows why there are four pieces, not two. A common slip is to multiply only tens by tens and ones by ones: 50 × 30 + 2 × 6 = 1512, which leaves out the two middle boxes.

Partial products

Partial products is the area model written as a list, without the drawing. Write the problem in columns, list each product underneath, lined up by place value, then add. For 63 × 45:

3 × 5 = 15
60 × 5 = 300
3 × 40 = 120
60 × 40 = 2400
Total: 15 + 300 + 120 + 2400 = 2835.

The standard algorithm

The standard algorithm, called long multiplication in England, packs the partial products into two rows. For 63 × 45, the first row is 63 × 5 = 315, which holds the 15 and the 300. The second row is 63 × 40 = 2520, which holds the 120 and the 2400. Add the rows: 315 + 2520 = 2835. The second row starts with a 0 because you are multiplying by 4 tens, not by 4.

Each row has its own carrying. In 63 × 5, 3 × 5 = 15, so write 5 and carry 1. Then 6 × 5 = 30, plus the carried 1 makes 31, so the row reads 315. Cross out those carries before starting the second row. For three and four digit numbers, see the multi-digit multiplication page.

How it is taught in school

In the US, Common Core grade 3 multiplies one digit numbers by multiples of 10, such as 9 × 80 (3.NBT.A.3). Grade 4 multiplies numbers of up to four digits by a one digit number and multiplies two two-digit numbers, using place value strategies and explaining them with equations, arrays or area models (4.NBT.B.5). Grade 5 multiplies multi-digit whole numbers fluently with the standard algorithm (5.NBT.B.5).

In England, Year 3 pupils multiply two-digit numbers by one-digit numbers, using mental methods and then formal written methods. Year 4 use a formal written layout for two-digit and three-digit numbers times a one-digit number, and Year 5 learn long multiplication for two-digit numbers. The grid method used in many English primary schools is the area model drawn as a table.

How parents can help

Make the times tables solid first. Every two digit multiplication is built from single facts like 7 × 4.
Practice multiplying tens out loud: 30 × 6, 70 × 8, 40 × 50.
Draw the area model together on squared paper, even if your child prefers the standard algorithm. It shows where every number comes from.
Ask for an estimate before every answer, rounding each number to the nearest ten.
Print a fresh worksheet, let your child mark it with the answer key, and read the worked steps together for any they missed.

Common mistakes

Multiplying only tens by tens and ones by ones. 52 × 36 is not 1500 + 12 = 1512; the middle pieces, 2 × 30 and 50 × 6, are missing. The answer is 1872.
Losing a zero: writing 40 × 6 as 24 instead of 240.
Forgetting the 0 at the start of the second row. In 63 × 45 the second row is 63 × 40 = 2520, not 63 × 4 = 252.
Adding a carried digit before multiplying instead of after. In 63 × 5 it is 6 × 5 + 1 = 31, not (6 + 1) × 5 = 35.
Lining up partial products badly, so tens get added to hundreds. Squared paper keeps every column straight.
Skipping the estimate. 37 × 24 is about 40 × 20 = 800, so an answer like 188 or 8880 is clearly wrong.

Questions people ask

How do you multiply two digit numbers?: Split each number into tens and ones, multiply every part by every part, and add. For 23 × 15: 20 × 10 = 200, 3 × 10 = 30, 20 × 5 = 100 and 3 × 5 = 15, so 23 × 15 = 345.
How do you multiply a 2 digit number by a 1 digit number?: Multiply the tens and the ones separately, then add. For 74 × 6: 70 × 6 = 420 and 4 × 6 = 24, so 74 × 6 = 444.
What is the area model for two digit multiplication?: A rectangle split into four boxes by place value. For 52 × 36, the boxes are 50 × 30 = 1500, 2 × 30 = 60, 50 × 6 = 300 and 2 × 6 = 12, which add up to 1872.
What is the difference between partial products and the standard algorithm?: Partial products writes all four pieces separately. The standard algorithm combines them into two rows, one for the ones digit and one for the tens digit. Both give the same answer.
What grade learns 2 digit by 2 digit multiplication?: In the US Common Core, grade 4, usually with area models and partial products (4.NBT.B.5), then the standard algorithm in grade 5 (5.NBT.B.5). In England, long multiplication by a two-digit number begins in Year 5.
Is there a free two digit multiplication worksheet with answers?: Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated November 4, 2026.

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