2-digit by 2-digit multiplication, step by step

To multiply two 2-digit numbers, split both into tens and ones and multiply every part by every part. The area model shows four partial products; the standard method writes them as two rows, with a placeholder zero in the second. 34 × 26 = 680 + 204 = 884. This page shows both, with a tool that steps through any problem.

The big idea: four parts

34 × 26 is (30 + 4) × (20 + 6). That makes four smaller multiplications: 30 × 20, 4 × 20, 30 × 6 and 4 × 6. The area model draws them as four rectangles.

3030 × 20 = 60030 × 6 = 18044 × 20 = 804 × 6 = 24206
600 + 80 + 180 + 24 = 884 (not to scale).

The standard method

  1. Multiply by the ones digit (6): 34 × 6 = 204. This is row 1.
  2. Write a 0 in the ones place of row 2. You are now multiplying by the 2 tens, so everything is worth ten times more.
  3. Multiply by the tens digit (2): 34 × 2 = 68, written after the 0: 680.
  4. Add the rows: 204 + 680 = 884.

Long multiplication step by step

Type any 2-digit × 2-digit problem. Each row and the final addition are shown.

Worked examples

23 × 12

23 × 2 = 46; 23 × 10 = 230; 46 + 230 = 276.

47 × 35

47 × 5 = 235; 47 × 30 = 1,410; 235 + 1,410 = 1,645.

99 × 99

99 × 9 = 891; 99 × 90 = 8,910; total 9,801. Or 100 × 99 − 99 = 9,801.

Common mistakes

34 × 26 = 272Forgot the placeholder 0 in the second row (204 + 68).Fix: the second row is tens, so start it with a 0.
34 × 26 = 624Multiplied only tens by tens and ones by ones (30 × 20 + 4 × 6).Fix: there are four parts, not two.
Carried digits mixed between rowsUsed row 1’s carries in row 2.Fix: cross out carries before starting the next row.
Answer far from the estimate34 × 26 is about 30 × 25 = 750.Fix: estimate first; 8,840 or 272 would stand out.

How to teach it at home

Grid on graph paper

Draw a 34 by 26 rectangle and split it into four parts. Count the big parts by multiplying.

Real totals

26 students each paying $34 for a trip: what is the total?

Check with a calculator

After working it out, check on a calculator. Find the row with the mistake if it differs.

By grade

Worksheets and practice

2-digit by 2-digit multiplication worksheet, page 1

2-digit by 2-digit multiplication worksheet: printable PDF with an answer key. · Make a fresh test

All multiplication

Last reviewed

Questions parents ask

How do you multiply 2-digit by 2-digit numbers?

Multiply the top number by the ones digit, then by the tens digit (with a 0 placeholder), and add the two rows. 34 × 26 = 204 + 680 = 884.

Why do you put a zero in the second row?

Because the second row multiplies by the tens digit, which is worth ten times more. The 0 shifts the row one place left.

What is the box method?

Another name for the area model: draw a grid, multiply each part, and add the four boxes.

How do you check 2-digit multiplication?

Estimate by rounding (34 × 26 is about 30 × 25 = 750) or swap the numbers and multiply again.

What grade learns 2-digit by 2-digit multiplication?

Grade 4 with models (4.NBT.B.5); grade 5 with the standard algorithm (5.NBT.B.5).