Change the numbers, layout and number of problems, then download a new PDF with its answer key.
2-digit by 2-digit multiplication multiplies by the ones and the tens separately, and adds the two results, which are called partial products. The five PDFs on this page have problems with two 2-digit numbers, on plain paper and on grid paper, 3-digit by 2-digit problems for grade 5, and story problems, and every sheet has an answer key. They follow standards 4.NBT.B.5 and 5.NBT.B.5 of the Common Core standards for grade 4 number and operations in base ten, and the notes below show the steps, the area model and the shortcuts.
Partial products. 204 + 680 = 884.
Quick answer: 2-digit by 2-digit multiplication multiplies two numbers from 10 to 99, such as 34 × 27 = 918, by finding four partial products and adding them. This page has 5 free printable worksheets with answer keys for grades 4 and 5. Updated October 2026.
How long multiplication works
To multiply two 2-digit numbers, multiply by the ones digit, then by the tens digit, and add the two results (called partial products). For 34 × 26:
34 × 6 = 204.
34 × 20 = 680. Write a 0 in the ones place first, then 34 × 2 = 68 in front of it.
Add: 204 + 680 = 884.
The answer keys on this page show both partial products and the final answer, so children can find exactly where a mistake happened.
What is on this page
Two sets of 2-digit by 2-digit problems.
Grid paper, which keeps every digit and partial product in the right column.
3-digit by 2-digit problems for grade 5.
Story problems with 2-digit numbers.
2-digit by 2-digit multiplication worksheets: what is in the set
There are 5 2-digit by 2-digit multiplication worksheets on this page, and every one has an answer key except for any cut-out games. Two sheets are plain 2-digit by 2-digit problems, one is on grid paper, one has 3-digit by 2-digit problems, and one has story problems.
Worksheet
What children do
Standard
2-Digit by 2-Digit Multiplication (Set A)
12 problems with space for two partial products.
4.NBT.B.5
2-Digit by 2-Digit Multiplication (Set B)
Another 12 long multiplication problems.
4.NBT.B.5
Grid Paper Long Multiplication
9 problems on grid paper with room for every step.
4.NBT.B.5
3-Digit by 2-Digit Multiplication
9 problems for grade 5.
4.NBT.B.5
2-Digit by 2-Digit Story Problems
Six story problems with two 2-digit numbers.
4.NBT.B.5
2 digit by 2 digit multiplication worksheets: partial products
The 2 digit by 2 digit multiplication worksheets use the method of partial products. The second number is split into ones and tens, the first number is multiplied by each, and the two results are added. Wikipedia’s article on multiplication algorithms describes this method, and others. These tables show the three steps for four problems. First, 34 × 26:
Step
Calculation
Result
Multiply by the ones digit 6
34 × 6
204
Multiply by the tens digit 2 (write a 0 first)
34 × 20
680
Add the partial products
204 + 680
884
Second, 57 × 43:
Step
Calculation
Result
Multiply by the ones digit 3
57 × 3
171
Multiply by the tens digit 4 (write a 0 first)
57 × 40
2,280
Add the partial products
171 + 2,280
2,451
Third, 48 × 15. The second partial product is just 48 × 10, so it is easy:
Step
Calculation
Result
Multiply by the ones digit 5
48 × 5
240
Multiply by the tens digit 1 (write a 0 first)
48 × 10
480
Add the partial products
240 + 480
720
Fourth, a 3-digit number, 235 × 46, as on the grade 5 sheet:
Step
Calculation
Result
Multiply by the ones digit 6
235 × 6
1,410
Multiply by the tens digit 4 (write a 0 first)
235 × 40
9,400
Add the partial products
1,410 + 9,400
10,810
Double digit multiplication worksheets: the area model
The double digit multiplication worksheets are easier to understand with the area model, which draws a rectangle that is split into four boxes. For 34 × 26, the sides are 30 + 4 and 20 + 6, so the boxes are 30 × 20, 4 × 20, 30 × 6 and 4 × 6. This table shows five problems with their four products:
Problem
Tens × tens
Ones × tens
Tens × ones
Ones × ones
Sum of the four
34 × 26
30 × 20 = 600
4 × 20 = 80
30 × 6 = 180
4 × 6 = 24
884
57 × 43
50 × 40 = 2000
7 × 40 = 280
50 × 3 = 150
7 × 3 = 21
2,451
48 × 15
40 × 10 = 400
8 × 10 = 80
40 × 5 = 200
8 × 5 = 40
720
62 × 37
60 × 30 = 1800
2 × 30 = 60
60 × 7 = 420
2 × 7 = 14
2,294
85 × 29
80 × 20 = 1600
5 × 20 = 100
80 × 9 = 720
5 × 9 = 45
2,465
The two products in the middle of each row are the two partial products of the standard method, with the tens products split in two. For 34 × 26, 80 + 600 = 680, which is the second line of the standard method, and 180 + 24 = 204, which is the first. A child who draws the area model once or twice sees where the zero comes from.
Long multiplication worksheets: how big is the product?
The long multiplication worksheets have products of three or four digits. A product of two 2-digit numbers is at least 100 and at most 9,801. This table counts the 8,100 pairs of 2-digit numbers by the size of the product:
Size of the product
Pairs of 2-digit numbers
Share of the 8,100 pairs
Example
3 digits (100 to 999)
1,490
18.4%
12 × 34 = 408
4 digits (1,000 to 9,801)
6,610
81.6%
57 × 43 = 2,451
Smallest product
1
—
10 × 10 = 100
Biggest product
1
—
99 × 99 = 9,801
More than four pairs in five give a four-digit product, so most of the answers on the worksheets have four digits. The estimate tells children which to expect: if both numbers are above 32, the product is above 1,000, since 32 × 32 = 1,024.
Multi digit multiplication: estimating by rounding both numbers
In multi digit multiplication, the best check is an estimate. To estimate, round both numbers to the nearest ten, and multiply. This table shows six problems, with the estimate and the exact product:
Problem
Round both numbers to the nearest ten
Estimate
Exact product
Difference
34 × 26
30 × 30
900
884
16
57 × 43
60 × 40
2,400
2,451
51
48 × 15
50 × 20
1,000
720
280
62 × 37
60 × 40
2,400
2,294
106
85 × 29
90 × 30
2,700
2,465
235
91 × 18
90 × 20
1,800
1,638
162
The estimate is not exact, and it can be far from the answer when both numbers are rounded the same way, as in 85 × 29. It is good enough to tell that the answer has the right number of digits and that no column is out of place. The estimating with rounding page has more about estimating.
5th grade multiplication: shortcuts and mental math
In 5th grade multiplication, children learn that the standard algorithm is not the only way. Some multipliers have shortcuts that save time, and they show how the numbers are linked. This table shows six, with an example of each:
The area model. Four boxes: 600, 80, 180 and 24.
Multiplier
Shortcut
Example
× 10
write a zero at the end
34 × 10 = 340
× 11
add the digits and put the sum between them (when it is under 10)
34 × 11 = 374 (3, 3 + 4, 4)
× 5
multiply by 10, then halve
48 × 5 = 480 ÷ 2 = 240
× 25
multiply by 100, then divide by 4
48 × 25 = 4,800 ÷ 4 = 1,200
× 9
multiply by 10, then subtract the number
34 × 9 = 340 − 34 = 306
× 15
multiply by 10, then add half of that
48 × 15 = 480 + 240 = 720
Each shortcut uses place value. To multiply by 5, children multiply by 10 and halve, since 5 is half of 10. To multiply by 25, they multiply by 100 and divide by 4, since 25 is a quarter of 100. The times tables worksheets page has the facts that these use.
Comparing the methods of multiplication
There are several ways to multiply two 2-digit numbers, and each is useful for something. This table compares five of them:
Method
What it does
Good for
Standard algorithm
two partial products, with a zero on the second line
fast, and used in grade 5 and beyond
Area model
four boxes for tens and ones
shows why the method works
Partial products
four products written in a list
few carries, and easy to check
Lattice (grid) method
a grid with diagonals for carries
neat, but it hides place value
Mental math
split one number and use the shortcuts
quick for easy numbers
The worksheets on this page use the standard algorithm, since that is the method that the standard 5.NBT.B.5 asks children to know, and the answer keys show both partial products. The area model is a good way to understand the algorithm first. The 2-digit by 1-digit multiplication and 3 and 4-digit by 1-digit multiplication pages cover the cases with one-digit multipliers.
Common mistakes with 2-digit by 2-digit multiplication
The most common mistake is to leave out the zero on the second line. This table shows five mistakes, what went wrong and the fix:
What the child writes or says
What went wrong
The fix
34 × 26 = 204 + 68 = 272
leaves out the placeholder zero on the second line
34 × 20 = 680, so the second line is 680, not 68
34 × 26 = 884, but the digits are in the wrong columns
writes the partial products out of line
use grid paper, and keep the ones under the ones
Multiplies 34 × 2 for the tens and writes 68
forgets that the 2 is 20
say “34 times 20”, and write the zero first
Adds the carries to the next digit before multiplying
carries mixed up with the multiplication
multiply first, then add the carry
57 × 43 = 2,451, but the child doubts it
does not estimate
estimate 60 × 40 = 2,400, so 2,451 is reasonable
2-digit by 2-digit multiplication word problems
Story problems use rows, trays and boxes. Ask children to estimate with rounded numbers, then multiply, and then compare the two:
Word problem
Working
Answer
A theater has 34 rows with 26 seats in each row. How many seats are there?
34 × 26
884 seats
A school buys 57 boxes of 43 crayons. How many crayons is that?
57 × 43
2,451 crayons
A baker makes 48 trays of 15 rolls. How many rolls is that?
48 × 15
720 rolls
A bus company runs 62 buses, and each holds 37 people. How many people can all the buses hold?
62 × 37
2,294 people
A garden has 85 rows of 29 plants. How many plants are in the garden?
85 × 29
2,465 plants
A warehouse has 235 shelves with 46 boxes on each. How many boxes is that?
235 × 46
10,810 boxes
Games and activities for 2-digit by 2-digit multiplication
Children learn 2-digit by 2-digit multiplication best when they play with it. These games use things that are found at home or in a classroom:
Area model draw: draw the four boxes for a problem on grid paper, and add the parts
Dice multiplication: roll four dice for two 2-digit numbers, and multiply them
Estimate first: estimate each problem, and see who is closest to the exact answer
Find the zero: give a worked example with the zero missing, and ask children to find the mistake
Shortcut hunt: find the problems in a list that can be done with a shortcut
Multiplication bingo: a bingo card with products, and calling cards with problems
Extra support and extra challenge with 2-digit by 2-digit multiplication
For children who need more support: make sure that 2-digit by 1-digit multiplication is secure, and use the area model. Write the zero on the second line before multiplying. Use grid paper, one digit to a box, and mark the ones column. Check every answer with an estimate, and use the answer key to see both partial products.
For children who need more challenge: ask for the multiplication of two numbers that gives the product 1,000 or just over, for 99 × 99 using 100 × 99 − 99, and for a 3-digit by 2-digit problem that has a product with five digits. Try to find a shortcut for 48 × 25 and 34 × 11.
How to tell that a child is ready to move on from 2-digit by 2-digit multiplication
Before moving on from 2-digit by 2-digit multiplication, check that the child can do all four of these things:
Estimate first. 30 × 30 = 900.
The child multiplies by the ones, and then by the tens with a zero.
The child adds the two partial products.
The child estimates and checks the product.
The child multiplies a 3-digit number by a 2-digit number.
When all four are true, 2-digit by 2-digit multiplication is secure, so the child is ready for grade 5 multiplication with larger numbers, or for the long division 3-digit by 1-digit page.
A 20-minute lesson on 2-digit by 2-digit multiplication
A short lesson is the best way to introduce 2-digit by 2-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:
Minutes
Activity
What to say or ask
0 to 3
Draw the area model for 34 × 26
What are the four boxes?
3 to 8
Find the four products and add them
What do we get?
8 to 13
Write 34 × 26 in columns with two partial products
Why is there a zero on the second line?
13 to 18
Estimate 34 × 26 by rounding to 30 × 30
Is 884 close to 900?
18 to 20
Start a worksheet and check one answer
Check with an estimate.
Where 2-digit by 2-digit multiplication fits across the grades
No skill stands alone. This table shows what children learn before and after 2-digit by 2-digit multiplication, with the standard that goes with each step:
This page is the last of the whole-number multiplication pages. The whole sequence is on the multiplication worksheets page.
Helping at home with 2-digit by 2-digit multiplication
Parents do not need to be experts to help with 2-digit by 2-digit multiplication. These suggestions work well, and each takes only a few minutes:
Ask the child to explain why there is a zero on the second line.
Use real numbers, such as the seats in a theater.
Ask for an estimate first, and compare it with the answer.
Use grid paper, one digit to a box.
Check each answer by dividing the product by one of the numbers.
How to check progress in 2-digit by 2-digit multiplication
A teacher or parent can check progress in 2-digit by 2-digit multiplication with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:
What you see
What it means
What to do next
The child leaves out the zero on the second line
The tens digit is being treated as ones
Write the zero before multiplying, and say “times 20”
The child gets 9 of 10 right in every set
2-digit by 2-digit multiplication is secure
Move on to larger numbers and decimals
The child makes mistakes in the partial products
The times tables or the carries are not yet secure
Practice 2-digit by 1-digit multiplication first
A five-day plan for 2-digit by 2-digit multiplication
Most children need about a week of short sessions for 2-digit by 2-digit multiplication. This plan follows the order of the worksheets on this page:
Day
What to do
Practice
Day 1
Multiply by multiples of 10, and use the area model
Grid paper
Day 2
Multiply by the ones, then by the tens, with the zero
Set A
Day 3
Add the partial products, and check with an estimate
Set B
Day 4
Multiply a 3-digit number by a 2-digit number
3-digit by 2-digit
Day 5
Story problems with two 2-digit numbers
Story problems
When the plan for 2-digit by 2-digit multiplication is complete, the child is ready for grade 5 multiplication. The whole sequence is on the multiplication worksheets page.
5th grade multiplication worksheets and multiplication worksheets grade 5
This page is also searched as 5th grade multiplication worksheets, multiplication worksheets grade 5, multiplication for 5th graders worksheet, multiplication for 5th graders, multiplication for fifth graders, multiplication worksheets for 5th graders, grade 5 multiplication worksheets, multiplication 5th grade worksheets and multiplication worksheet 5th grade. All of them are these free PDFs, with answer keys. For multiplication practice for 5th graders that goes beyond this page, the multiplication worksheets hub has the 3-digit sets, and the 5th grade math page has fractions and decimals.
Multiplication and division worksheets grade 5
Many families want multiplication and division worksheets grade 5 or 5th grade multiplication and division worksheets in the same set. Multiplication and division are linked: use the division worksheets page to check a product by dividing it, and the long division worksheets for 2-digit divisors. We counted all 8,100 problems from 10 × 10 to 99 × 99, and 6,610 of them (82%) have a product of 1,000 or more.
Frequently asked questions
6 quick answers
Why do you put a zero on the second line?
The second line multiplies by the tens digit, so the result is tens. The zero holds the ones place: 34 × 20 = 680, not 68.
What grade learns 2-digit by 2-digit multiplication?
Grade 4 multiplies two 2-digit numbers (4.NBT.B.5), and grade 5 uses the standard algorithm fluently with larger numbers (5.NBT.B.5).
How do you multiply two 2-digit numbers?
Multiply the first number by the ones digit of the second, then by the tens digit with a zero written first, and add the two results. For 34 × 26: 34 × 6 = 204, 34 × 20 = 680, and 204 + 680 = 884.
Why do you put a zero on the second line?
Because the second line multiplies by the tens digit, so the result is in tens. The zero holds the ones place: 34 × 20 = 680, not 68.
What grade learns 2-digit by 2-digit multiplication?
Grade 4 multiplies two 2-digit numbers (4.NBT.B.5), and grade 5 uses the standard algorithm fluently with larger numbers (5.NBT.B.5).
Where can I download free 5th grade multiplication worksheets?
Open any worksheet in the gallery above, choose US Letter or A4, then print or save the PDF. They are free and each has an answer key.
