Multi-Digit Multiplication Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Multi-Digit Multiplication.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Multiplying numbers with two or more digits using the standard algorithm, partial products, or the area (box) model.

Think of a rectangle with sides 23 and 47. You can break it into smaller rectangles: $20 \times 40$ , $20 \times 7$ , $3 \times 40$ , and $3 \times 7$ , then add the pieces. That's partial products—the standard algorithm just organizes this neatly.

Read the full concept explanation →

How to Use These Examples

Read the first worked example with the solution open so the structure is clear.
Try the practice problems before revealing each solution.
Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Multi-digit multiplication is ordinary multiplication with place-value bookkeeping.

Common stuck point: The procedure for multi-digit multiplication is the easy part; the trap is forgetting the zero or place shift in a tens partial product. Asking "Can I split a factor by place value without changing the product?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Can I split a factor by place value without changing the product?

Worked Examples

Example 1

easy

Compute

47 \times 36

Answer

1692

First step

Multiply 47 by 6 (ones digit of 36):

47 \times 6 = 282

Full solution

2
Multiply 47 by 30 (tens digit of 36): $47 \times 30 = 1410$ .
3
Add the partial products: $282 + 1410 = 1692$ .

Multi-digit multiplication uses the standard algorithm: multiply by each digit of the second number (accounting for place value) and sum the partial products.

Example 2

medium

Compute

215 \times 14

Example 3

medium

Compute

36 \times 24

using partial products.

Example 4

medium

Use the area model to find

14 \times 23

Example 5

medium

Compute

25 \times 28

Example 6

hard

Compute

111 \times 111

Example 7

hard

Use the difference-of-squares trick to compute

98 \times 102

Example 8

challenge

Use the trick 'to square a two-digit number ending in 5, write

n(n+1)

followed by

25

' to find

75^2

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

medium

Compute

83 \times 57

Example 2

hard

Compute

246 \times 38

Example 3

easy

Compute

23 \times 4

Example 4

easy

Compute

34 \times 2

Example 5

easy

Compute

50 \times 6

Example 6

easy

Compute

12 \times 12

Example 7

easy

Compute

25 \times 4

Example 8

easy

Estimate

48 \times 21

by rounding.

Example 9

easy

Compute

7 \times 60

Example 10

easy

Compute

13 \times 5

Example 11

medium

Compute

34 \times 27

using partial products.

Example 12

medium

Compute

46 \times 18

Example 13

medium

Compute

123 \times 4

Example 14

medium

Compute

25 \times 16

using a friendly regrouping.

Example 15

medium

Compute

99 \times 7

using a near-round shortcut.

Example 16

medium

A theater has 38 rows with 24 seats each. How many seats total?

Example 17

medium

Compute

52 \times 50

Example 18

medium

Compute

63 \times 21

using partial products.

Example 19

medium

Compute

204 \times 3

Example 20

challenge

Compute

123 \times 45

using partial products, then verify by estimation.

Example 21

challenge

A warehouse stacks boxes 18 per layer in 26 layers, across 4 identical pallets. How many boxes total?

Example 22

challenge

Without full multiplication, find the ones digit of

47 \times 83

Example 23

easy

Compute

32 \times 3

Example 24

easy

Compute

15 \times 8

Example 25

easy

Compute

11 \times 11

Example 26

easy

Compute

9 \times 11

quickly.

Example 27

medium

Compute

72 \times 18

Example 28

medium

Compute

125 \times 8

Example 29

medium

Compute

58 \times 29

Example 30

medium

A classroom has

24

rows of

15

chairs. How many chairs total?

Example 31

medium

Compute

304 \times 7

Example 32

medium

A box holds

36

chocolates. How many chocolates are in

25

boxes?

Example 33

medium

Compute

145 \times 6

Example 34

medium

Compute

103 \times 12

Example 35

hard

Compute

234 \times 56

Example 36

hard

A garden has

42

rows of

35

plants. How many plants in total?

Example 37

hard

A factory produces

375

widgets per day. How many widgets in

4

weeks (28 days)?

Example 38

challenge

Find the units digit of

123 \times 456 \times 789

← Back to Multi-Digit Multiplication Formula Explained Practice Mode

Related Concepts

Multiplication Place Value Addition Long Division Multiplying Decimals

Background Knowledge

These ideas may be useful before you work through the harder examples.

multiplicationplace valueaddition