Multi-Digit Addition and Subtraction Examples in Math

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

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

Concept Recap

Adding and subtracting numbers with three or more digits using the standard algorithm, which involves regrouping (carrying) in addition and borrowing in subtraction.

Imagine stacking blocks in columns for ones, tens, and hundreds. When the ones column adds up to more than 9, you bundle 10 ones into 1 ten and carry it over—just like exchanging 10 pennies for a dime.

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 addition and subtraction stack numbers by place value, regrouping a bundle of 10 up (carry) or unbundling one down (borrow) as columns overflow or fall short.

Common stuck point: The procedure for multi-digit addition and subtraction is the easy part; the trap is misaligning columns by left-justifying. Asking "Am I stacking large numbers by place value and regrouping by tens to add or subtract?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Am I stacking large numbers by place value and regrouping by tens to add or subtract?

Worked Examples

Example 1

easy
Calculate 347+256347 + 256 using column addition.

Answer

603

First step

1
Line up by place value: ones: 7+6=137+6=13, write 3, carry 1.

Full solution

  1. 2
    Tens: 4+5+1=104+5+1=10, write 0, carry 1.
  2. 3
    Hundreds: 3+2+1=63+2+1=6.
  3. 4
    Result: 603.
Column addition works right to left: ones, then tens, then hundreds, carrying when a column exceeds 9.

Example 2

medium
Calculate 803−457803 - 457 using column subtraction with borrowing.

Example 3

medium
Add three numbers: 458+267+134458 + 267 + 134.

Example 4

medium
Find the missing digit: 4□7+285=7524 \square 7 + 285 = 752.

Example 5

hard
Two numbers differ by 245245 and sum to 10031003. Find them.

Example 6

challenge
Solve the cryptarithm ABCD‾−DCBA‾=6174\overline{ABCD} - \overline{DCBA} = 6174 where digits are distinct (Kaprekar's constant). One valid value is A=7,B=6,C=4,D=1A=7, B=6, C=4, D=1: verify.

Practice Problems

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

Example 1

easy
Calculate 528+364528 + 364.

Example 2

medium
A school library has 1,250 books. They donate 387 books. How many books remain?

Example 3

easy
Add: 234+152234 + 152.

Example 4

easy
Add: 146+27146 + 27.

Example 5

easy
Subtract: 578−234578 - 234.

Example 6

easy
Subtract: 63−2863 - 28.

Example 7

easy
Add: 305+198305 + 198.

Example 8

easy
Subtract: 450−120450 - 120.

Example 9

easy
Add: 1200+3451200 + 345.

Example 10

easy
Subtract: 700−200700 - 200.

Example 11

medium
Add: 4867+29544867 + 2954.

Example 12

medium
Subtract: 400−167400 - 167.

Example 13

medium
Subtract: 5003−17485003 - 1748.

Example 14

medium
Find the missing number: 385+□=612385 + \square = 612.

Example 15

medium
A theater seats 12501250 people. 874874 tickets are sold. How many seats remain?

Example 16

medium
Add three numbers: 128+467+295128 + 467 + 295.

Example 17

medium
Subtract: 8000−34568000 - 3456.

Example 18

medium
Estimate then compute 4980+30154980 + 3015, and state the exact sum.

Example 19

medium
Subtract: 6004−28766004 - 2876.

Example 20

challenge
A number minus 12671267 equals 34583458. Then 20002000 is added. What is the final value?

Example 21

challenge
Using each of the digits 1,2,3,41,2,3,4 once, form two two-digit numbers whose SUM is as large as possible. What is that sum?

Example 22

challenge
In the puzzle A7‾+2B‾=92\overline{A7} + \overline{2B} = 92 where A,BA,B are single digits, find AA and BB.

Example 23

easy
Add: 456+321456 + 321.

Example 24

easy
Subtract: 865−432865 - 432.

Example 25

easy
Subtract: 92−4792 - 47.

Example 26

easy
A bakery made 128128 cupcakes on Monday and 9595 on Tuesday. How many cupcakes total?

Example 27

easy
Subtract: 500−250500 - 250.

Example 28

medium
Add: 3654+27893654 + 2789.

Example 29

medium
Subtract: 7000−28497000 - 2849.

Example 30

medium
Find the missing number: □+478=1024\square + 478 = 1024.

Example 31

medium
A school store had $2,500\$2,500 at the start of the day. By closing time they had taken in $1,387\$1,387 and paid out $845\$845. How much money do they have at closing?

Example 32

medium
Subtract: 1000−11000 - 1.

Example 33

medium
A train holds 1,2481,248 passengers. After a stop, 367367 get off and 185185 get on. How many passengers are now on the train?

Example 34

medium
Subtract: 10000−456710000 - 4567.

Example 35

medium
Add four numbers: 234+567+123+456234 + 567 + 123 + 456.

Example 36

hard
A bus carries 5858 students. Three buses leave the school. How many students go on the trip if no bus is fully loaded — bus 1 has 5252, bus 2 has 4848, bus 3 has 5757 students?

Example 37

hard
What is the largest 4-digit number you can make using each of 0,3,5,80, 3, 5, 8 exactly once? What is the smallest 4-digit number? Find their difference.

Example 38

hard
Find AA and BB digits in the puzzle: A48‾+2B5‾=803\overline{A48} + \overline{2B5} = 803.

Example 39

hard
At the start of the year, a charity had \$15,420. They received \$8,365 in donations and spent \$11,278. How much do they have at the end of the year?

Example 40

challenge
Three consecutive integers add to 1,5031,503. What is the smallest of them?
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Background Knowledge

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

additionsubtractionplace value