3-Digit Subtraction

3-digit subtraction involves subtracting one three-digit number from another, where each number lies between 100 and 999. It is useful in everyday situations such as finding the difference between quantities, calculating change or comparing values. In 3-digit subtraction, the number from which the other number is taken away is called the minuend, and the number being subtracted is called the subtrahend. The result is known as difference. 
 

To subtract 3-digit numbers, we follow the place-values of the digits. To subtract accurately, we start with the ones place, then the tens and finally the hundreds. If the digit in the top number is smaller than the digit below it in any place, we borrow from the next higher place value to make subtraction possible. 
 

• Ones place: In ones place, the ones digit is subtracted. If needed, borrow one ten, which will become 10 ones. 

• Tens place: Here, the tens digits are subtracted. Borrowing from the hundreds place is done, if the top digit is smaller. 

• Hundreds place: Here, the hundreds digits are subtracted, including any borrowed value from earlier steps. 

3-digit subtraction with regrouping, also known as borrowing, happens when we subtract one three-digit number from another and need to borrow from the next higher place value.

When the digit on top of a column is smaller than the digit below it, we regroup by borrowing from the next higher place value, such as the tens or hundreds place, to complete the subtraction.

Example: Let’s subtract 512 − 278

   5 1 2
– 2 7 8

 ______

Step 1: Subtract the Ones Place

Ones column: 2 − 8 → 2 is smaller than 8, so we need to borrow.

Borrow 1 ten from the tens place: 1 ten = 10 ones.

Update digits: Tens place becomes 0, Ones place becomes 12.

Subtract: 12 − 8 = 4

Step 2: Tens column: 0 − 7 → 0 is smaller than 7, so borrow 1 hundred from the hundreds place.

Update digits: Hundreds place becomes 4, Tens place becomes 10.

Subtract: 10 − 7 = 3

Step 3: Hundreds column: 4 − 2 = 2

Final answer:

   5 1 2
– 2 7 8

_________

   2 3 4

3-digit subtraction without regrouping means we are subtracting one 3-digit number from another, and we do not need to borrow at all.

In this case, every digit in the top number is bigger than or equal to the digit below. This allows subtraction without the need for borrowing.

Example: Let’s subtract 864 – 432
   8 6 4
– 4 3 2

Step 1: Subtract the digits in the ones place
4 – 2 = 2

Step 2: Repeat the same for the digits in the tens place

6 – 3 = 3
 

Step 3: Subtract the digits in the hundreds place

8 – 4 = 4

Final Answer:

   864

– 432 

______

   432
 

3-digit subtraction is very easy to learn with right techniques and practices. These tips and tricks will help students to build confidence and accuracy, while support parents and teachers to guide students in the learning process. 
 

• Line up numbers correctly: Students should learn to write the minuend above the subtrahend, and to align the hundreds under the hundreds, tens under the tens and ones under the ones. Checking it beforehand to subtracting will prevent place-value errors. 

• Work from right to left: Students should always remember that 3-digit subtraction always starts at the ones place, then moves to the tens place and finally the hundreds. Tracking this order will keep your work logical. 

• Check with addition: After finding the difference, students can add it back to the subtrahend. If the sum matches the minuend, your answer is correct. This simple practice will help in avoiding wrong calculations. 

• Practice zero rules: When there are zeros in tens or ones place, learn to borrow across more than one digit. It is easier if you know how to handle these quick steps, while doing 3-digit subtraction. 

• Use visual aids and tools: Parents and teachers can make visual aids like number lines, place value charts or demonstrations to show borrowing, and subtracting. These visual representations will make abstract steps easier to follow. 

• Encourage explanation by students: Ask students to explain each step as they subtract. This helps in memorizing the steps, also parents and teachers can highlight any errors occurring. 

• Provide varied practice: Parents and teachers can make use of 3-digit subtraction worksheets, having problems including 3-digit subtraction with and without regrouping. 

• Connect to real life contexts: Apply 3-digit subtraction to everyday situations, like finding change after shopping or calculating remaining items, to show the relevance of the concept in real life. 

3-digit subtraction is not only for learning, it’s a skill which used in daily life. Whether figuring out how much money is left after shopping, calculating distances, or keeping track of items at home, subtracting larger numbers helps children solve real-world problems. 

• Shopping and Money: When buying items, we use subtraction to find out the remaining change. For example, if we have $500 and spend $275 on toys, the remaining amount is $500 − $275 = $225.

• Time and Schedules: Subtraction helps calculate how much time has passed or is left. For instance, if a class starts at 9:00 AM and ends at 11:45 AM, the duration is 11:45 − 9:00 = 2 hours 45 minutes.

• Travel and Distance: To know how far we still need to travel, we subtract the distance already covered from the total distance. For example, for a 350-mile trip with 120 miles completed, the remaining distance is 350 − 120 = 230 miles.

• Counting and Inventory: In a library with 300 books, if 145 are borrowed, the remaining books are 300 − 145 = 155.

• Classroom Activities: Teachers use subtraction to determine attendance. If a school has 460 students and 38 are absent, then 460 − 38 = 422 students are present.