# 3 Digit Math Problems

Three-digit numbers have three digits ranging from 100 to 999. These numbers are composed of hundreds, tens, and unit digits, which give them a unique value and place in the number system. Understanding and working with 3-digit numbers is an essential skill in mathematics.

They play a crucial role in developing math skills as they provide real-life contexts for applying mathematical concepts. Solving word problems helps students understand how to use mathematical operations such as addition and subtraction in practical situations. It enhances critical thinking and problem-solving abilities and promotes a deeper understanding of mathematical concepts.

## Addition of 3 Digit Math Problems

### Problem 1: Adding two 3-digit numbers

Example problem: 342 + 178 Solution steps and calculations:

- Line up the numbers vertically, aligning the units, tens, and hundreds of digits.
- Start by adding the units digits: 2 + 8 = 10. Write down 0 and carry over 1 to the tens column.
- Add the tens digits: 4 + 7 + 1 (carried over) = 12. Write down 2 and carry over 1 to the hundreds column.
- Add the hundreds of digits: 3 + 1 (carried over) = 4.
- Therefore, 342 + 178 = 520.

To add two 3-digit numbers, we start from the rightmost digit and move to the left, carrying over any excess values to the next column. By summing the corresponding digits in each column, we obtain the result. In the given example, the units column gives us 0, the tens column gives us 2, and the hundreds column gives us 4, resulting in 520.

### Problem 2: Adding a 2-digit and a 3-digit number

Example problem: 97 + 534 Solution steps and calculations:

- Line up the numbers vertically, aligning the units, tens, and hundreds of digits.
- Add the units digits: 7 + 4 = 11. Write down 1 and carry over 1 to the tens column.
- Add the tens digits: 9 + 3 + 1 (carried over) = 13. Write down 3 and carry over 1 to the hundreds column.
- Add the hundreds of digits: 5 + 1 (carried over) = 6.
- Therefore, 97 + 534 = 631.

Adding a 2-digit and a 3-digit number is similar to adding two 3-digit numbers. We start from the rightmost digit and move to the left, carrying over any excess values. In the given example, the units column gives us 1, the tens column gives us 3, and the hundreds column gives us 6, resulting in 631.

## Subtraction 3 Digit Math Problems

### Problem 1: Subtracting a 3-digit number from another 3-digit number

Example problem: 572 – 294 Solution steps and calculations:

- Line up the numbers vertically, aligning the units, tens, and hundreds of digits.
- Start by subtracting the units digits: 2 – 4. Since 4 is greater than 2, borrow 1 from the tens column, making it 12 – 4 = 8.
- Subtract the tens digits: 7 – 9 (borrowed 1) = -2. Since we cannot have a negative digit, borrow 1 from the hundreds column, making it 17 – 9 = 8.
- Subtract the hundreds of digits: 5 – 2 = 3.
- Therefore, 572 – 294 = 278.

To subtract a 3-digit number from another 3-digit number, we start from the rightmost digit and move to the left. If the digit being subtracted is greater than the corresponding digit in the minuend, we borrow from the next column. In the given example, the units column gives us 8, the tens column gives us -2, and the hundreds column gives us 3, resulting in a difference of 278.

### Problem 2: Subtracting a 2-digit number from a 3-digit number

Example problem: 765 – 87 Solution steps and calculations:

- Line up the numbers vertically, aligning the units, tens, and hundreds of digits.
- Subtract the units digits: 5 – 7. Since 7 is greater than 5, borrow 1 from the tens column, making it 15 – 7 = 8.
- Subtract the tens digits: 6 – 8 (borrowed 1) = -2. Since we cannot have a negative digit, borrow 1 from the hundreds column, making it 16 – 8 = 8.
- Subtract the hundreds of digits: 7 – 0 = 7.
- Therefore, 765 – 87 = 678.

When subtracting a 2-digit number from a 3-digit number, the process is similar to subtracting two 3-digit numbers. We start from the rightmost digit and move to the left, borrowing from the next column if needed. In the given example, the units column gives us 8, the tens column gives us -2, and the hundreds column gives us 7, resulting in a difference of 678.

## Mixed Addition and Subtraction Word Problems

### Problem 1: Mixed addition and subtraction involving 3-digit numbers

Example problem: 432 + 275 – 167 Solution steps and calculations:

- Perform addition first: 432 + 275 = 707.
- Then subtract 707 – 167 = 540.

When faced with mixed addition and subtraction word problems involving 3-digit numbers, it is important to follow the order of operations (BIDMAS/BODMAS). In this case, addition is performed first, resulting in 707. Then, the subtraction is carried out, resulting in the final answer of 540.

### Problem 2: Mixed addition and subtraction with multiple 3-digit numbers

Example problem: 846 – 219 + 374 Solution steps and calculations:

- Perform the subtraction first: 846 – 219 = 627.
- Then, perform the addition: 627 + 374 = 1001.

In this example of mixed addition and subtraction with multiple 3-digit numbers, we start with subtraction to obtain 627. Then, we perform the addition operation, resulting in the final answer, 1001.

**Conclusion**

Practicing 3-digit addition and subtraction, especially through word problems, helps develop essential math skills such as critical thinking, problem-solving, and applying mathematical concepts in real-life scenarios. It enhances numerical fluency and provides a solid foundation for more advanced math topics.

To strengthen math skills further, it is crucial to continue practicing and solving word problems involving 3-digit addition and subtraction. Regular practice will improve computational abilities and enhance logical reasoning and analytical thinking, empowering individuals to tackle more complex math problems in the future.