Problem 168 - Prealgebra

Question

In the following exercises, subtract and then check by adding. $$ 268-106 $$

Step-by-Step Solution

Answer

268 - 106 = 162. Checking: 162 + 106 = 268.

Step 1: Subtract the numbers

To subtract 106 from 268, align the numbers by their place values (units, tens, hundreds) and subtract each digit starting from the rightmost (units) side. 268 -106 ---- Take 8 units and subtract 6 units to get 2 units. Take 6 tens and subtract 0 tens to get 6 tens. Take 2 hundreds and subtract 1 hundred to get 1 hundred. So, the result is 162.

Step 2: Check the result by adding

To verify the subtraction, add the difference (162) to the subtracted number (106). The sum should be the original number (268). 162 +106 ---- Add 2 units and 6 units to get 8 units. Add 6 tens and 0 tens to get 6 tens. Add 1 hundred and 1 hundred to get 2 hundreds. So, the sum is 268, which confirms the subtraction was correct.

Key Concepts

Subtraction

Subtraction is one of the basic arithmetic operations. It involves finding the difference between two numbers. In our exercise, we are subtracting 106 from 268.
Here's how you can do it:
1. **Align the numbers by their place values**: Make sure the digits are properly lined up according to hundreds, tens, and units.
2. **Start from the rightmost place value (units)**: Subtract the units first, followed by the tens, and then the hundreds. In our exercise:

• 268
• 106

Subtract:
8 (units) - 6 (units) = 2 units
6 (tens) - 0 (tens) = 6 tens
2 (hundreds) - 1 (hundred) = 1 hundred
Therefore, 268 - 106 = 162.

Addition

Addition is another basic arithmetic operation, often used to verify subtraction. If you add the difference (result of subtraction) to the subtracted number, you should get the original number.
For our exercise, we can check the result by adding 162 (difference) and 106 (subtracted number).
Step-by-step:
1. Align the numbers by place values.
2. Start from the rightmost place value (units) again.
In our example:

• 162
• 106

Add up:
2 (units) + 6 (units) = 8 units
6 (tens) + 0 (tens) = 6 tens
1 (hundred) + 1 (hundred) = 2 hundreds
Therefore, 162 + 106 = 268, which confirms our subtraction result was correct.

Place Value

Place value is crucial in arithmetic operations. It refers to the value given to a digit based on its position within a number.
In the number 268:

• 8 is in the units place, so its value is 8.
• 6 is in the tens place, so its value is 60.
• 2 is in the hundreds place, so its value is 200.

Correct alignment during subtraction (or addition) ensures each digit in the corresponding place value column is used properly.
For our subtraction:

• 268
• 106

Aligning the place values:
Units: 8 and 6
Tens: 6 and 0
Hundreds: 2 and 1. This alignment helps avoid calculation errors.
Always align numbers from the right-side, starting with the smallest place value.

Basic Arithmetic

Basic arithmetic involves operations like addition, subtraction, multiplication, and division. Mastering these is important for solving more complex math problems.
In our exercise:

• We used **subtraction** to find the difference between 268 and 106.
• We used **addition** to verify our subtraction result.

These operations rely on core ideas like place value, proper alignment, and understanding how to carry digits when needed.
Practice more problems to get familiar with these steps.
The better you understand these concepts, the easier it will be to solve math problems correctly in the future.