Find the missing number in the equation: 138.009 + 341.981 − 146.305 = 123.600 + ?

Introduction / Context:
This problem tests your ability to handle decimal addition and subtraction and to solve for an unknown value in a simple equation. Accurate decimal arithmetic is essential in financial calculations, measurements, and data analysis.

Given Data / Assumptions:

• Given identity: 138.009 + 341.981 − 146.305 = 123.600 + ?.
• We must find the value of the missing number represented by the question mark.
• All values are decimals with three decimal places, and we assume exact arithmetic.

Concept / Approach:
We first simplify the left hand side by performing decimal addition and subtraction. The simplified result is the total value on the left side. Then we set this equal to 123.600 plus the unknown and rearrange the equation to solve for the unknown. This is a standard linear equation technique: unknown = total − known part.

Step-by-Step Solution:
Step 1: Compute the sum of 138.009 and 341.981. Step 2: 138.009 + 341.981 = 479.990. Step 3: Subtract 146.305 from 479.990: 479.990 − 146.305 = 333.685. Step 4: So the left hand side equals 333.685. Step 5: The equation is now 333.685 = 123.600 + ?. Step 6: Rearrange to find the unknown: ? = 333.685 − 123.600. Step 7: Perform the subtraction: 333.685 − 123.600 = 210.085.

Verification / Alternative check:
Substitute ? = 210.085 back into the right hand side. Compute 123.600 + 210.085 = 333.685. This matches the simplified left hand side, which confirms that the equation is balanced. Therefore 210.085 is the correct value for the missing number. We can also check that decimal alignment was handled correctly in each step, especially in subtraction where mistakes are common.

Why Other Options Are Wrong:
199.570 would give 123.600 + 199.570 = 323.170, which is too small compared to 333.685.
295.050 gives 123.600 + 295.050 = 418.650, which is much larger than 333.685.
120.085 gives 243.685, which again does not match the left side.

Common Pitfalls:
A frequent error is misaligning decimal points when adding or subtracting, which leads to incorrect results. Another issue is subtracting the smaller number from the larger without carefully tracking the correct order. Always write decimals with the same number of decimal places and subtract column by column.

Final Answer:
The missing number that balances the equation is 210.085.