Evaluate the numerical expression 10 + 10(9) by correctly applying the standard order of operations for multiplication and addition, and find the final value.

Introduction / Context:
This question reinforces the rule that multiplication must be performed before addition when evaluating numerical expressions. The notation 10(9) means 10 multiplied by 9. Such expressions appear frequently in aptitude tests and in algebra, and misunderstanding the order of operations can lead to incorrect answers even though the numbers look simple.

Given Data / Assumptions:

• The expression is 10 + 10(9).
• 10(9) represents 10 multiplied by 9.
• The required operations are multiplication and addition.
• We use the standard BODMAS or PEMDAS convention.

Concept / Approach:
According to BODMAS or PEMDAS, we first evaluate brackets, then orders (powers and roots), then division and multiplication from left to right, and finally addition and subtraction from left to right. Here, there are no brackets that change the order, but 10(9) clearly indicates a multiplication. Therefore we perform 10 × 9 before adding the remaining 10.

Step-by-Step Solution:
Begin with the expression: 10 + 10(9).Recognize that 10(9) = 10 × 9.Compute the multiplication: 10 × 9 = 90.Substitute back into the expression: 10 + 90.Add the numbers: 10 + 90 = 100.

Verification / Alternative check:
If someone treated the expression incorrectly, they might think of 10 + 10 as 20 and then multiply the result by 9, getting 180. However, that would require parentheses around the sum, written as (10 + 10) × 9. Since no such brackets are present, this interpretation is wrong. Rechecking the original expression confirms that only 10 is outside, and 10(9) is a separate term that must be evaluated first. The correct answer remains 100.

Why Other Options Are Wrong:
Option a, 180, comes from the incorrect interpretation (10 + 10) × 9. Option b, 110, suggests mistakenly adding 10 and 9 and then adding 10 again. Option d, 19, looks like someone added 10 and 9 only. Option e, 90, uses the product alone and ignores the initial 10. None of these follow the proper order of operations.

Common Pitfalls:
One frequent mistake is to read 10(9) as if it were 10 + 9 or to treat the whole expression as a simple left to right addition and multiplication without respecting precedence. Some students also forget that juxtaposition like 10(9) always means multiplication. To avoid these issues, always apply the multiplication before addition rule consistently, especially in mixed expressions.

Final Answer:
The value of the expression 10 + 10(9) is 100.