Column A: (109)(87-14)
Column B: (109)(87)-(109)(14)
Column B: (109)(87)-(109)(14)
Show Hint
- Quantity A is greater
- Quantity B is greater
- The two quantities are equal
- The relationship cannot be determined from the information given
The Correct Option is C
Solution and Explanation
This question tests the understanding of the distributive property of multiplication over subtraction.
Step 2: Key Formula or Approach:
The distributive property states that for any numbers a, b, and c:
\[ a(b - c) = ab - ac \] Step 3: Detailed Explanation:
Let's analyze the two columns in terms of the distributive property.
Let \(a = 109\), \(b = 87\), and \(c = 14\).
Column A is in the form \(a(b - c)\).
Column B is in the form \(ab - ac\).
According to the distributive property, these two expressions are algebraically identical. Therefore, the quantities must be equal.
Step 4: Verification by Calculation (Optional):
We can also calculate the value in Column A.
\[ (109)(87 - 14) = (109)(73) \] For Column B, we can factor out the common term 109:
\[ (109)(87) - (109)(14) = 109 \times (87 - 14) = (109)(73) \] Both columns simplify to the same expression.
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