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Chapter 0: Problem 4

Determine how many different values can arise by inserting one pair of parentheses into the given expression. $$ 5 \cdot 3 \cdot 2+6 \cdot 4 $$

Short Answer

Expert verified
By inserting one pair of parentheses, we can obtain two different values from the given expression: 54 and 480.

Step by step solution

01

Identify the candidates for parentheses insertion

In the given expression, we have three operations: multiplication between 5 and 3, multiplication between 3 and 2, and addition between 2 and 6. Similarly, we have multiplication between 6 and 4. Hence, there are a total of 4 possible placements for parentheses.
02

Insert parentheses and calculate values

Now, we will insert the parentheses and calculate the resulting values for each case: 1. \((5 \cdot 3) \cdot 2 + 6 \cdot 4\): \(15 \cdot 2 + 24 = 30 + 24 = 54\) 2. \(5\cdot (3 \cdot 2) + 6 \cdot 4\): \(5 \cdot 6 + 24 = 30 + 24 = 54\) 3. \(5 \cdot 3 \cdot( 2 + 6) \cdot 4\): \(5 \cdot 3 \cdot 8 \cdot 4 = 5 \cdot 24 \cdot 4 = 120 \cdot 4 = 480\) 4. \(5 \cdot 3 \cdot 2 + (6 \cdot 4)\): \(30 + 24 = 54\)
03

Identify the unique values

After calculating the values for each case, we observe that there are two unique values: 54 and 480. Therefore, by inserting one pair of parentheses, we can obtain two different values from the given expression.

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