Question 17 of 25intermediate🔍 AnalyzeNumerical2 marks

If 47 − 56 + 14 − 8 + 2 − 8 + 5 = −4, then find the value of −47 + 56 − 14 + 8 − 2 + 8 − 5 without calculating the full expression.

Correct Answer

Step 1: Observe that the second expression is the additive inverse (negative) of the first expression.

Step 2: First expression: 47 − 56 + 14 − 8 + 2 − 8 + 5 = −4

Step 3: Second expression: −47 + 56 − 14 + 8 − 2 + 8 − 5 = −(47 − 56 + 14 − 8 + 2 − 8 + 5)

Step 4: ∴ Second expression = −(−4) = 4

Exercise: Figure it Out (Section 5) | Q: 4 | (Page Page 19)
For More Understanding

Explanation

The chapter explains that the second expression is the additive inverse of the first expression. Each term in the second expression is the negative of the corresponding term in the first expression. If the first expression equals −4, then its additive inverse equals 4. This is because −(47 − 56 + 14 − 8 + 2 − 8 + 5) = −47 + 56 − 14 + 8 − 2 + 8 − 5.

Solution Steps

  1. Step 1: Observe that the second expression is the additive inverse (negative) of the first expression

  2. Step 2: First expression: 47 − 56 + 14 − 8 + 2 − 8 + 5 = −4

  3. Step 3: Second expression: −47 + 56 − 14 + 8 − 2 + 8 − 5 = −(47 − 56 + 14 − 8 + 2 − 8 + 5)

  4. Step 4: Therefore, second expression = −(−4) = 4

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