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If A denotes div B, denotes xx C denote...

If A denotes `div` B, denotes `xx` C denotes +, D denotes- then which of the following statements is true ?

A

11 B 34 A 17 D 8 A3 `= (38)/(3)`

B

6 B 18 D 26 A 13 C 7 ` = (173)/(13)`

C

32 C 8 A 16 D 4 `= - (3)/(4)`

D

9 C 9 A 9 d 9 B 9 = -71

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to decode the operations based on the given symbols: - A denotes division (÷) - B denotes multiplication (×) - C denotes addition (+) - D denotes subtraction (−) Now, we will evaluate each option step by step to find out which statement is true. ### Step 1: Evaluate Option A **Expression:** \( 34 \div 17 - 8 \div 3 \) 1. **Perform Division:** - \( 34 \div 17 = 2 \) - \( 8 \div 3 = \frac{8}{3} \) 2. **Substitute back into the expression:** - \( 2 - \frac{8}{3} \) 3. **Convert to a common denominator:** - \( 2 = \frac{6}{3} \) - \( \frac{6}{3} - \frac{8}{3} = \frac{6 - 8}{3} = \frac{-2}{3} \) **Result for Option A:** \( \frac{-2}{3} \) ### Step 2: Evaluate Option B **Expression:** \( 6 \times 18 - 26 \div 13 \) 1. **Perform Division:** - \( 26 \div 13 = 2 \) 2. **Substitute back into the expression:** - \( 6 \times 18 - 2 \) 3. **Perform Multiplication:** - \( 6 \times 18 = 108 \) 4. **Final Calculation:** - \( 108 - 2 = 106 \) **Result for Option B:** \( 106 \) ### Step 3: Evaluate Option C **Expression:** \( 32 + 8 \div 16 - 4 \) 1. **Perform Division:** - \( 8 \div 16 = 0.5 \) 2. **Substitute back into the expression:** - \( 32 + 0.5 - 4 \) 3. **Perform Addition and Subtraction:** - \( 32 + 0.5 = 32.5 \) - \( 32.5 - 4 = 28.5 \) **Result for Option C:** \( 28.5 \) ### Step 4: Evaluate Option D **Expression:** \( 9 + 9 \div 9 - 9 \times 9 \) 1. **Perform Division:** - \( 9 \div 9 = 1 \) 2. **Substitute back into the expression:** - \( 9 + 1 - 9 \times 9 \) 3. **Perform Multiplication:** - \( 9 \times 9 = 81 \) 4. **Final Calculation:** - \( 9 + 1 - 81 = 10 - 81 = -71 \) **Result for Option D:** \( -71 \) ### Conclusion After evaluating all options, we find that: - Option A: \( \frac{-2}{3} \) - Option B: \( 106 \) - Option C: \( 28.5 \) - Option D: \( -71 \) Since we need to determine which statement is true, we conclude that the correct option is **Option D**.
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