Let's solve the questions one by one:

1st Section: Identify whether the statements are True (D) or False (Y).

• I. "Sadece çarpma ve bölme işleminin olduğu parantez olmayan ifadelerde her zaman önce çarpma daha sonra bölme işlemi yapılır."

  • This statement is False (Y) because according to the order of operations (BODMAS/PEMDAS), multiplication and division are performed from left to right, depending on their order in the expression, not necessarily multiplication first.

• II. "102 – (34 ÷ 2 + 18) işlemi yapılırken ilk olarak parantezin içindeki çarpma işlemi yapılır."

  • This statement is False (Y) because inside the parentheses, division happens before addition according to the order of operations, not multiplication.

• III. "Parantezin de bulunduğu iç içe verilen işlemlerde, toplama ve çıkarma işlemleri her zaman en son yapılır."

  • This statement is True (D) because within parentheses, we perform the operations according to BODMAS/PEMDAS rules. Addition and subtraction are always done last after any other operations (such as multiplication or division).

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2nd Section: Fill in the blanks with the appropriate word.

• I. "Sadece toplama ve çıkarma işlemlerinin bulunduğu parantezsiz bir ifadede toplama ve çıkarma işlemlerinden, önce soldaki yapılır."

  • The correct answer is soldaki because for addition and subtraction, operations are performed from left to right.

• II. "3 + 12 ÷ 3 işleminde önce bölme yapılır."

  • The correct answer is bölme because division takes precedence over addition.

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3rd Section: Solve the expression.

The expression is: $(16 - 3 \cdot 5) + (5^3 - 2^5) - (4 \cdot 3 \cdot 7) - 103$

Let's break it down step by step:

• First part: $16 - 3 \cdot 5 = 16 - 15 = 1$
• Second part: $5^3 - 2^5 = 125 - 32 = 93$
• Third part: $4 \cdot 3 \cdot 7 = 84$

Now substitute the results back into the expression: $1 + 93 - 84 - 103 = 94 - 84 - 103 = 10 - 103 = -93$

So, the answer is -93.

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Would you like more details on any of the steps, or do you have any other questions?

Related questions:

1. How does the order of operations (BODMAS/PEMDAS) work in mathematical expressions?
2. Why do we solve parentheses before other operations in math?
3. Can you give an example of when division might come before multiplication in an expression?
4. What happens if we change the position of parentheses in a complex expression?
5. How do powers (exponents) affect the order of operations?

Tip:

Always remember that multiplication and division, as well as addition and subtraction, are performed from left to right based on their position in the expression, not according to strict priority between them.