https://r2.erweima.ai/mathbot/image/1726697797895a4tseot8.jpg

The image contains a list of mathematical expressions to solve. Let me go through each one step by step:

**a)** \((-12 + 24 - 18) \div (-6)\)

- First, perform the operations inside the parentheses:
  \(-12 + 24 = 12\), and then \(12 - 18 = -6\).
  
- Now divide by \(-6\):
  \[
  -6 \div (-6) = 1
  \]

**b)** \((-3) \cdot (6 - 8 + 4 - 3)\)

- Simplify inside the parentheses:
  \(6 - 8 = -2\), \(-2 + 4 = 2\), and \(2 - 3 = -1\).
  
- Now multiply by \(-3\):
  \[
  (-3) \cdot (-1) = 3
  \]

**c)** \((45 - 18 + 81) \div (-9)\)

- Simplify inside the parentheses:
  \(45 - 18 = 27\), and then \(27 + 81 = 108\).
  
- Now divide by \(-9\):
  \[
  108 \div (-9) = -12
  \]

**d)** \((12 - 7 - 8 + 1) \cdot (-2)\)

- Simplify inside the parentheses:
  \(12 - 7 = 5\), \(5 - 8 = -3\), and \(-3 + 1 = -2\).
  
- Now multiply by \(-2\):
  \[
  (-2) \cdot (-2) = 4
  \]

**e)** \((-35 - 42 - 63) \div (+7)\)

- Simplify inside the parentheses:
  \(-35 - 42 = -77\), and then \(-77 - 63 = -140\).
  
- Now divide by \(+7\):
  \[
  -140 \div 7 = -20
  \]

**f)** \((+4) \cdot (-8 + 5 - 6 + 2)\)

- Simplify inside the parentheses:
  \(-8 + 5 = -3\), \(-3 - 6 = -9\), and \(-9 + 2 = -7\).
  
- Now multiply by \(+4\):
  \[
  4 \cdot (-7) = -28
  \]

**g)** \((-72 + 24 - 48 - 12) \div (+12)\)

- Simplify inside the parentheses:
  \(-72 + 24 = -48\), \(-48 - 48 = -96\), and \(-96 - 12 = -108\).
  
- Now divide by \(+12\):
  \[
  -108 \div 12 = -9
  \]

**h)** \((-6 + 4 - 3 - 5) \cdot (-10)\)

- Simplify inside the parentheses:
  \(-6 + 4 = -2\), \(-2 - 3 = -5\), and \(-5 - 5 = -10\).
  
- Now multiply by \(-10\):
  \[
  -10 \cdot (-10) = 100
  \]

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Here are the final answers:

- a) \(1\)
- b) \(3\)
- c) \(-12\)
- d) \(4\)
- e) \(-20\)
- f) \(-28\)
- g) \(-9\)
- h) \(100\)

Would you like any more details on a specific step or clarification?

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Here are some related questions:

1. How do we handle the order of operations in expressions like these?
2. Can we always assume that division by a negative number will result in a negative outcome?
3. How can we use parentheses to change the outcome of expressions like the ones above?
4. What happens when multiplying or dividing multiple negative numbers?
5. How do you solve more complex expressions that involve multiple operations?

**Tip**: Always simplify inside parentheses before moving on to multiplication or division for clarity!

Desarrollar los siguientes ejercicios:
a) (-12 + 24 - 18) : (-6)
b) (-3) * (6 - 8 + 4 - 3)
c) (45 - 18 + 81) : (-9)
d) (12 - 7 - 8 + 1) * (-2)
e) (-35 - 42 - 63) : (+7)
f) (+4) * (-8 + 5 - 6 + 2)
g) (-72 + 24 - 48 - 12) : (+12)
h) (-6 + 4 - 3 - 5) * (-10)

Solve mathematical expressions using the order of operations (PEMDAS) with parentheses, division, and multiplication. Exercises include simplification of expressions like (-12 + 24 - 18) ÷ (-6) and (-72 + 24 - 48 - 12) ÷ (+12), suitable for students in Grades 6-8.

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