QUESTION 4 4.1 Arrange the following in descending order: $$ -8 ;-1 ; 8 ;-16 ; 12 ;-12 ; 9 $$ 4.2 Insert brackets to make the following true: $$ 4.2 .1-4-3 imes-3-2=11 $$ $$ 4.2 .2 \quad 8 \div 2 imes 4+5-3 imes 2=0 $$

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QUESTION 4 4.1 Arrange the following in descending order: $$ -8 ;-1 ; 8 ;-16 ; 12 ;-12 ; 9 $$ 4.2 Insert brackets to make the following true: $$ 4.2 .1-4-3 	imes-3-2=11 $$ $$ 4.2 .2 \quad 8 \div 2 	imes 4+5-3 	imes 2=0 $$

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Alright, I need to tackle these two math problems step by step. Let's start with the first one.

**4.1 Arrange the following in descending order: $$ -8 ; -1 ; 8 ; -16 ; 12 ; -12 ; 9 $$**

First, I'll list out the numbers to get a clear view:
-8, -1, 8, -16, 12, -12, 9

To arrange them in descending order, I need to identify the largest numbers first and then proceed to the smallest. Let's compare them:

- 8 is greater than -8, -1, -16, -12, and 9.
- 12 is greater than -8, -1, -16, -12, and 9.
- 9 is greater than -8, -1, -16, and -12.
- -1 is greater than -8 and -16.
- -8 is greater than -16.
- -12 is greater than -16.

Wait, I think I made a mistake here. Let's re-examine:

- 8 is greater than -8, -1, -16, -12, and 9.
- 12 is greater than 8, -8, -1, -16, and -12.
- 9 is greater than -8, -1, -16, and -12.
- -1 is greater than -8 and -16.
- -8 is greater than -16.
- -12 is greater than -16.

So, the order from greatest to least should be:
12, 9, 8, -1, -8, -12, -16

But let me double-check:
- 12 > 9 > 8 > -1 > -8 > -12 > -16

Yes, that seems correct.

**4.2 Insert brackets to make the following true:**

**4.2.1 $$ -4 - 3 	imes -3 - 2 = 11 $$**

First, let's understand the original expression without brackets:
-4 - 3 * (-3) - 2

Calculating step by step:
1. Multiply 3 and -3: 3 * (-3) = -9
2. Subtract 9 from -4: -4 - 9 = -13
3. Subtract 2: -13 - 2 = -15

But the desired result is 11, not -15. So, I need to insert brackets to change the order of operations.

Let's try different placements:

1. **( -4 - 3 ) × ( -3 - 2 )**
   - Calculate inside the first bracket: -4 - 3 = -7
   - Calculate inside the second bracket: -3 - 2 = -5
   - Multiply: -7 * -5 = 35
   - This doesn't equal 11.

2. **( -4 - 3 × -3 ) - 2**
   - Calculate inside the bracket: -4 - (3 * -3) = -4 - (-9) = -4 + 9 = 5
   - Subtract 2: 5 - 2 = 3
   - This doesn't equal 11.

3. **-4 - ( 3 × -3 - 2 )**
   - Calculate inside the bracket: 3 * -3 = -9; -9 - 2 = -11
   - Subtract from -4: -4 - (-11) = -4 + 11 = 7
   - This doesn't equal 11.

4. **( -4 - 3 ) × ( -3 - 2 )**
   - Already tried, gives 35.

5. **-4 - 3 × ( -3 - 2 )**
   - Calculate inside the bracket: -3 - 2 = -5
   - Multiply: 3 * -5 = -15
   - Subtract from -4: -4 - (-15) = -4 + 15 = 11
   - This equals 11, which is the desired result.

So, the correct placement of brackets is:
-4 - 3 × ( -3 - 2 ) = 11

**4.2.2 $$ 8 \div 2 	imes 4 + 5 - 3 	imes 2 = 0 $$**

First, let's understand the original expression without brackets:
8 ÷ 2 × 4 + 5 - 3 × 2

Calculating step by step:
1. Divide 8 by 2: 8 ÷ 2 = 4
2. Multiply by 4: 4 * 4 = 16
3. Add 5: 16 + 5 = 21
4. Subtract 3 * 2: 21 - 6 = 15

But the desired result is 0, not 15. So, I need to insert brackets to change the order of operations.

Let's try different placements:

1. **( 8 ÷ 2 ) × ( 4 + 5 ) - 3 × 2**
   - Calculate inside the first bracket: 8 ÷ 2 = 4
   - Calculate inside the second bracket: 4 + 5 = 9
   - Multiply: 4 * 9 = 36
   - Subtract 3 * 2: 36 - 6 = 30
   - This doesn't equal 0.

2. **8 ÷ ( 2 × 4 ) + 5 - 3 × 2**
   - Calculate inside the bracket: 2 * 4 = 8
   - Divide 8 by 8: 8 ÷ 8 = 1
   - Add 5: 1 + 5 = 6
   - Subtract 3 * 2: 6 - 6 = 0
   - This equals 0, which is the desired result.

So, the correct placement of brackets is:
8 ÷ ( 2 × 4 ) + 5 - 3 × 2 = 0

4.1. Descending order: 12, 9, 8, -1, -8, -12, -16 4.2.1. Inserted brackets: -4 - 3 × ( -3 - 2 ) = 11 4.2.2. Inserted brackets: 8 ÷ ( 2 × 4 ) + 5 - 3 × 2 = 0

QUESTION 4 4.1 Arrange the following in descending order: \( -8 ;-1 ; 8 ;-16 ; 12 ;-12 ; 9 \) 4.2 Insert brackets to make the following true: \( 4.2 .1-4-3 \times-3-2=11 \) \( 4.2 .2 \quad 8 \div 2 \times 4+5-3 \times 2=0 \)

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