Sure! Let's break down each problem one by one and find out their respective values.
### (i) [tex]\(-3 \times 4\)[/tex]
First, we multiply [tex]\(-3\)[/tex] and [tex]\(4\)[/tex]:
[tex]\[ -3 \times 4 = -12 \][/tex]
So, the answer is [tex]\(-12\)[/tex].
### (iv) [tex]\(\frac{(-4) \times(-9)}{(-6)}\)[/tex]
First, we multiply [tex]\(-4\)[/tex] and [tex]\(-9\)[/tex]:
[tex]\[ -4 \times -9 = 36 \][/tex]
Next, we divide the result by [tex]\(-6\)[/tex]:
[tex]\[ \frac{36}{-6} = -6 \][/tex]
So, the answer is [tex]\(-6.0\)[/tex] (written as a floating point number).
### (ii) [tex]\(-2 \times -6 \times -3\)[/tex]
We can multiply these step by step:
[tex]\[ -2 \times -6 = 12 \][/tex]
Then multiplying [tex]\(12\)[/tex] by [tex]\(-3\)[/tex]:
[tex]\[ 12 \times -3 = -36 \][/tex]
So, the answer is [tex]\(-36\)[/tex].
### (v) [tex]\(\frac{8 \times (-8)}{12 - 16}\)[/tex]
First, we multiply [tex]\(8\)[/tex] and [tex]\(-8\)[/tex]:
[tex]\[ 8 \times -8 = -64 \][/tex]
Next, we need to compute the denominator, which is [tex]\(12 - 16\)[/tex]:
[tex]\[ 12 - 16 = -4 \][/tex]
Now, we divide the results:
[tex]\[ \frac{-64}{-4} = 16 \][/tex]
So, the answer is [tex]\(16.0\)[/tex] (written as a floating point number).
### (iii) [tex]\(9 \times (5 - 7)\)[/tex]
First, we need to compute the expression inside the parentheses:
[tex]\[ 5 - 7 = -2 \][/tex]
Then, we multiply [tex]\(9\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[ 9 \times -2 = -18 \][/tex]
So, the answer is [tex]\(-18\)[/tex].
### (vi) [tex]\(\frac{(-2)^2 \times (-5)}{(-8) + 10}\)[/tex]
First, we calculate [tex]\((-2)^2\)[/tex]:
[tex]\[ (-2)^2 = 4 \][/tex]
Next, we multiply [tex]\(4\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[ 4 \times -5 = -20 \][/tex]
Now, we compute the denominator, which is [tex]\((-8) + 10\)[/tex]:
[tex]\[ -8 + 10 = 2 \][/tex]
Finally, we divide the results:
[tex]\[ \frac{-20}{2} = -10 \][/tex]
So, the answer is [tex]\(-10.0\)[/tex] (written as a floating point number).
### Summary of Results
- (i) [tex]\(-3 \times 4\)[/tex] = [tex]\(-12\)[/tex]
- (iv) [tex]\(\frac{(-4) \times(-9)}{(-6)}\)[/tex] = [tex]\(-6.0\)[/tex]
- (ii) [tex]\(-2 \times-6 \times-3\)[/tex] = [tex]\(-36\)[/tex]
- (v) [tex]\(\frac{8 \times(-8)}{12-16}\)[/tex] = [tex]\(16.0\)[/tex]
- (iii) [tex]\(9 \times(5-7)\)[/tex] = [tex]\(-18\)[/tex]
- (vi) [tex]\(\frac{(-2)^2 \times(-5)}{(-8)+10}\)[/tex] = [tex]\(-10.0\)[/tex]
These are the detailed step-by-step solutions for each of the given expressions.
