Sure, let's go through each problem step-by-step:
### a) Calculate [tex]\( -200 \times -40 \)[/tex]
When you multiply two negative numbers, the product is positive. So:
[tex]\[ -200 \times -40 = 8000 \][/tex]
### b) Calculate [tex]\( -96 \div (-12) \)[/tex]
When dividing two negative numbers, the quotient is positive. Thus:
[tex]\[ -96 \div (-12) = 8.0 \][/tex]
### c) Calculate [tex]\( -56 \times y^2 \div 7 \times y \)[/tex]
We simplify this expression step by step. First, note that this can be rewritten as:
[tex]\[ \left( \frac{-56 \times y^2}{7 \times y} \right) \][/tex]
Since [tex]\( y^2 = y \times y \)[/tex], this simplifies to:
[tex]\[ \frac{-56 \times y \times y}{7 \times y} \][/tex]
We can cancel one [tex]\( y \)[/tex] from the numerator and the denominator:
[tex]\[ \frac{-56 \times y}{7} \][/tex]
Now, [tex]\(\frac{-56}{7} = -8\)[/tex]:
[tex]\[ -8 \times y \][/tex]
Since [tex]\( y \)[/tex] is non-zero and cancels out, we get:
[tex]\[ -8.0 \][/tex]
### d) Determine the product of [tex]\( -16 \times -8 \)[/tex]
For multiplying two negative numbers, the product is positive. So:
[tex]\[ -16 \times -8 = 128 \][/tex]
### e) Determine the quotient of [tex]\( -96 \div 12 \)[/tex]
When a negative number is divided by a positive number, the quotient is negative. Thus:
[tex]\[ -96 \div 12 = -8.0 \][/tex]
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Combining all the results:
a) [tex]\( -200 \times -40 = 8000 \)[/tex]
b) [tex]\( -96 \div (-12) = 8.0 \)[/tex]
c) [tex]\( -56 \times y^2 \div 7 \times y = -8.0 \)[/tex]
d) [tex]\( -16 \times -8 = 128 \)[/tex]
e) [tex]\( -96 \div 12 = -8.0 \)[/tex]
