Question

writing mathematical language symbolically

write the given verbal expressions symbolically then calculate the results.

note: place all negative numbers in the symbolic form in parentheses.

for multiplication, \\(3*4 = 3 \cdot 4\\)
for division, \\(12/3 = 12 \div 3\\)
for exponents, \\(6\wedge2 = 6^2\\)

write the symbolic representation of

negative nine minus the product of six and two

calculated results:

write the symbolic representation of

negative four subtracted from the quotient of negative twenty-four and eight

calculated results:

Explanation:

Translate the first expression

The first verbal expression is: "negative nine minus the product of six and two".

• "negative nine" is written as \((-9)\) because the instructions state to place all negative numbers in parentheses.
• "minus" represents subtraction: \(-\).
• "the product of six and two" is written as \(6 \cdot 2\) based on the multiplication instruction \(3 \cdot 4\).

Combining these, the symbolic representation is:

$$(-9) - 6 \cdot 2$$

Calculate the first result

Using the order of operations, perform multiplication before subtraction:

• Multiply: \(6 \cdot 2 = 12\)
• Subtract: \(-9 - 12 = -21\)

Translate the second expression

The second verbal expression is: "negative four subtracted from the quotient of negative twenty-four and eight".

• "negative four" is written as \((-4)\).
• "subtracted from" means we subtract this value from another expression, so it will be placed at the end: \(- (-4)\).
• "the quotient of negative twenty-four and eight" is written as \((-24) \div 8\) based on the division instruction \(12 \div 3\).

Combining these, the symbolic representation is:

$$(-24) \div 8 - (-4)$$

Calculate the second result

Using the order of operations, perform division before subtraction:

• Divide: \((-24) \div 8 = -3\)
• Subtract: \(-3 - (-4) = -3 + 4 = 1\)

Answer:

Question 1

Write the symbolic representation of negative nine minus the product of six and two: <blank>\((-9) - 6 \cdot 2\)</blank>

Calculated results: <blank>-21</blank>

Question 2

Write the symbolic representation of negative four subtracted from the quotient of negative twenty-four and eight: <blank>\((-24) \div 8 - (-4)\)</blank>

Calculated results: <blank>1</blank>