Which of the following expressions can be used to describe the low temperature on Wednesday? Select all that apply.
[tex]$16+(-18)(-4)$[/tex]
[tex]$16(4)+(-8)$[/tex]
[tex]$(16-18)(-4)$[/tex]
[tex]$[16+(-18)](-4)$[/tex]
Answer (2)
Evaluate the first expression: 16 + ( − 18 ) ( − 4 ) = 88 .
Evaluate the second expression: 16 ( 4 ) + ( − 8 ) = 56 .
Evaluate the third expression: ( 16 − 18 ) ( − 4 ) = 8 .
Evaluate the fourth expression: [ 16 + ( − 18 )] ( − 4 ) = 8 . The third and fourth expressions are equivalent: ( 16 − 18 ) ( − 4 ) , [ 16 + ( − 18 )] ( − 4 ) .
Explanation
Understanding the Problem We are given four expressions and asked to determine which of them could represent the low temperature on Wednesday. Since we don't know what the actual low temperature was, we need to evaluate each expression and see which ones are equal.
Evaluating Expression 1 Let's evaluate the first expression: 16 + ( − 18 ) ( − 4 ) .
Remember that multiplying two negative numbers results in a positive number. So, ( − 18 ) ( − 4 ) = 72 . Therefore, 16 + 72 = 88 .
Evaluating Expression 2 Now, let's evaluate the second expression: 16 ( 4 ) + ( − 8 ) .
First, we multiply 16 by 4 , which gives us 64 . Then, we add − 8 to 64 , which is the same as subtracting 8 from 64 . So, 64 − 8 = 56 .
Evaluating Expression 3 Next, let's evaluate the third expression: ( 16 − 18 ) ( − 4 ) .
First, we subtract 18 from 16 , which gives us − 2 . Then, we multiply − 2 by − 4 . Since multiplying two negative numbers results in a positive number, we have ( − 2 ) ( − 4 ) = 8 .
Evaluating Expression 4 Finally, let's evaluate the fourth expression: [ 16 + ( − 18 )] ( − 4 ) .
First, we add 16 and − 18 , which is the same as subtracting 18 from 16 . So, 16 − 18 = − 2 . Then, we multiply − 2 by − 4 . Since multiplying two negative numbers results in a positive number, we have ( − 2 ) ( − 4 ) = 8 .
Comparing the Results Now, we compare the results. The first expression equals 88 , the second equals 56 , the third equals 8 , and the fourth equals 8 . Therefore, the third and fourth expressions are equivalent.
Final Answer The expressions that can be used to describe the low temperature on Wednesday are ( 16 − 18 ) ( − 4 ) and [ 16 + ( − 18 )] ( − 4 ) .
Examples
Understanding how to evaluate different mathematical expressions is crucial in many real-life situations. For example, when calculating the total cost of items with discounts and taxes, you need to correctly apply the order of operations to arrive at the correct final price. Similarly, in science, different formulas require you to evaluate expressions to find values like velocity, energy, or force. Knowing how to manipulate and evaluate expressions accurately ensures you can solve problems effectively in various fields.
The two expressions that can describe the low temperature on Wednesday are ( 16 − 18 ) ( − 4 ) and [ 16 + ( − 18 )] ( − 4 ) , both of which evaluate to 8 . The first expression evaluates to 88 and the second to 56 , so they are not considered. Each expression was evaluated step-by-step to confirm their values.
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