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Evaluate
ⓐ To evaluate
substitute
for
in the expression.
Subtract. |
ⓑ To evaluate
Subtract. |
When we first introduced the operation symbols, we saw that the expression may be read in several ways as shown below.
Be careful to get and in the right order!
Translate and then simplify:
ⓐ the difference of
and
ⓑ subtract from
ⓐ A
difference means subtraction. Subtract the numbers in the order they are given.
Translate. | |
Simplify. |
ⓑ
Subtract means to take
away from
Translate. | |
Simplify. |
Translate and simplify:
Translate and simplify:
It’s hard to find something if we don’t know what we’re looking for or what to call it. So when we solve an application problem, we first need to determine what we are asked to find. Then we can write a phrase that gives the information to find it. We’ll translate the phrase into an expression and then simplify the expression to get the answer. Finally, we summarize the answer in a sentence to make sure it makes sense.
The temperature in Urbana, Illinois one morning was degrees Fahrenheit. By mid-afternoon, the temperature had dropped to degrees Fahrenheit. What was the difference between the morning and afternoon temperatures?
Step 1. Identify what we are asked to find. | the difference between the morning and afternoon temperatures |
Step 2. Write a phrase that gives the information to find it. | the difference of and |
Step 3. Translate the phrase to an expression.
The word difference indicates subtraction. |
|
Step 4. Simplify the expression. | |
Step 5. Write a complete sentence that answers the question. | The difference in temperature was degrees Fahrenheit. |
The temperature in Anchorage, Alaska one morning was By mid-afternoon the temperature had dropped to below zero. What was the difference between the morning and afternoon temperatures?
45 degrees Fahrenheit
The temperature in Denver was degrees Fahrenheit at lunchtime. By sunset the temperature had dropped to What was the difference between the lunchtime and sunset temperatures?
9 degrees Fahrenheit
Geography provides another application of negative numbers with the elevations of places below sea level.
Dinesh hiked from Mt. Whitney, the highest point in California, to Death Valley, the lowest point. The elevation of Mt. Whitney is feet above sea level and the elevation of Death Valley is feet below sea level. What is the difference in elevation between Mt. Whitney and Death Valley?
Step 1. What are we asked to find? | The difference in elevation between Mt. Whitney and Death Valley |
Step 2. Write a phrase. | elevation of Mt. Whitney−elevation of Death Valley |
Step 3. Translate. | |
Step 4. Simplify. | |
Step 5. Write a complete sentence that answers the question. | The difference in elevation is feet. |
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