Problem 51 - Elementary Algebra

Question

On January 4 , the high temperature in Minneapolis was \(9^{\circ} \mathrm{F}\). The low temperature was \(-4^{\circ} \mathrm{F}\). Find the difference of these temperatures.

Step-by-Step Solution

Answer

The temperature difference is \(13^{\circ} \mathrm{F}\).

Step 1: Identify the Given Temperatures

The high temperature given is \(9^{\circ} \mathrm{F}\) and the low temperature is \(-4^{\circ} \mathrm{F}\).

Step 2: Write the Formula for Temperature Difference

The formula to find the difference between two temperatures is: \[ \text{Difference} = T_{\text{high}} - T_{\text{low}} \]

Step 3: Substitute the Values into the Formula

Substitute the given temperatures into the formula: \[ \text{Difference} = 9 - ( -4 ) \]

Step 4: Simplify the Expression

To simplify, recall that subtracting a negative number is the same as adding a positive number: \[ \text{Difference} = 9 + 4 \]

Step 5: Calculate the Temperature Difference

Add the numbers together to get the final result: \[ \text{Difference} = 13^{\circ} \mathrm{F} \]

Key Concepts

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Let's begin with some basics. Basic algebra is the section of mathematics that deals with the general rules of arithmetic and their applications. It involves variables, equations, and arithmetic operations. When working with basic algebra, remember: you can perform operations with numbers and variables just as you do with regular numbers.

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Subtraction is one of the fundamental arithmetic operations. It is the process of finding the difference between two numbers. When performing subtraction, it is essential to remember the order of the numbers. For example, in our exercise, we need to subtract the low temperature from the high temperature. The formula we use is: \[ \text{Difference} = T_{\text{high}} - T_{\text{low}}\] This formula works because subtraction tells us how much one number is larger than another. Remember to always keep the minuend (the number from which you subtract) first and the subtrahend (the number you subtract) second.

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Negative numbers can be tricky, but they follow the same rules as positive numbers with a few additions. When you subtract a negative number, it's the same as adding a positive number. This is crucial when dealing with temperature differences. In our example, we have: \[ \text{Difference} = 9 - (-4) \] Subtracting -4 is the same as adding +4: \[ \text{Difference} = 9 + 4 \] This switch from subtraction to addition happens because two negatives make a positive.

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Arithmetic operations include addition, subtraction, multiplication, and division. In our temperature difference problem, you encounter both subtraction and addition. Here are some helpful points to remember: * Subtraction: Finding how much one number differs from another. * Addition: Combining two numbers to get a sum. In our example, first, we set up the subtraction: \[ \text{Difference} = 9 - (-4) \] Then, we transform this into addition: \[ \text{Difference} = 9 + 4 \] Finally, we perform the addition and get: \[ \text{Difference} = 13 \] Understanding these basic arithmetic operations makes solving such problems much easier.