Question

The temperature at sunset was reported to be \(19^{\circ} \mathrm{F}\). By midnight, it is reported to be \(-27^{\circ} \mathrm{F}\). What is the amount of the decrease?

Short answer

Answer: The decrease in temperature from sunset to midnight is \(46^{\circ} \mathrm{F}\).

Step-by-step solution

Identify the temperatures at sunset and midnight

The temperature at sunset is \(19^{\circ} \mathrm{F}\), and the temperature at midnight is \(-27^{\circ} \mathrm{F}\).

Calculate the decrease in temperature

To find the decrease in temperature, we need to subtract the temperature at midnight from the temperature at sunset: \((19^{\circ} \mathrm{F}) - (-27^{\circ} \mathrm{F})\).

Simplify the expression

Now, we will simplify the expression: \((19^{\circ} \mathrm{F}) - (-27^{\circ} \mathrm{F})= 19^{\circ} \mathrm{F} + 27^{\circ} \mathrm{F}= 46^{\circ} \mathrm{F}\).

Write the final answer

The amount of the decrease in temperature from sunset to midnight is \(46^{\circ} \mathrm{F}\).

Key concepts

Negative Numbers Subtraction

Understanding how to handle negative numbers in subtraction can be a bit tricky, but it's a fundamental skill in arithmetic. To subtract a negative number is essentially the same as adding its positive counterpart. Imagine owing your friend \(27; if you suddenly don't owe them anything, it's like you've gained \)27. This is similar to what happens with negative numbers in subtraction.

So, when you see an equation like \(19^{\textbackslash circ} \textbackslash mathrm{F}\) minus \( -27^{\textbackslash circ} \textbackslash mathrm{F}\) (from our exercise), think of it as \(19^{\textbackslash circ} \textbackslash mathrm{F}\) plus \(27^{\textbackslash circ} \textbackslash mathrm{F}\) because subtracting a negative is like adding a positive. This principle is vital to correctly calculate changes in values such as temperature drops, account balances or elevation changes.

Basic Arithmetic Operations

The bedrock of mathematics features four essential operations: addition, subtraction, multiplication, and division. These are referred to as the basic arithmetic operations. In the context of our temperature problem, we focus on subtraction, which involves finding the difference between two numbers. When dealing with subtraction and a negative number, as mentioned previously, we convert the operation to addition.

Let's recap our problem: The initial temperature (subtrahend) was \(19^{\textbackslash circ} \textbackslash mathrm{F}\), and the temperature later (minuend) was \(\textendash27^{\textbackslash circ} \textbackslash mathrm{F}\). To calculate the decrease, we convert the subtraction into addition due to the negative sign of the second number, resulting in \(19^{\textbackslash circ} \textbackslash mathrm{F}\) + \(27^{\textbackslash circ} \textbackslash mathrm{F}\), equaling \(46^{\textbackslash circ} \textbackslash mathrm{F}\). Always remembering that subtraction of a negative number converts to addition ensures accuracy in your calculations and helps you intuitively understand the process.

Temperature Conversion

The concept of temperature conversion is pivotal when working with different temperature scales, such as Fahrenheit, Celsius, and Kelvin. These scales are used across various regions and scientific disciplines, so converting temperatures from one scale to another is a common task.

Although our original exercise didn't require a conversion between temperature scales, understanding the basics is beneficial. To convert Fahrenheit to Celsius, for example, you subtract 32 from the Fahrenheit temperature and then divide by 1.8. Conversely, to convert Celsius to Fahrenheit, you multiply the Celsius temperature by 1.8 and then add 32. While this conversion wasn't necessary for our problem, learning it can help in understanding weather reports, cooking instructions, and scientific data in different temperature scales.