Video: Solving Word Problems Involving Addition and Subtraction of Rational Numbers

One day, the temperature started at −8°F, dropped 2°F, and then rose 9°F by noon to reach the days maximum temperature. The next day, the temperature started at −14°F, rose 5°F, and then again rose another 4°F by noon to reach the days maximum temperature. Find the difference between the highest temperatures on those two days.

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Video Transcript

One day, the temperature started at negative eight degrees Fahrenheit, dropped two degrees Fahrenheit, and then rose nine degrees Fahrenheit by noon to reach the day’s maximum temperature. The next day, the temperature started at negative 14 degrees Fahrenheit, rose five degrees Fahrenheit, and then again rose another four degrees Fahrenheit by noon to reach the day’s maximum temperature. Find the difference between the highest temperatures on those two days.

Let’s begin by looking at what happened to the temperature on day one. It started at negative eight degrees Fahrenheit. We are then told it dropped two degrees Fahrenheit, which means we need to subtract two from negative eight. Finally, it rose nine degrees Fahrenheit, so we need to add nine to this. Negative eight minus two is equal to negative 10. Adding nine to this gives us negative one. The temperature at noon on day one was negative one degrees Fahrenheit.

We could show this working on a number line. The temperature initially dropped two degrees from negative eight. This takes us to negative 10. It then rose by nine degrees, taking us back up to negative one degrees Fahrenheit. There is a difference of plus seven degrees from the initial temperature to the temperature at noon.

On day two, we are told the temperature started at negative 14 degrees Fahrenheit. It rose five degrees Fahrenheit, so we need to add five to negative 14. It then rose by another four degrees Fahrenheit, so we need to add another four. Doing this in two steps, we can firstly add five to negative 14. This gives us negative nine. Adding another four to this gives us negative five. The temperature at noon on day two was negative five degrees Fahrenheit. A quicker method here would have been to have added nine to negative 14. This is because the temperature rose by a total of nine degrees Fahrenheit.

We are asked in the question to find the difference between these highest temperatures, the difference between negative one and negative five. If we consider a number line again, we can see the difference between negative one and negative five. To get from negative five to negative one, we would need to add four. And to get from negative one to negative five, we would subtract four. This means that the difference between the highest temperatures on the two days is four degrees Fahrenheit. When calculating the difference between two numbers, we would always choose the positive value.

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