Video: Evaluating Algebraic Fractions Involving Decimal Numbers

Video Transcript

If 𝑚 equals twenty-one point four, 𝑝 equals twenty-three point four, and 𝑛 equals nine, evaluate 𝑚 plus 𝑛 plus 𝑝 all divided by 𝑝 to the nearest tenth.

In order to evaluate our expression, 𝑚 plus 𝑛 plus 𝑝 divided by 𝑝, we need to take our values for 𝑚, 𝑝, and 𝑛 and plug those into our expression. We will replace 𝑚 with the value twenty-one point four. Replace 𝑛 with the value nine. And replace both 𝑝’s with the value twenty-three point four.

Now we need to simplify. First we need to add all the numbers on our numerator to simplify our numerator. The numerator is the top portion of your fraction, so let’s add twenty-one point four plus nine plus twenty-three point four. This results in fifty-three point eight. divided by twenty-three point four, which equals two point two nine nine one four five three. However, it tells us to round to the nearest tenth. The first place value to the right of the decimal is our tenths place. So when it says to round to the nearest tenth, our final answer should be ending in a tenths place.

So we need to decide how to round. We must look at the place value to the right of the one that we’re rounding to in order to decide whether to keep our two a two or two rounded up to a three. So we look at the hundredths place. That’s where the nine is. Number zero through four would keep the two the same. Numbers five through nine would make the two round up to a three. So since nine is our- in our hundredth place and we’re rounding to the tenths place, our two will turn into a three. So our final answer is two point three.