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Math 106: Contemporary Math9 chapters | 106 lessons

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Lesson Transcript

Instructor:
*Maria Airth*

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

Estimating is a method of calculating a result that is close to, but not exactly, the correct answer to a math problem. Why would you ever need to do this? This lesson reviews estimating and answers the question as to why you would do it.

Thanks for joining me for this lesson on **estimation**. When we estimate, we find an answer that is close to, but not exactly, the accurate answer for a problem. The symbol for estimation is a curvy equal sign like this. Note that if an answer is exact, you will see the exact equal sign (=). But, if it is an estimate, you show it by using a symbol that is also only close to but not exactly the equal sign. The symbol and the definition are similar in that way.

So, why on Earth would you ever want to get close to the right answer without actually doing the math correctly to get the exact right answer? Obviously, on a math test, you will want to get accurate answers, but in the real world often all you really need is a close approximation of the answer for it to be good enough to work with. Some areas of life where you might benefit by being able to estimate quickly include:

- Estimating how much you owe at the store so you can double check the stated amount before paying
- Estimating how far you will be able to get on your remaining fuel
- Estimating whether you will have time for all your errands in a day

All of these areas of everyday life are made easier, more efficient, and less costly if you have been able to estimate correctly.

One place that I find myself using estimation on a regular basis is when I'm shopping. Say I've gone into the store with exactly $15.00 in my pocket and I need five items. I have to be really careful not to go over my limit, so I estimate the values of each item I pick up by rounding to the nearest dollar. Here's my list:

Item | Exact Price | Estimate |
---|---|---|

Toilet paper | $5.75 | (about) $6.00 |

Milk | $1.30 | $1.00 |

Bread | $0.95 | $1.00 |

Apples | $2.60 | (can go up to) $3.00 |

Cheese | $2.20 | $2.00 |

By rounding the values to the nearest dollar, I can quickly add up the estimates to get $13.00, and feel confident that I have enough money to purchase all these items. If the items ring up to more than $15.00, I would be quite surprised and ask to have the total checked.

If we were to add up these accurately, it would come out to $12.80. My estimate was close enough (another meaning of the word estimate) to the exact total to allow me to gauge what I could get at the store. I'm sure you can see how this might come in handy next time you are in a hurry and only have a limited amount to spend.

So, knowing that you have enough money to purchase all you need at the store is nice, but if you make a mistake, you can just put something back to reduce your bill. No big deal! What about estimating the fuel remaining in your car and how far you can get with it? This is an everyday problem that can have dire consequences if you get it wrong.

If I know that my car gets about 25 miles per gallon and has a tank capacity of about 23 gallons, I can estimate how far I can go on my remaining fuel. The first thing I would do is to round my tank capacity down to 20. Then, I can estimate about 5 gallons per quarter tank.

So, if I see that my fuel gauge is just over half way, I would round to half and think that is approximately 10 gallons times 25 miles per gallon. That gives me about 250 miles to go.

Notice that I rounded everything down. This gives a buffer of just a few extra gallons. Estimation is not exact, thus, when estimating consider the consequence of being wrong and estimate in the direction that will give you the best outcome if you are wrong.

When you are busy, it is easy to accidentally get behind and end up late for appointments. Estimating time can help make sure this doesn't happen. When estimating time, like estimating with money and fuel, estimate in the direction that is going to give you more time rather than less.

Let's say you want to know if you will have enough time to go shopping, get gas, and get back to work during your lunch break. Well, you can estimate the times. You have 60 minutes for lunch. It takes about 20 minutes to shop, 20 to get gas, and another 10 to get to and from the parking lot. With this estimation, you would have just enough time to get these errands done, but it would be tight as you can see.

Thus far, I have talked about the real-world application of estimation, but you can use it when calculating math solutions in a more academic setting, as well. I'm sure you know that it is important to check your answers when doing any math work. Estimation can give you a quick way to check that your answer makes sense. For example, 375 + 205 + 120 + 515; if we estimate first, we would estimate 400 + 200 + 100 + 500 = 1,200.

This is really fast and gives us an idea of where we should end up. If we were to use a calculator and end up with a result of 700, we would immediately know that there was a problem and go back to find it (in this case, the last number, 515, was left out of the result). The correct sum is 1,215. So, estimating prior to working out an exact calculation helps to ensure that mistakes are caught.

It is a good idea to estimate your answer even if you intend to use a calculator because it is easy to type numbers incorrectly into a calculator or computer. Knowing where you are headed helps to know if you have gotten there.

Did you notice anything similar about all of these scenarios? Each of the scenarios involved being in a hurry and using multiples of ten. Estimation is best used when you need a close enough answer in a short space of time. It can be used to make quick decisions before an accurate calculation is required. Also, the easiest way to estimate is to round to the nearest multiple of ten - this is because the tens are so easy for us to work with. Remember, estimating is about getting a close enough answer as easily as possible.

At the beginning of this lesson, I defined **estimation** as a process by which an answer that is close to, but not exactly, the correct answer is found. There are many specific reasons why a person might want to estimate, but the main reasons to estimate are:

- Needing an approximate answer in a hurry
- Wanting to have an idea of the accurate answer before the calculation is completed

We also learned that rounding to the nearest multiple of ten is the easiest, most efficient way to estimate in both real-world and academic scenarios.

This math lesson can teach you how to:

- Recall what it means to estimate
- Understand the importance of estimation
- List real world examples that use estimation in every day life
- Demonstrate estimation using non-real world examples
- Consider easy ways to estimate

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Math 106: Contemporary Math9 chapters | 106 lessons

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