Estimate
An estimate is a value you arrive at that is close to but not necessary equal to the exact value. It is an approximate value. Estimation is the process of arriving at an approximate value, or estimate.
Estimation strategies
There are many different estimation strategies that people use. Most estimation strategies work by breaking up a problem into simpler parts, often by making allowances that will keep the value close to, but not equal to the original problem. Below are a few examples of estimation strategies we may use in everyday life.
General things to remember
- Change numbers to end in 0s and 5s where possible. These are usually easier to do arithmetic with. Try to keep track of your changes; if you change some value to be bigger, maybe change another to be smaller to keep the estimate more accurate.
- The larger the numbers involved, the less difference small variations will make, so you can simplify these more for an estimate than you may for smaller numbers; 35,357 + 2231 = 37,588 is not much different from 35,000 + 2000 = 37,000, in terms of percentage difference.
- Practice! The most effective estimation strategy is the strategy that works for you, but many strategies can be used for a given situation, and in many cases, using multiple strategies can make the estimation even more efficient and accurate.
Rounding to the nearest 0
Given the problem
22 × 12 = ?
we can break the problem up in a number of different ways, such as:
22 × 10 = 220
or
20 × 12 = 240
Both of these rely on changing the values such that they end in 0s, making it easier for us to estimate the answer. Multiplying by 10 is one of the easiest multiplication problems we learn, since it involves just adding a 0 to whatever is being multiplied by 10.
The exact value is 264, and our second, more accurate estimation, was 240. Depending on how accurate we need to be, 240, or even 220 may be a good enough estimation of 264.
Breaking the problem up into multiple parts
Given the problem
2345 + 123 = ?
we can break it up into something we can calculate quickly such as:
2300 + 100 = 2400
and
40 + 20 = 60
In the first part, we just removed the 45 and 23 so that we could easily add 100 to 2300. In the second part we changed the 45 and 23 to 40 and 20, since it is part of a larger number, and the 5 and 3 won't make a big difference in the final number. 40 + 20 is the same as 4 + 2 with an added zero, giving us 60. Then we sum both:
2400 + 60 = 2460
The exact answer is 2468, which is very close to our estimate.
Grouping numbers
Some numbers are easier to work with especially once we are more comfortable with basic arithmetic. Given the problem
14 + 73 + 41 + 26 = ?
we can group 14 + 41 and 73 + 26. If we round to the closest 0, we get:
10 + 40 = 50
and
70 + 30 = 100
Note that in either of these we can remove the 0s when adding if we want to simplify it further, then add the 0s back after we've finished adding.
100 + 50 = 150
The exact answer is 154, which is quite close to our estimate.
Using averages
Given the problem
420 + 377 + 399 + 408 = ?
we can see that that all of the values are close to 400, or that their differences more or less cancel each other out such that estimating them as 400 works; 420 is a difference of 20 from 400 and 377 is a difference of 23. Knowing this, we can just multiply 400 by the number of values, 4, to get the following estimate:
400 × 4 = 1600
The exact value is 1604, so our estimate is very close.
Estimation in everyday life
There are many ways in which basic estimation can be helpful in everyday life.
Estimating cost
If you are buying some 5 pieces of candy that cost 50 cents each, and your total comes to $10.15, you can quickly know that there has been a mistake using estimation. You should be getting closer to 20 pieces of candy for that price.
Another way you can use estimation in shopping is to make sure you have enough money to buy the things you want. For example, if you have a budget of $20 to spend on groceries, you can round each item you're buying up to make sure you have enough. If something costs $1.50, you can estimate it as $2. If something costs $1.12, you could estimate it as $1, trying to keep your estimations relatively even. To be safe you could also round everything up so instead of saying something worth $1.12 is $1, you could say it's worth $2, or $1.50. The idea is to make it simpler for you to add in your head while still ensuring you have enough money. How accurate you want to be is up to you.
Estimating time
Estimating time is something you are likely to do frequently in your everyday life. This can come in many different forms, from estimating travel time/distance, to how much time an activity may take, to how much you can fit into your day based on how much time you have. For example, say that you have soccer practice from 4-5 pm, and your friend wants to watch a movie at 5:30 pm. Do you have time to clean up and get to the theater by 5:30 pm? This depends on how long it takes you to clean up, whether you'd need to go home to do it, and how long it'd take you to get to the theater, among many other potential factors. As long as you make an estimate of how long each activity should take you, and the estimates sum to less than 30 minutes, you would be able to make it in time.
There are many other ways that estimation can be useful in everyday life, the above are just two examples.