basic mathematics image
 basic mathematics image

Cluster estimation


Cluster estimation can be used to estimate sums and products when the numbers you are adding or multiplying cluster near or is close in value to a single number

Example # 1:

Estimate 699 + 710 + 695 + 705 + 694 + 715

Carefully examine all the numbers above. You should notice that they all cluster around 700

Therefore, 700 + 700 + 700 + 700 + 700 + 700 will give us a good estimate for the answer.

Instead of adding 700 six times, just do 6 × 700.

700 × 6 = 4,200 is a good estimate of the sum

In fact, the real answer 699 + 710 + 695 + 705 + 694 + 715 = 4,218. Thus 4,200 is indeed close to the real answer

Example # 2:

Estimate 257 + 247 + 255 + 245

Carefully examine all the numbers above. You should notice that they all cluster around 250

Therefore, 250 + 250 + 250 + 250 will give us a good estimate for the answer.

Instead of adding 250 four times, just do 4 × 250.

250 × 4 = 1,000 is a good estimate of the sum

In fact, 257 + 247 + 255 + 245 = 1004. Thus 1000 is indeed close to the real answer

Example # 3:

Estimate 23 × 18 × 22 × 17

This time, you are estimating a multiplication problem. However,you will still use cluster estimation to estimate the product.

Just notice that all numbers above cluster around 20

Therefore, 20 × 20 × 20 × 20 will give us a good estimate for the answer.

Multiply the 2s to get 16.

Then, just put four zeros after 16 to get 160,000

The real answer is 23 × 18 × 22 × 17 = 154,836.

It is not a very good estimate, but we can live with that

In general, addition will give better estimates

Example # 4:

Estimate 8 × 11 × 12

Just notice that all numbers above cluster around 10

Therefore, 10 × 10 × 10 will give us a good estimate for the answer.

10 × 10 × 10 = 1000

The real answer is 8 × 11 × 12 = 1056.



Fun math game: Destroy numbered balls by adding to 10







Page copy protected against web site content infringement by Copyscape












 
Copyright © 2008. Basic-mathematics.com. All right reserved