# 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.

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.

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.

## Recent Articles

1. ### Why the Rule of 72 Works

Oct 15, 18 11:05 AM

why the rule of 72 works- math explanation of where the 72 came from.

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

## Recent Lessons

1. ### Why the Rule of 72 Works

Oct 15, 18 11:05 AM

why the rule of 72 works- math explanation of where the 72 came from.

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.