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Cluster estimationCluster 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
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