Can someone help me please, I am having a hard time understanding these three problems
Clustering:
133 + 98 + 121 + 92 + 96
Substitute compatible numbers:
134 x 19
Front-end estimation with adjustment:
2,152 + 8,376
Of course! I'll explain how to solve each problem step by step.
1. Clustering:
To solve the clustering problem, you need to add the given numbers - 133, 98, 121, 92, and 96.
First, cluster the numbers by adding those that end in the same digits:
133 + 98 = 231
121 + 91 = 212
92 + 96 = 188
Now, add the clustered numbers together:
231 + 212 + 188 = 631
So, the sum of 133, 98, 121, 92, and 96 is 631.
2. Substitute Compatible Numbers:
To solve the substitute compatible numbers problem, you need to multiply two given numbers - 134 and 19.
To make the multiplication easier, you can use substitute compatible numbers. These are numbers that are close to the given numbers and easier to work with.
For example, you can round 134 to 130 and multiply it by 20 instead of 19. This approximation will give you a close enough answer.
So, 130 x 20 = 2600.
However, since you used substitute numbers, you need to adjust the answer. Multiply the difference between the substitute number and the original number by the other original number and add it to your previous answer.
In this case, the difference between 19 and 20 is 1, which you multiply by 134:
1 x 134 = 134
Finally, adjust your previous answer by adding the adjustment:
2600 + 134 = 2734
So, the approximate product of 134 and 19 is 2734.
3. Front-End Estimation with Adjustment:
To solve the front-end estimation with adjustment problem, you need to add two given numbers - 2,152 and 8,376.
Using front-end estimation, you only consider the leftmost digit of each number and ignore the rest:
2,000 + 8,000 = 10,000
This gives you an estimate of 10,000.
However, you need to adjust the answer by adding the difference between the original numbers and your estimation:
2,152 - 2,000 = 152
8,376 - 8,000 = 376
Now, add the adjustments to your estimation:
10,000 + 152 + 376 = 10,528
So, the sum of 2,152 and 8,376 is 10,528.
I hope this explanation helps you understand how to solve these problems! If you have any more questions, feel free to ask.