Let the greatest element in a set be 445 and the range of the set be 254. What is the smallest element of this set?
We know that, in order to calculate the range of any set, we subtract the smallest element from the largest element. In this question, we are given the largest or greatest element and the range of the set and need to calculate the smallest element. We can do this by using the formula or by using the number line. Substituting in our values gives us 254 is equal to 445 minus 𝑥, where 𝑥 is the smallest element of the set. Adding 𝑥 to both sides of this equation gives us 𝑥 plus 254 is equal to 445. We can then subtract 254 from both sides of this equation to work out the value of 𝑥. 𝑥 is equal to 191 as 445 minus 254 is 191. We can therefore conclude that the smallest element of the set is 191.
As already mentioned, we could also have calculated this using a number line. We know that the greatest value is 445. The range is the difference between the greatest or largest value and the smallest value. In this case, we are told it is 254. The difference between the smallest and greatest value is 254, which means we can subtract this from 445 to calculate the smallest value. Once again, this gives us an answer of 191.