Video Transcript
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.
