How many equal sections divide a directed line segment if it is to be partitioned with a 2:7 ratio? 2, the least number given in the ratio 2, the least number given in the ratio
14, the least common multiple of the numbers given in the ratio

9, the sum of the numbers given in the ratio

5, the difference of the numbers given in the ratio

7, the greatest number given in the ratio

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  9, the sum of the numbers given in the ratio

Step-by-step explanation:

The reduced ratio 2 : 7 means that two parts correspond to one length and 7 parts correspond to the other length. That is, there are a total of 2+7 = 9 parts in the full length of the segment.

It is convenient to think of the line segment as being divided into 9 equal parts.

Additional comments

It is often helpful to consider the total number of "ratio units" in a given ratio. For example, in this problem, the shorter segment is 2/9 of the whole, and the longer one is 7/9 of the whole.

It can also be useful to consider what a "ratio unit" represents. If the whole segment is 27 inches long, then each of the 9 ratio units will represent 3 inches, for example. This means the division 2:7 is 2(3 in):7(3 in) = 6 in : 21 in.

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step-by-step explanation: