To solve this problem, we will first add the two numbers in the ratio together which are 3 and 7. This will give us the total ratio. So, 3 + 7 equals 10.
The total ratio is representing the original length of the wood. Each unit in this ratio corresponds to a certain length of the wood.
We're asked to find what fraction of the original length is the longer piece. The longer piece corresponds to the larger number in the ratio. That larger number is 7.
To find the fraction of the original length that corresponds to the larger piece, we'll divide the larger number in the ratio (7) by the total ratio (10). So we have 7 over 10.
Therefore, the longer piece of wood corresponds to 0.7 of the original length. This means that the longer piece is 70% of the original length of the wood.