Final answer:
The crust and mantle combined are proportionally larger than the outer and inner cores combined by a fraction of 71/200. This calculation involves adding and comparing fractions that represent the respective sizes of Earth's layers.
Step-by-step explanation:
The question covers a mathematical comparison between the sizes of the different layers of the Earth as given by fractions.
To find out the difference in size between the crust and mantle combined versus the outer and inner cores combined, we can add up the fractions corresponding to each pair of layers and then calculate the difference between the two sums.
For the crust and mantle combined, the given fractions are 1/200 for the crust and 9/20 for the mantle. Adding these up gives us the total proportion of Earth occupied by these two layers:
1/200 + 9/20 = 1/200 + 180/200 = 181/200
For the outer core and inner core combined, the given fractions are 7/20 for the outer core and 1/5 for the inner core. Adding these gives us the total proportion for the cores:
7/20 + 1/5 = 35/100 + 20/100 = 55/100 = 110/200
To find the difference, we subtract the sum related to the cores from the sum for the crust and mantle:
181/200 - 110/200 = 71/200
Therefore, the crust and mantle combined are larger than the outer and inner cores combined by a fraction of 71/200. This fraction represents the difference in size between these two groups of Earth's layers.