Final answer:
The ratio of gravel to decking in a garden, subtract the gravel portion (2/7) from the total (7/7) to get the decking area (5/7), then simplify the ratio 2/7 to 5/7 to get the answer in simplest form, which is 2:5.
Step-by-step explanation:
The question involves finding the ratio of gravel to decking in a garden when 2/7 of its area is covered with gravel and the rest with decking. To find this ratio, let's denote the total area of the garden as 1, or 7/7, to make it easier to work with fractions. Now, if 2/7 of the area is gravel, then the area of the decking is the remainder, which is 7/7 minus 2/7, resulting in 5/7.
The ratio of the gravel area to the decking area will therefore be the fraction representing the gravel area (2/7) divided by the fraction representing the decking area (5/7).
To simplify the ratio of gravel to decking, we divide both the numerator and the denominator by the same number, which is the numerator of the gravel's fraction (2):
Gravel to Decking Ratio = (2/7) ÷ (5/7) = 2/5.
This means for every 2 units of area of gravel, there are 5 units of area of decking, making the simplest form of the gravel to decking ratio 2:5.