Convert the map scale to a unit rate.How many inches represent one mile? Show your work. Interpret the meaning of the unit rate. 3/10 in = 7/8 mile
To convert the map scale to a unit rate, we need to determine how many inches represent one mile.
Given that 3/10 inches represent 7/8 mile, we can set up the following proportion to find the unit rate:
(3/10 inches) / (7/8 mile) = (x inches) / (1 mile)
To solve for x, we cross-multiply and then divide:
(3/10) * 1 mile = (7/8) * x inches
Simplifying the equation, we have:
3/10 = 7/8 * x
Now, we can isolate x by dividing both sides of the equation by (7/8):
x = (3/10) / (7/8)
To divide fractions, we multiply by the reciprocal of the divisor:
x = (3/10) * (8/7)
Multiplying across, we get:
x = (3 * 8) / (10 * 7)
Simplifying further, we have:
x = 24/70
Now, interpreting the meaning of the unit rate:
From our calculation, we find that 24/70 inches represent one mile. This means that for every 24/70 inches on the map, the actual distance on the ground is one mile. The unit rate of 24/70 inches per mile tells us the scale of the map. This means that if we measure a distance of 24/70 inches on the map, it will correspond to a distance of one mile in reality.