Convert the map scale to a unit rate. How many inches represent one mile? Show your work. Interpret the meaning of the unit rate. 3/10in.=7/8mi.
3/10 in : 7/8 mi = 3/10 in: 4620 in = 1:15400
divide both sides by 7/8
3/10 * 8/7 = 12/35 in = 1 mi
to get the unit rate, you want to end up with 1:n for some value of n.
so, for example,
3 pt : 4 gal = 3pt : 8*4 pt = 3:32
Now divide by 3 to get 1 : 32/3
You can always multiply or divide both sides of a ratio to get the unit (1) on one side. ratios are just fractions.
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ok, thx
thank you, oobleck
can you explain, im confused
To convert the map scale to a unit rate, we need to find how many inches represent one mile. Let's first examine the given ratio: 3/10in. = 7/8mi.
To convert the fraction 3/10in. to a unit rate, we can multiply both the numerator and denominator by the same number to have a denominator of 1. In this case, we will multiply them by 8.
((3/10in.) * (8/8)) = 24/80in.
Next, we'll do the same for the fraction 7/8mi., multiplying both the numerator and denominator by the same number to get a denominator of 1. In this case, we will multiply them by 10.
((7/8mi.) * (10/10)) = 70/80mi.
Now, we have the ratios of 24/80in. to 70/80mi. To simplify these fractions, we can divide both the numerator and denominator by their greatest common factor, which is 10.
(24/10)in. / (70/10)mi.
(12/5)in. / (7/10)mi.
So, the conversion ratio is 12/5 inches to 7/10 miles.
Interpretation: The unit rate indicates that for every 5/10 (or 1/2) mile on the map, it represents 12 inches in real life.