Converting map scale to unit rate. How many inches are in a mile?
3/10 in = 7/8 mi
My answer: multiply the numerator by 8; I would get 24/10; 24/10 is equal to 70 in; 24/35 is equal to 24/10; So my answer would be 24/10 and/or 12/35?
7/8 * 8/7 = 1, so
3/10 * 8/7 = 24/70 = 12/35 in/mi
or, to convert miles to inches,
1 mi * (3/10 in)/(7/8 mi) = 3/10 * 8/7 = 12/35 mi
you are correct, except for the typos.
Your question was:
How many inches are in a mile?
What follows in your post is a mystery to me.
1 mile
= 5280 ft
= 5280(12) inches
= 63,360 inches
Now what is your map scale ?
Are we to find that scale?
does 3/10 inch on your map represent 7/8 mile?
then 3/10 inch -----> (7/8)(63,360) inches or 55440 inches
then 1 inch -----> (55440)(10/3) or 184,800
so the scale is 1 : 184,000
(go metric !)
Well, well, well, looks like we've got a mathematical clown act going on here! Let me straighten things out for you, my friend.
No need to complicate things with fractions. We have a simple equation: 3/10 inches = 7/8 miles.
To find out how many inches are in a mile, simply multiply both sides of the equation by 8. That gives you:
(3/10) * 8 = (7/8) * 8
Don't worry about the arithmetic; I got your back. On the left side, we have 24/10 inches, which can be simplified to 12/5 inches. On the right side, we have 7 miles. So, the correct answer is:
There are 12/5 inches in a mile. But to make it easier to understand, we can say that there are approximately 2.4 inches in a mile.
I hope that clears things up for you, my mathematically inclined friend!
To convert the given map scale of 3/10 in = 7/8 mi to find how many inches are in a mile, you can use the concept of unit rates.
First, you need to find the unit rate, which is the ratio of inches to miles. To do this, you can set up a proportion where the two fractions are equal:
3/10 in = 7/8 mi
To convert inches to miles, you want the denominator of the mi fraction (8) to be 1 mile. To do this, you can multiply both the numerator and denominator of the mi fraction by a factor of 10:
3/10 in = (7/8) * (10/10) mi
3/10 in = 70/80 mi
Simplifying the mi fraction by dividing both the numerator and denominator by their greatest common divisor (which is 10 in this case), you get:
3/10 in = 7/8 mi
Now you can see that the unit rate is 3/10 in per 7/8 mi. Therefore, there are 3/10 inches in 7/8 mile.
To find out how many inches are in 1 mile, you can set up another proportion with the given unit rate:
(3/10 in) / (7/8 mi) = x in / 1 mi
Cross-multiply to solve for x:
(3/10) * (1) = (7/8) * (x)
3/10 = 7/8 * x
Now, you need to isolate x by multiplying both sides of the equation by the reciprocal of 7/8:
(3/10) * (8/7) = (7/8) * (x) * (8/7)
24/70 = x
Simplifying the fraction 24/70, you get:
12/35 = x
Therefore, there are 12/35 inches in 1 mile.
So, your answer is indeed 12/35 or approximately 0.3429 inches per mile.