What is the easiest way to figure out how to set up an equation that consists of the is/of..this is hard for me to set up a the problem correctly..Help!

Question

such as : If 1/4 inch on a map represents 8 miles, how many miles are represented by 3 and 3/4 inches on the map?

Answer 1

1/4 inch represents 8 miles

how many 1/4 inch segments are in 3 3/4 inches ?

you can divide 3 3/4 by 1/4 to get (15/4)/(1/4)=(15/4)*(4/1)=15

you have 15 groups of 8 which is 15*8=120 miles

another way to look at it:

each inch has 4 quarters(1/4), you have 3 inches, 3*4=12 plus 3/4 has 3 quarters(1/4) for a total of 15 quarters(1/4)

Answer 2

Hi Kristin,

 

1/4 inch on a map represents miles=8

 

1 inch on a map represents  miles=8÷1/4=8×4

 

3 3/4=15/4 inch on a map represents miles=8×4×15/4=8×15=120 miles

Answer 3

The easiest way to set this up is as a proportion:

 

3 3/4          x

------  =  -------      where x is the unknown number of miles represented by 3 3/4 inches

(1/4)         8  

 

The ratio of 3 3/4 inches to 1/4 inch is the same as the unknown x miles is to 8 miles.  Now solve for x.

 

Well since the answer cat is now out of the bag, I'll go ahead and solve for x:

 

8*4*(15/4) = x

8*15 = x

120 miles = x