I am not a Math student whatsoever :S this is in my Geography course and I'm very confused can anyone help me out? I'm a History Major *shy face*

Imagine that a woodlot 2x3km in size has been marked on two separate maps. Map A has a scale (in mixed units) of 1cm: 80m and Map B has a scale of 5mm:110m.

a. What are the Representative Fractions of Map A and Map B
b. Which map has the larger scale? (Where 1/10 is a larger scale than 1/20)
c. Which ma shows the most detail of woodlot
d. What are the dimensions of the woodlot (in mm) on each of the two maps...

Any help and guidance would help. I want to learn this, I need to learn it...

2. First we will need to know how to interpret the scales. the scales are given as ratios. for instance, when they say the scale is 1cm : 80m it means that each cm on the map represents 80m on the ground. also, ratios can be represented as fractions, so $\displaystyle 1 cm:80 m$ is the same as $\displaystyle \frac {1 cm}{80 m}$. so this is how we convert them to fractions, of course we have to have the same units for this to work, which is why the second thing you need to know is the conversion factors.

Conversion Factors:
1 m = 100 cm
1 m = 1000 mm
1 km = 1000 m

Now let's get to it.

Originally Posted by Ozmozis
Imagine that a woodlot 2x3km in size has been marked on two separate maps. Map A has a scale (in mixed units) of 1cm: 80m and Map B has a scale of 5mm:110m.

a. What are the Representative Fractions of Map A and Map B
For map A, we have:

Scale: $\displaystyle \frac {1 cm}{80 m} = \frac {10^{-2} m}{80 m} = \frac {1}{8000}$ ------> representative fraction for map A (The size of the lot on the map is 1/8000 th of it's size in real life)

For map B, we have:

Scale: $\displaystyle \frac {5 mm}{110 m} = \frac {5 \times 10^{-3} m}{110 m} = \frac {1}{550000}$ -------> representative fraction for map B (The size of the lot on the map is 1/550000 th of it's size in real life)

b. Which map has the larger scale? (Where 1/10 is a larger scale than 1/20)
map A has the larger scale, since $\displaystyle \frac {1}{8000} > \frac {1}{550000}$

c. Which ma shows the most detail of woodlot
i would guess the one that has the larger scale, so map A

d. What are the dimensions of the woodlot (in mm) on each of the two maps...
for map A, on which the lot is 1/8000 th of it's actual size, the size of the woodlot on the map would be:

$\displaystyle \frac {1}{8000} \times 2 km \times \frac {1}{8000} \times 3 km = \frac {1}{4000} km \times \frac {3}{8000} km = 250 mm \times 375 mm$

for map B, on which the lot is 1/550000 th of it's actual size, the size of the woodlot on the map would be:

$\displaystyle \frac {1}{550000} \times 2 km \times \frac {1}{550000} \times 3 km = \frac {1}{275000} km \times \frac {3}{550000} km = \frac {40}{11} mm \times \frac {60}{11} mm$

3. Originally Posted by Jhevon
i fixed the LaTex erros i had, so check now. the LaTex error... was there because i made an error in the code that i typed to get the "pretty" math format
Alright, now I'm staring to piece it together

Thanks stranger

4. Originally Posted by Ozmozis
Alright, now I'm staring to piece it together

Thanks stranger
sorry, i had one more error to fix, in the intro. now everything should be ok. if you see any more LaTex errors around the place, tell me, also, if you have any questions about anything, ask me