Hey I am trying to help my son in math.

The question is, The scale of a district map is 1 over 10000. Find the distance on the map, in centimeters, for each of the following distances.

a) 800m

b) 5 km

I need to see how this is worked out.

the map probably has a scale of 1 : 10 000

which means 1 cm on the map = 10 000 cm in the real world
so convert 800 m to cm
800 m = 80 000 cm

now you can just reason it out ...
if 10 000 cm needs 1 cm on the map
then 80 000 cm will need 8 cm on the map

or
you could set up a ratio
x/80 000 = 1/10 000
cross-multiply to get
10000x=80000 , divide both sides by 10000
x = 8

do the second one the same way ...
5 km = 5 000 m = 500 000

x/500 000 = 1/ 10 000
10 000x = 500 000
x = 50

thank you

Sure! I can help you with that.

To find the distance on the map, we need to use the scale of the map. In this case, the scale is given as 1 over 10000. This means that for every 1 unit of distance in real life, the map represents 10000 units of distance.

Now let's work out the distances on the map for each given distance:

a) 800 meters:
Since the scale is given in terms of 1 unit of real distance to 10000 units on the map, we can set up a proportion to solve for the distance on the map.

1 unit of real distance / 10000 units on the map = 800 meters / x units on the map.

By cross-multiplying, we get:
800 meters * 10000 units on the map = x units on the map.

Now calculate:
800 * 10000 = 8,000,000.

The distance on the map for 800 meters is 8,000,000 units.

b) 5 kilometers:
Similar to the previous case, we set up a proportion:

1 unit of real distance / 10000 units on the map = 5 kilometers / x units on the map.

By cross-multiplying, we get:
5 kilometers * 10000 units on the map = x units on the map.

Now calculate:
5 * 10000 = 50,000.

The distance on the map for 5 kilometers is 50,000 units.

Therefore, the distance on the map for 800 meters is 8,000,000 units and for 5 kilometers is 50,000 units.

Please note that these distances are given in arbitrary units based on the scale of the map. If you want to convert them into centimeters, you need to know the conversion rate for the arbitrary units to centimeters.