Steply

Scale drawings and maps

Geometry · 20 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Multiply both sides
  2. Change the unit
  3. Check

The steps for Scale 1 : 50000, 3 cm on the map. Every solution names its steps, so you always know what comes next.

Worked examples

Map scale 1 cm : 5 km, 7 cm on the map Easy

The question

Question: with the scale 1 cm : 5 km, how long is 7 cm on the map for real?

map → real

The scale means: 1 cm on the map is 5 km for real.

1 cm → 5 km

1 Multiply both sides

On the map we have 7 cm.

That is 7 times 1 cm.

So the real length is 7 times 5 km too.

7 cm → 5 × 7 km

We multiply both sides by the same number, 7.

× 7 on both sides

5 times 7 is 35.

So the real length is 35 km.

7 cm → 35 km

2 Check

Let's check: go back.

35 divided by 5 should give the map length, 7.

35 ÷ 5 = 7

We get it again.

So 35 km is right!

Let's look back.

First: multiply both sides.

Last: check.

Answer
7 cm → 35 km

▶ Watch it solved

Map scale 1 cm : 5 km, 2.5 cm on the map Medium

The question

Question: with the scale 1 cm : 5 km, how long is 2.5 cm on the map for real?

map → real

The scale means: 1 cm on the map is 5 km for real.

1 cm → 5 km

1 Multiply both sides

On the map we have 2.5 cm.

That is 2.5 times 1 cm.

So the real length is 2.5 times 5 km too.

2.5 cm → 5 × 2.5 km

We multiply both sides by the same number, 2.5.

× 2.5 on both sides

Forget the points: 5 times 25 is 125.

The numbers have 1 digit after the point.

So the answer has 1 too: 12.5.

5 × 25 = 125 → 12.5

So the real length is 12.5 km.

2.5 cm → 12.5 km

2 Check

Let's check: go back.

12.5 divided by 5 should give the map length, 2.5.

12.5 ÷ 5 = 2.5

We get it again.

So 12.5 km is right!

Let's look back.

First: multiply both sides.

Last: check.

Answer
2.5 cm → 12.5 km

▶ Watch it solved

Scale 1 : 50000, 3 cm on the map Harder

The question

Question: with the scale 1 : 50000, how long is 3 cm on the map for real?

map → real

The scale 1 : 50000 means: 1 cm on the map is 50000 cm for real.

Everything is 50000 times bigger.

1 cm → 50000 cm

1 Multiply both sides

On the map we have 3 cm.

That is 3 times 1 cm.

So the real length is 3 times 50000 cm too.

3 cm → 50000 × 3 cm

We multiply both sides by the same number, 3.

× 3 on both sides

50000 times 3 is 150000.

So the real length is 150000 cm.

3 cm → 150000 cm

2 Change the unit

150000 cm is a big number.

100 cm make 1 m, so we divide by 100.

100 cm = 1 m

150000 divided by 100 is 1500.

So it is 1500 m.

150000 cm = 1500 m

1000 m make 1 km, so we divide by 1000 too.

1000 m = 1 km

So it is 1.5 km.

1500 m = 1.5 km

3 Check

Let's check: go back.

150000 divided by 50000 should give the map length, 3.

150000 ÷ 50000 = 3

We get it again.

So 1.5 km is right!

Let's look back.

First: multiply both sides.

Then: change the unit.

Last: check.

Answer
1500 m = 1.5 km

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. map scale 1 cm : 5 km, 7 cm on the map
    Answer
    7 cm → 35 km
  2. map scale 1 cm : 2 km, 6 cm on the map
    Answer
    6 cm → 12 km
  3. map scale 1 cm : 10 km, 4 cm on the map
    Answer
    4 cm → 40 km
  4. scale 1 cm : 3 m, 5 cm on the drawing
    Answer
    5 cm → 15 m
  5. map scale 1 cm : 4 km, 12 km in real life
    Answer
    3 cm → 12 km
  6. scale 1 cm : 2 m, 8 m in real life
    Answer
    4 cm → 8 m
  7. map scale 1 cm : 25 km, 3 cm on the map
    Answer
    3 cm → 75 km
  8. scale 1 : 100, 4 cm on the drawing
    Answer
    400 cm = 4 m

Medium

  1. map scale 1 cm : 5 km, 2.5 cm on the map
    Answer
    2.5 cm → 12.5 km
  2. scale 1 : 50, 6 cm on the drawing
    Answer
    300 cm = 3 m
  3. scale 1 : 200, 7 cm on the plan
    Answer
    1400 cm = 14 m
  4. map scale 1 cm : 20 km, 90 km in real life
    Answer
    4.5 cm → 90 km
  5. scale 1 cm : 4 m, 10 m in real life
    Answer
    2.5 cm → 10 m
  6. map scale 1 mm : 2 m, 35 mm on the map
    Answer
    35 mm → 70 m

Harder

  1. scale 1 : 50000, 3 cm on the map
    Answer
    1500 m = 1.5 km
  2. scale 1 : 25000, 8 cm on the map
    Answer
    2000 m = 2 km
  3. scale 1 : 20, 2.5 cm on the model
    Answer
    2.5 cm → 50 cm
  4. map scale 1 cm : 15 km, 4.2 cm on the map
    Answer
    4.2 cm → 63 km
  5. map scale 1 cm : 50 km, 175 km in real life
    Answer
    3.5 cm → 175 km
  6. scale 1 : 1000, 6.5 cm on the plan
    Answer
    6500 cm = 65 m