Lesson 9: Map Scale

§Text Passage

1Summary 重點摘要

Map scale is the ratio of map distance to real distance. For example, 1:50000 means 1 cm on map = 50000 cm real = 500 m. Learn to calculate real distance and map distance.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Block 1: Reading the ScaleA scale of 1:50000 gives the ratio of map distance to real distance: 1 cm on the map stands for 50000 cm in reality, that is 500 m. Likewise 1:100000 means 1 cm on the map stands for 100000 cm, that is 1 km. Why express it as a ratio? Because a map must shrink a vast area onto paper, and the scale states the shrinkage factor once for the whole sheet; every part of the map shrinks by the same factor, which is what makes measured distances accurate. The foundation of every conversion is 1 km = 1000 m = 100000 cm, to be known by heart. A common mistake is to read 1:50000 as '1 cm on the map equals 5 km in reality', although 50000 cm is only 0.5 km; after reading the scale, run one unit conversion and be clear about what 1 cm really stands for.
2. Block 2: Find Real DistanceGiven the map distance, find the real distance by multiplying the map distance by the denominator of the scale: map distance × denominator = real distance. For example, on a scale of 1:200000 with 3 cm on the map, the real distance = 3 × 200000 = 600000 cm, which converts to 6000 m, that is 6 km. Why multiply? Because 1 cm on the map stands for 200000 cm in reality, so 3 cm on the map is 3 such amounts, and finding 'how many times' uses multiplication. It is best to multiply first and convert units afterwards, writing the middle steps out for easy checking. Another example: on a scale of 1:50000, 8 cm on the map gives 8 × 50000 = 400000 cm = 4 km. A common mistake is to skip the unit conversion and write 600000 cm straight down as 6 km, out by a hundred thousand; cm to km divides by 100000, so write each step clearly.
3. Block 3: Find Map DistanceGiven the real distance, find the map distance by dividing the real distance by the denominator of the scale: real distance ÷ denominator = map distance. For example, a real distance of 10 km on a scale of 1:50000: first convert 10 km into 1000000 cm, then compute 1000000 ÷ 50000 = 20 cm, so the map should show 20 cm. Why convert first? Because both sides of the scale are in cm; only after the real distance is in cm does the quotient give the map centimetres. Multiplication and division undo each other, so forward and backward calculations check each other: 20 × 50000 = 1000000 cm = 10 km, matching the question. A common mistake is to divide 10 ÷ 50000 without converting, producing a tiny number; another is to convert the wrong way, treating 10 km as 10000 cm, when km to cm multiplies by 100000, not by 10000.
4. Block 4: Unit ConversionUnit conversion is where scale questions most often go wrong, so three relations must be fixed in mind: 1 km = 1000 m, 1 m = 100 cm, and 1 km = 100000 cm. Why do km and cm differ a hundred-thousand-fold? Because kilometres to metres multiplies by a thousand, and metres to centimetres multiplies by a hundred again, and a thousand times a hundred is a hundred thousand. When solving, look first at the units given: if the question gives km, convert to cm before dividing by the denominator; if the answer is wanted in km, divide the cm result by 100000. For example, 3 km = 3000 m = 300000 cm, and 250000 cm = 2.5 km. A common mistake is to multiply by only one thousand from km to cm, missing the second hundred; write out every middle step — first 3 km = 3000 m, then 3000 m = 300000 cm — and the chain stays orderly.
5. Block 5: Linear ScaleSome maps show no numerical scale but a drawn line marked '0, 1 km, 2 km'; this is a linear scale: a fixed length on the map stands for 1 km in reality. Why do maps favour it? Because after a map is photocopied larger or smaller, a numerical scale fails, while a linear scale shrinks and grows together with the picture and stays accurate. How to use it: measure with a ruler the length of the segment from 0 to 1 km; if it measures 2 cm, then 2 cm on the map stands for 1 km, from which the numerical scale follows as 1:50000, since 1 km = 100000 cm and 100000 ÷ 2 = 50000. A common mistake is to measure from the edge of the ruler instead of the 0 mark; before measuring, align the ruler's 0 mark with the start of the segment.
6. Block 6: Word ProblemThe steps for a full word problem: confirm the scale, multiply the map distance by the denominator to get real centimetres, and finally convert to the unit the question asks for. For example, two places 4 cm apart on a map of scale 1:250000 have real distance 4 × 250000 = 1000000 cm = 10 km. Why follow fixed steps? Because word problems carry large numbers and a tangled order invites mid-way errors; writing step by step keeps the work clear and makes checking easy. Another example: two towns 12 cm apart on a 1:50000 map are 12 × 50000 = 600000 cm = 6 km apart in reality. A common mistake is to stop at cm when the question asks for km and no conversion is made; read what unit the question finally wants, and the last step of the answer is always the conversion to that unit.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Scale = map distance : real distance
• Real distance = map distance × scale denominator
• Map distance = real distance ÷ scale denominator
• 1 km = 1000 m = 100000 cm
• Always convert units first