A scale ratio shows how measurements on a drawing relate to actual sizes. In our example, 1 centimeter on the drawing represents 7 meters in real life. This can be written as 1 to 7 or as a fraction 1 seventh. When we create scaled drawings, all measurements shrink or grow by the same factor to maintain the correct proportions.
To solve scale problems, we set up a proportion. The ratio of drawing length to real length equals the scale ratio. For our room that is 14 meters long, we set up the equation: unknown drawing length over 14 meters equals 1 centimeter over 7 meters. It's crucial to keep the units consistent in our proportion. This method works because ratios remain constant in scaled drawings.
To solve our proportion, we cross multiply. This means multiplying the unknown by 7 meters equals 1 centimeter times 14 meters. Simplifying, we get question mark times 7 equals 14 centimeters. Dividing both sides by 7 gives us 2 centimeters. We can verify our answer by checking that the ratio 2 centimeters to 14 meters simplifies to 1 centimeter to 7 meters, confirming our solution is correct.
Let's visually verify our solution. The actual room is 14 meters long, shown here in blue. Our scaled drawing is only 2 centimeters, shown in red. When we place a ruler next to our drawing, we can clearly see it measures 2 centimeters. The scale factor of one-seventh means our drawing is one-seventh the size of the real object. This visual comparison confirms our mathematical solution is correct.
Let's practice with more examples using the same 1 to 7 scale. For a 21 meter garden, our proportion is unknown over 21 equals 1 over 7. Cross multiplying gives us 3 centimeters. For a 35 meter building, we get 5 centimeters. And for a 7 meter path, we get exactly 1 centimeter. The key steps are always the same: identify the scale, set up the proportion, cross multiply, solve for the unknown, and verify your answer. This consistent method works for any scale ratio problem.