Using Reciprocal Scale Factors
Using Reciprocal Scale Factors is a Grade 7 math skill in Illustrative Mathematics, Chapter 1: Scale Drawings. Students learn that if a scale factor converts from drawing to actual, the reciprocal scale factor converts from actual to drawing, allowing two-way conversion between drawings and reality.
Key Concepts
To scale a copy back to the size of the original figure, you use the reciprocal of the original scale factor. If the scale factor from an original figure to a copy is $k$ (where $k \neq 0$), the scale factor from the copy back to the original is $\frac{1}{k}$.
Common Questions
What is a reciprocal scale factor?
If the scale factor from drawing to actual is k, then the scale factor from actual to drawing is 1/k. These two factors are reciprocals of each other.
How do you use a reciprocal scale factor?
To find a drawing length from an actual length, multiply by the reciprocal of the drawing-to-actual scale factor. To go back, multiply by the original scale factor.
What is an example of reciprocal scale factors?
If 1 cm in a drawing represents 50 cm in reality (scale factor 50), then to find the drawing size of a 200 cm wall: 200 times (1/50) equals 4 cm.
Why are reciprocal scale factors useful?
They let you convert in both directions without setting up a new proportion each time. Knowing one scale factor immediately gives you the other.
What chapter covers reciprocal scale factors in Illustrative Mathematics Grade 7?
Using reciprocal scale factors is covered in Chapter 1: Scale Drawings in Illustrative Mathematics Grade 7.