Question

rectangle z is a scaled copy of rectangle y.
image of rectangle y (height: 9½, width: 5½) and rectangle z (height: 4¾, width: 2¾)
what scale factor takes rectangle y to rectangle z?
text box submit

Explanation:

Step1: Convert mixed numbers to improper fractions

For the height of rectangle Y: \(9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{19}{2}\)
For the height of rectangle Z: \(4\frac{3}{4}=\frac{4\times4+3}{4}=\frac{19}{4}\)
For the width of rectangle Y: \(5\frac{1}{2}=\frac{5\times2 + 1}{2}=\frac{11}{2}\)
For the width of rectangle Z: \(2\frac{3}{4}=\frac{2\times4+3}{4}=\frac{11}{4}\)

Step2: Calculate the scale factor using height (or width, since it's a scaled copy)

Scale factor \(=\frac{\text{Height of Z}}{\text{Height of Y}}=\frac{\frac{19}{4}}{\frac{19}{2}}\)
When dividing fractions, multiply by the reciprocal: \(\frac{19}{4}\times\frac{2}{19}=\frac{19\times2}{4\times19}=\frac{2}{4}=\frac{1}{2}\)
(We can also check with width: \(\frac{\frac{11}{4}}{\frac{11}{2}}=\frac{11}{4}\times\frac{2}{11}=\frac{2}{4}=\frac{1}{2}\))

Answer:

\(\frac{1}{2}\)