# More: In-Depth Discussion of the Reasoning Activities in "Teaching Fractions and Ratios for Understanding"

By Susan J. Lamon | Go to book overview

Chapter 15
Applications: Similarity and Percents
1. 12:9 = 4:3 = 8:6.
2. Congruent rectangles have the same dimensions. The ratios of their widths would be 1:1.
3. One way to do this is to scale down using a scale factor whose denominator does not evenly divide 8 and 12. For example, using a scale factor of 1/5, we get a rectangle whose dimensions are 1.6 × 2.4 units.
4. a. By nesting the rectangles and drawing the diagonal, of the R rectangle, we can see that b, c, and d belong to the same family.
 a. The ratio of the sides is 1.5:1.
5. We can determine the scale factor by comparing the bottom segments of the shape. From the smaller to the larger, this segment grew from 4 units to 10 units, thus increasing by a factor of 2.5. Because the figures are similar, the other segments must increase by the same factor. 6 (2.5) = 15 units.
6. a. When we enlarge the square, its length and width are both changed by the scale factor 3.
 a. The area, however, increases to 9 times the original area.Click for a larger version
7. a. 10% of 80 = 8, 5% of 80 = 4, so 15% of 80 = 12
 a. 5 = 10% of 50, 15 = 30% of 50 b. 10% of 70 = 7, 20% of 70 = 14 c. 21 is 50% of 42; 21 is 10% of 210; 21 is 5% of 420; 21 is 35% of 60 d. 27 is 50% of 54; 27 is 10% of 270; 27 is 5% of 540; 27 is 45% of 60
8. Marvin should buy the book at store C or store E. In either case, the book is half price.
9. Suppose the car cost \$100. (Of course it does not, but we can use that amount to help think about the problem.) Then Mike sold the car to Kathy for \$90. If Kathy gained 10% when she sold it back to him, she must have sold it for \$99. In the end, Mike lost \$9. \$9 out of \$100 is 9%. Mike had a 9% loss.

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