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Ratio and Proportion Study Guide
Ratios: A ratio is a number pair that compares two quantities. The numerator is the
first term mentioned and the denominator is the second term mentioned. Remember to
simplify all fractions and do not make improper fractions into mixed numbers.
Rob’s sister Luann has 6 compact discs and 38 DVDs. Write the ratio of as a
fraction in lowest terms.
1. Luann’s compact discs to DVDs.
______________
2. Luann’s DVDs to compact discs. ______________
3. Compare compact discs to the total number of Luann’s collection. _________
Equal Ratios: You can write equal ratios by multiplying or dividing both terms of the
ratio by the same nonzero number.
Write three equal ratios for each situation.
4. 3 guitars to 2 keyboards _______________
5. 40 country CDs to 30 classical CDs _______________
6. 8 Mozart compact discs to 4 Beethoven compact discs __________________
Proportions: A proportion is formed when two ratios are equal. A quick way to
determine if two ratios are a proportion is to find the cross products. If the cross
products are equal the two ratios form a proportion. You can also simply the ratios. If
the ratios are simplified to same ratio it is a proportion.
Tell whether these ratios equivalent (yes or no)?
7. 21 = 75
28
100
____________
8. 70 = 110
84
320
_____________
Use a proportion to solve. Show all work.
9. If 3 pairs of socks cost $3.30, how much will 5 pairs of socks cost?
Solving proportions: To solve proportions look to see if you can multiply or divide by
numbers that are up and down or left and right. If you are unable to multiply or divide
you must use cross products. Multiply two numbers diagonally and divide by the
number with the variable.
Solve each proportion and show work.
10. 7 = 8
35 n
11. n = 20
9
4
__________
12. 4 = n
3
78 __________
___________
13. 8 = 9
4
n ____________
14. Of the students in Ms. Yadav’s fourth-period math class, 16 are wearing athletic
shoes, 10 are wearing boots, and 4 are wearing other kinds of shoes.
a. What fraction of Ms. Yadav’s students are wearing boots?
b. Suppose 1200 students attend the middle school where Ms. Yadav teaches. How
many students are wearing athletic shoes?
Similar Figures: To find the missing side of a similar figure set up a proportion and
solve. Remember to match corresponding sides.
The polygons in each pair are similar. Write a proportion, then find each missing
length.
15.
16.
17.
18. The shadow of a flagpole is 9.6 meters long. The shadow of a meter stick is
1.2 meters long. What is the height of the flagpole? Hint: Make a picture.
19. Elena wants to enlarge some of the photographs from her trip to China.
The original photographs are 4 inches wide and 6 inches long. The length
of the enlargements will be 15 inches. How wide will the enlargements be?
Scale Drawings: Make a proportion and solve. Remember the scale can be written
as a ratio to begin the proportion.
The length and width on a scale drawing of some rooms at the Science Center are
listed below. Find the actual length and width of each rectangular room. Use the
scale: 1cm = 1.5 m.
20. Auditorium: length = 14 cm
21. Office: length = 3.2 cm
width = 16 cm
width = 2.8 cm
22. The dinosaur exhibit at the Science Center includes a model of a
stegosaurus. The scale of the model is 20 centimeters to 2.5 meters.
actual height of a stegosaurus was about 3.5 meters. How tall is the
model?
The