The document discusses ratios, proportions, and how to write and solve them. It provides examples of writing ratios for measurements like width to height. It also demonstrates how to set up and solve proportions using variables, cross products, and equations to find missing values like angle measures when given a ratio relationship. Examples include finding side lengths of triangles when the extended ratio and perimeter are given.

2. Students will be able to write and solve
ratios
Students will be able to write and solve
proportions

3. Comparison of two quantities by division
Written as:
• a/b
• a : b
• a to b
Always write in simplest form (reduced
form)
Make sure units of measure are the same

4. A bonsai tree is 18 in wide and stands 2 ft
tall. What is the ratio of the width
compared to the height?
First convert measurements to either
inches or feet
Then write the ratio in simplest form
18 : 24  3 : 4

5. A pigmy rattlesnake has an average length
of 18 inches, while a Western
diamondback rattlesnake averages 5ft. 6in.
What is the ratio of the length of a pigmy to
a Western diamondback rattlesnake?
18 : 66  3 : 11

6.  The measures of two supplementary angles
are in the ratio 1:4. What are the measures
of the angles?
 Write the ratio in words: angle 1: angle 2
 Then write using variables: x : 4x
 Set up an equation: x + 4x = 180
 Solve the equation: x = 36
 Substitute x back into the ratio
Angle 1 = 1(36) = 36
 Angle 2 = 4(36) = 144

7.  The measures of two complementary angles
are in the ratio 1:3. What are the measures
of the angles?
 Write the ratio in words: angle 1 : angle 2
 Then write using variables: x : 3x
 Set up an equation: x + 3x = 90
 Solve the equation: x = 22.5
 Substitute x back into the ratio
Angle 1 = 1(22.5) = 22.5
 Angle 2 = 3(22.5) = 67.5

8. Compares 3 or more numbers
Written as
• a : b : c

9. The lengths of the sides of a triangle are in
the extended ratio 4 : 7 : 9. The perimeter
is 60 cm. What are the lengths of the
sides?
Write an equation: 4x + 7x + 9x = 60
Solve for x: x = 3
So the lengths of the sides are:
• 4(3) = 12
• 7(3) = 21
• 9(3) = 27

10. When two ratios are equal
Use cross products to solve proportions
a = c  ad = bc
b d

12. x/6 = y/7 What ratio completes the
equivalent proportion?
• x/y = ?
• 6/x = ?
• (y + 7)/7 = ?

13. 9 = a
2 14
 15 = 3
m+1 m
 X = X+2
X – 1 X

14. Pg. 368
#2 – 20 even, 21, 26 – 28 all, 37 - 40 all
18 problems
