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

 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

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

 A pigmy rattlesnake has 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

 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

 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

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

 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

 When two ratios are equal  Use cross products to solve proportions

 9 = a 2 14  15 = 3 m+1 m

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

 Pg. 436  #9 – 32, 40 – 43 