Ratios & Proportions - Easier Dr. Fowler  CCM Ratios & Proportions - Easier

A ratio of one number to another number is the quotient of the first number divided by the second. The Denominator ≠ 0)

A ratio is a comparison of two quantities by division A ratio is a comparison of two quantities by division. In the rectangles below, the ratios of shaded areas to unshaded areas are all equal. These are considered equivalent ratios.

A ratio can be written in a variety of ways.   a:b a/b a to b You can use ratios to compare quantities, compare prices, describe rates, and many real world problems.

2 & 9 are called the EXTREMES A proportion is an equation that states that two ratios are equal, such as: 3 & X are called the MEANS 2 & 9 are called the EXTREMES

Which pairs of ratios are True Proportions? Cross Multiply No! Yes

Example - There is a law stating the ratio of the width to length of the American flag should be 10 to 19. Which is not the correct ratio?

= faculty 1 students 15 1 x 15 675 15x = 675 x = 45 faculty Using ratios for Proportions The ratio of faculty members to students in one school is 1:15. There are 675 students. How many faculty members are there? faculty 1 students 15 = 1 x 15 675 15x = 675 x = 45 faculty

First - Set up & solve the proportion. Ex) 3 is to 2 as x is to 18. 3 Now cross multiply x ____ = ____ 2 18 2x = 54 2 2 x = 27

Solve the Proportion! Ex) Now Reduce 16m = 8 16 16 m =

1cm 11cm 30km x 1x = 330 x = 330 km ____ = _____ Ex) A map has a scale of 1 cm = 30 km. If two cities are 11 cm apart on the map, what is the actual distance between the two cities to the nearest tenth of a km? First – Set up Your proportion! 1cm 11cm ____ = _____ 30km x 1x = 330 x = 330 km

$8 / 3 = $2.67 per pound $11 / 5 = $2.20 per pound Ex) Which is a better deal: Buying 3 pounds of candy for $8, or 5 pounds for $11? Compare the ratios of each similarly! $8 / 3 = $2.67 per pound $11 / 5 = $2.20 per pound 5 pounds for $11 is the better deal

You can find the missing length of a side in a pair of similar figures, by using proportions ΔRST ~ ΔUVW R x ft. U 6 ft. S T W V 35 ft. 7 ft. 6 7 x = 30 feet = x 35

Solve for x. Round to the nearest tenth. 12 in. 4 in. 20 in. x in.. 4 x x = 6.7 inches = 12 20

Excellent Job !!! Well Done