Entry task…. 1) The table below gives the wins and losses of a baseball team. In which year did the team have the best record? Explain. YearWinsLoses

Ratios and Proportions 7.1 Learning Target : I can write a ratio to compare two quantities

A proportion is an equation stating that two ratios are equal. In the proportion, the values a and d are the extremes. The values b and c are the means. When the proportion is written as a:b = c:d, the extremes are in the first and last positions. The means are in the two middle positions.

Solving Proportions

The Cross Products Property can also be stated as, “In a proportion, the product of the extremes is equal to the product of the means.” Reading Math

One thing we have to always watch for, are the measurements in the same unit. In tis example we have inches and feet. We have to convert one so they are the same.

Slope, a ratio we’ve been using for years! Write a ratio expressing the slope of l. Substitute the given values. Simplify.

Example 3A: Solving Proportions Solve the proportion. Cross Products Property Simplify. Divide both sides by 56. 7(72) = x(56) 504 = 56x x = 9 REMEMBER!

How to Use Ratios? The ratio of boys and girls in the class is 12 to11. 4cm 1cm This means, for every 12 boys you can find 11 girls to match. There could be just 12 boys, 11 girls. There could be 24 boys, 22 girls. There could be 120 boys, 110 girls…a huge class What is the ratio if the rectangle is 8cm long and 2cm wide? Still 4 to 1, because for every 4cm, you can find 1cm to match The ratio of length and width of this rectangle is 4 to 1.. The ratio of cats and dogs at Joe’s home is 2 to 1 How many dogs and cats does Joe have? We don’t know, all we know is if they’d start a fight, each dog has to fight 2 cats.

Using Extended Ratios The lengths of the sides of a triangle are in the ratio of 4:7:9. The perimeter of the triangle is 260. What is the length of each side? What does a ratio of 4:7:9 mean? How can we use this?

On your own…. The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle? x + y + z = 180° x + 6x + 13x = 180° 20x = 180° x = 9° y = 6x y = 6(9°) y = 54° z = 13x z = 13(9°) z = 117°

Example 5: Problem-Solving Application 1 Understand the Problem The answer will be the length of the room on the scale drawing. Marta is making a scale drawing of her bedroom. Her rectangular room is 12 feet wide and 15 feet long. On the scale drawing, the width of her room is 5 inches. What is the length?

Example 5 Continued 2 Make a Plan Let x be the length of the room on the scale drawing. Write a proportion that compares the ratios of the width to the length.

Solve 3 Example 5 Continued Cross Products Property Simplify. Divide both sides by (15) = x(12.5) 75 = 12.5x x = 6 The length of the room on the scale drawing is 6 inches.

Things to Remember…. In a ratio, the denominator of the fraction cannot be zero because division by zero is undefined. Remember! You must compare apples to apples not oranges Remember!

Homework p. 436 #9-16, 17,19,23,25,44