Section 8.1 Ratio and Proportion

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Presentation transcript:

Section 8.1 Ratio and Proportion OBJECTIVE: To write ratios and solve proportions BIG IDEA: Proportionality ESSENTIAL UNDERSTANDINGS: A ratio can be written to compare two quantities An equation can be written stating that two ratios are equal If the equation contains a variable, it can be solved to find the value of the variable MATHEMATICAL PRACTICE: Attend to precision

Ratio of a to b: a ____________________ of two quantities by division Ratio of a to b: a ____________________ of two quantities by division. You can write the ratio of two numbers a and b, where , in three ways: You usually express a and b in the same unit and write the ratio in simplest form. Students need to be comfortable with ratios written as fractions, as well as decimals and percents. Ratio

EX 1: Simplify the ratios B) C) D) EX 1: Simplify the ratios

A) length of a tennis racket: 2 feet 4 inches length of a table tennis paddle: 10 inches B) diameter of table tennis ball: 40 mm diameter of tennis ball: 6.8 cm EX 2: Write the ratio of the first measurement to the second measurement

3. Triangle XYZ has an area of 3. Triangle XYZ has an area of . The ratio of the base of to the height of the triangle is 2:1. Find the base and height of the triangle. Using Ratios

4. The measures of the angles in a triangle are in an extended ratio 3:4:8. Find the measures of the angles. Using Ratios

Proportion: an ____________________ that states that _______________ ratios are equal. The first and last numbers in a proportion are the ____________________. The middle two numbers are the ____________________. Proportion

Properties of Proportions Cross Product Property: the product of the ____________________ equals the product of the ____________________ 1) Reciprocals 2) Switch the means 3) Add the denominator to the numerator Properties of Proportions

EX 5: Solve the proportion A) B) C) D) EX 5: Solve the proportion

EX 6: Solve for the dimensions of the building A photo of a building has the following measurements: width of and height of 2.75 in a) The actual building is wide. How tall is the actual building? b) The door height in the photo is 0.5 inches. What is the height of the door in the actual building? EX 6: Solve for the dimensions of the building