Lesson 3.5-3.6 Write Ratios and Solve Proportions Essential Question: How do you write ratios and solve proportions?

Before we start… The contents of a bag of dried mixed fruits and their amounts are as follows: papayas (12), bananas (14), dates (8), pineapples (16) and raisins (10). Use ratios to compare the amounts of each fruit to the total bag.

Before we start… Imagine you have a lemonade stand and the recipe calls for 4 cups of water, 1 cup of lemon juice, and 1 cup of sugar. How would you triple the recipe and still have lemonade worth consuming?

𝑎 𝑏 𝑎:𝑏 a to b What is a ratio? Uses division to compare two numbers. You can write the ratio of a to b as: 𝑎 𝑏 𝑎:𝑏 a to b

What are equivalent ratios? Ratios that have the same value. 9:5, 18:10, 3:1 2 3

How do you write a ratio? To write a ratio, you make a fraction comparing the two numbers. Put the ratio in simplest form by reducing.

Volleyball A volleyball team plays 14 home matches and 10 away matches. a. Find the ratio of home matches to away matches. b. Find the ratio of home matches to all matches.

CD Collection Derek and his brother decide to combine their CD collections. Derek has 44 CDs, and his brother has 52 CDs. Find the specified ratio. a. The number of Derek’s CDs to the number of his brother’s CDs. b. The number of Derek’s CDs to the number of CDs in the entire collection.

Contest Of the 30 champions of the National Spelling Bee from 1974 to 2003, 16 are boys. Find the ratio of the number of champions who are girls to the number who are boys.

What is a proportion? An equation that states that two ratios are equivalent

How do you write a proportion? You set two ratios equal to each other. Ratios must compare corresponding quantities.

How do you solve a proportion? You will use cross products to set up an equation. Cross product?

Cross Products are EQUAL What is a cross product? The product of the numerator of one ratio and the denominator of the other ratio. Cross Products are EQUAL

How do you set up a cross product? Multiply across and set the products equal. If 𝒂 𝒃 = 𝒄 𝒅 then 𝒂𝒅=𝒃𝒄.

Solve 11 6 = 𝑥 30

Solve 𝑤 35 = 4 7

Solve 4 𝑥 = 8 𝑥−3

Solve 𝑚 5 = 𝑚−6 4

Solve 5𝑥 𝑥+1 = 30 9

Solve 𝑝+15 42 = 𝑝−5 14

Elevators The elevator that takes passengers from the lobby of the John Hancock Center in Chicago to the observation level travels 150 feet in 5 seconds. The observation level is located on the 94th floor, at 1029 feet above the ground. Find the time it takes to travel from the lobby to the observation level.

Astronomy When two full moons appear in the same month, the second full moon is called a blue moon. On average, 2 blue moons occur every 5 years. Find the number of blue moons that are likely to occur in the next 25 years.

Reading A student can read 7 pages of a book in 10 minutes Reading A student can read 7 pages of a book in 10 minutes. How many pages of the book can the student read in 30 minutes?

What is a scale? The relationship between the model’s dimensions and the actual object’s dimensions. Scale Measure: Actual Measure

What is a scale model? A three-dimensional model of an object in which the dimensions of the model are in proportion to the dimensions of the object.

Model Ships The ship model kits sold at a hobby store have a scale of 1 ft: 600 ft. A completed model of the Queen Elizabeth II is 1.6 feet long. Estimate the actual length of the Queen Elizabeth II.

Scale Model An exhibit at Tobu World Square in Japan includes a scale model of the Empire State Building. The model was built using a scale of 1 m: 25 m. The height of the actual Empire State Building is 443.2 meters. What is the height of the model?

Sculpture Strawberry Point, Iowa, has a strawberry sculpture that is 15 feet tall. If the scale of this model is 10 feet to 1 inch, how tall was the actual strawberry?

Architecture An architect draws a blueprint for the front of a townhouse. On the blueprint, the townhouse is 50 centimeters wide. If the scale of the blueprint is 1 centimeter to 0.5 meter, how wide is the front of the townhouse?

How do write ratios and solve proportions?

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