HR:______ Date
Chapter 5 Notes
Math 7 Plus
Ratios, Proportions, and Similarity
Name:_________________________________ HR:______ Date:_________________ Section: 5.1
Pages: 222 - 225
Objectives: Students find equivalent rations to create proportions. Vocabulary Words:
Ratio – a comparison of two quantities by division. Three ways to write a ratio… 6 to 15, 6:15, or . Equivalent ratio – ratios that make the same comparison. They are identical when written in simplest form. Proportion – an equation that states that two ratios are equivalent. Ratios that are equivalent are said to be proportional.
Ex. 1 Find two ratios that are equivalent to each given ratio.
Ex. 2 Simplify to tell whether the ratios form a proportion.
Ex. 2 Alternative Method – Compare cross products.
Ex. 3 There are 675 students and 30 teachers in the middle school. What is the ratio of teachers to students? Understand Pick Strategy Implement
Conclude
Name:_________________________________ HR:______ Date:_________________ Section:
5.2
Pages: 226 - 229
Objectives: Students work with rates and ratios. Vocabulary Words:
Rate – a comparison of two quantities that have different units. Example: 150 miles per 3 hours Unit Rate – a rate in which the second quantity is 1. Example: 30 miles per hour Unit Price – a unit rate used to compare price per item.
Ex. 1 Write as a unit rate. Ana Maria’s heart beats 225 times in 3 minutes. How many times does her heart beat per minute?
Ex. 2 Chemistry- Density = mass divided by volume. A nickel has a mass of 5 g and a volume of approximately 0.689 cm3. What is the approximate density of a nickel?
Ex 3. Traveling- rate = distance divided by time. A bicyclist rides the first 60 kilometers of a 220 kilometer race in 1.5 hours. What is the bicyclist’s average speed?
Ex. 4 Find the unit price to find the better price. A 16 oz box of crackers costs $3.99 and a 38 oz box of crackers costs $6.99. Which is the better buy?
Name:_________________________________ HR:______ Date:_________________ Section:
5.3
Pages: 230 - 234
Objectives: Students use one or more conversion factors to solve problems. Vocabulary Words:
Conversion factors – a fraction whose numerator and denominator represent the same quantity but use different units; the fraction is equal to 1 because the numerator and denominator are equal. Examples
Ex. 1 Convert each measure.
Ex. 2 Use conversion factors to find each of the following.
Ex. 3 Brian bought a picture that is 90 cm long. To the nearest tenth of an inch, how long is Brian’s picture? Hint: Use the conversion table on page 232 of textbook. Understand Pick Strategy
Implement
Conclude
Name:_________________________________ HR:______ Date:_________________ Section:
5.4
Pages: 237 - 241
Objectives: Students solve proportions. Vocabulary Words:
Cross Products – The product of numbers on the diagonal when comparing two ratios. Cross products are equal when two ratios are proportional. Example -
Ex. 1 Tell whether the ratios are proportional.
Ex. 2 Solve each proportion.
Ex. 3 An elevator travels 342 feet as it goes from the lobby of a building to the top floor. It takes 7 seconds to travel the first 133 feet. If the elevator travels at the same rate, how much longer does it take to reach the top floor? Understand Pick Strategy
Implement
Conclude
Name:_________________________________ HR:______ Date:_________________ Section: 5.5
Pages: 246 - 249
Objectives: Students determine whether figures are similar and find missing dimensions in similar figures. Vocabulary Words: Similar – similar figures have the same shape but NOT necessarily the same size. Corresponding sides – sides of two figures that are in the same relative position. Corresponding angles – angles of two figures that are in the same relative position. Corresponding angles are congruent when two figures are similar. Corresponding sides of right triangle TR and WU SR and VU TS and WV Corresponding angles of right triangle
Math 7 Plus
Ratios, Proportions, and Similarity
Name:_________________________________ HR:______ Date:_________________ Section: 5.1
Pages: 222 - 225
Objectives: Students find equivalent rations to create proportions. Vocabulary Words:
Ratio – a comparison of two quantities by division. Three ways to write a ratio… 6 to 15, 6:15, or . Equivalent ratio – ratios that make the same comparison. They are identical when written in simplest form. Proportion – an equation that states that two ratios are equivalent. Ratios that are equivalent are said to be proportional.
Ex. 1 Find two ratios that are equivalent to each given ratio.
Ex. 2 Simplify to tell whether the ratios form a proportion.
Ex. 2 Alternative Method – Compare cross products.
Ex. 3 There are 675 students and 30 teachers in the middle school. What is the ratio of teachers to students? Understand Pick Strategy Implement
Conclude
Name:_________________________________ HR:______ Date:_________________ Section:
5.2
Pages: 226 - 229
Objectives: Students work with rates and ratios. Vocabulary Words:
Rate – a comparison of two quantities that have different units. Example: 150 miles per 3 hours Unit Rate – a rate in which the second quantity is 1. Example: 30 miles per hour Unit Price – a unit rate used to compare price per item.
Ex. 1 Write as a unit rate. Ana Maria’s heart beats 225 times in 3 minutes. How many times does her heart beat per minute?
Ex. 2 Chemistry- Density = mass divided by volume. A nickel has a mass of 5 g and a volume of approximately 0.689 cm3. What is the approximate density of a nickel?
Ex 3. Traveling- rate = distance divided by time. A bicyclist rides the first 60 kilometers of a 220 kilometer race in 1.5 hours. What is the bicyclist’s average speed?
Ex. 4 Find the unit price to find the better price. A 16 oz box of crackers costs $3.99 and a 38 oz box of crackers costs $6.99. Which is the better buy?
Name:_________________________________ HR:______ Date:_________________ Section:
5.3
Pages: 230 - 234
Objectives: Students use one or more conversion factors to solve problems. Vocabulary Words:
Conversion factors – a fraction whose numerator and denominator represent the same quantity but use different units; the fraction is equal to 1 because the numerator and denominator are equal. Examples
Ex. 1 Convert each measure.
Ex. 2 Use conversion factors to find each of the following.
Ex. 3 Brian bought a picture that is 90 cm long. To the nearest tenth of an inch, how long is Brian’s picture? Hint: Use the conversion table on page 232 of textbook. Understand Pick Strategy
Implement
Conclude
Name:_________________________________ HR:______ Date:_________________ Section:
5.4
Pages: 237 - 241
Objectives: Students solve proportions. Vocabulary Words:
Cross Products – The product of numbers on the diagonal when comparing two ratios. Cross products are equal when two ratios are proportional. Example -
Ex. 1 Tell whether the ratios are proportional.
Ex. 2 Solve each proportion.
Ex. 3 An elevator travels 342 feet as it goes from the lobby of a building to the top floor. It takes 7 seconds to travel the first 133 feet. If the elevator travels at the same rate, how much longer does it take to reach the top floor? Understand Pick Strategy
Implement
Conclude
Name:_________________________________ HR:______ Date:_________________ Section: 5.5
Pages: 246 - 249
Objectives: Students determine whether figures are similar and find missing dimensions in similar figures. Vocabulary Words: Similar – similar figures have the same shape but NOT necessarily the same size. Corresponding sides – sides of two figures that are in the same relative position. Corresponding angles – angles of two figures that are in the same relative position. Corresponding angles are congruent when two figures are similar. Corresponding sides of right triangle TR and WU SR and VU TS and WV Corresponding angles of right triangle
