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Example 6-4d Objective Solve problems involving scale drawings

Example 6-4d Vocabulary Scale drawing A representation of an object that is too large or too small to be drawn or built at actual size

Example 6-4d Vocabulary Scale model A representation of an object that is too large or too small to be drawn or built at actual size

Example 6-4d Vocabulary Scale A ratio of a given length on a drawing or model to its corresponding actual length

Lesson 6 Contents Example 1Find a Missing Measurement Example 2Find the Scale Factor Example 3Find the Scale Example 4Construct a Scale Model

Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. 1/4 BingstonAlanton Define the variable X = actual distance Find the actual distance Using the scale given, write a ratio map distance actual distance X

Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. 1/4 Write the second ratio with data given in problem map distance actual distance map distance actual distance X Keep units of measure the same on each line X = actual distance

Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. 1/4 Write a proportion with the 2 ratios map distance actual distance map distance actual distance X Solve with cross multiplication of the numbers 1x = 1x = 5(1.5)

Example 6-1a MAPS The distance from Bingston to Alanton is 1.5 inches on the map. Find the actual distance. 1/4 Use Identify Property to multiply 1  x X 1x = 5(1.5) x Bring down = x = Multiply 5  1.5 x = 7.5 Add dimensional analysis x = 7.5 miles Answer: x = 7.5 miles

Example 6-1c MAPS The distance from Springfield to Capital City is 1.4 inches on the map. Find the actual distance. Answer: x = 9.8 miles 1/4

Example 6-2a Find the scale factor for the map. Write a ratio with the scale 2/4 For a scale factor, must have the same units Since inch is a smaller unit than mile, convert 5 miles to inches

Example 6-2a Find the scale factor for the map. Since we know how many inches in a foot, Write the ratio and multiply by a conversion ratios of inches in a foot 2/4 1 foot  12 in Cancel out same units Remember to put inches in the denominator so they can be cancelled out

Example 6-2a Find the scale factor for the map. Multiply the numerators 2/4 1 foot  12 in 1 Bring down unit of measure of foot 1 foot Multiply the denominators Bring down unit of measure of mi 6060 mi

Example 6-2a Find the scale factor for the map. 2/4  1 foot 60 mi Since we know how many feet in a mile, Use the ratio and multiply by a conversion ratios of feet in a mile Remember to put feet in the denominator so they can be cancelled out 5280 feet 1 mile 3

Example 6-2a Find the scale factor for the map. 2/4  1 foot 60 mi 5280 feet 1 mile 3 Cancel out same units of foot Cancel out same units of mile 1 3 Multiply numerator Multiply denominator 316,800 Answer: The scale factor =

Example 6-2c Find the scale factor for the map. Answer: 2/4

Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? 3/4 Write a ratio of the wall to the scale drawing 15 feetActual room Scale drawing6 inches Write a ratio for the scale The scale will always be 1 unit for whatever the drawing is using Actual room Scale drawing 1 inch Since the actual distance is unknown define a variable x feet

Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? 3/4 Write a proportion using the 2 ratios 15 feetActual room Scale drawing6 inches Actual room Scale drawing 1 inch x feet 15 feet 6 inches = x feet 1 inch Cross multiply the numbers 6x =6x = 15(1)

Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? 3/4 Bring down the 6x = Actual room Scale drawing 1 inch x feet 15 feet 6 inches = x feet 1 inch 6x = 6x = 15(1) Multiply 15  1 6x = 15 Ask “what is being done to the variable”? The variable is being multiplied by 6 Do the inverse on each side of the equal sign

Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? 3/4 Bring down the 6x = 15 Actual room Scale drawing 1 inch x feet 6 6x = 15 Using the fraction bar, divide both sides by 6 6 Combine “like” terms 1  x Bring down = 1  x = Combine “like” terms 1  x = 2.5 Use Identity Property to multiply 1  x x Bring down = 2.5 x = 2.5

Example 6-3a SCALE DRAWINGS A wall in a room is 15 feet long. On a scale drawing it is shown as 6 inches. What is the scale of the drawing? 3/4 Write the scale of the drawing Actual room Scale drawing 1 inch x feet 6 6x =  x = 2.5 x = 2.5 Substitute the value of x 2.5 feet Bring down the 1 inch 1 inch Answer: Can also be written: or 1 inch = 2.5 feet 2.5 feet = 1 inch

Example 6-3c SCALE DRAWINGS The length of a garage is 24 feet. On a scale drawing the length of the garage is 10 inches. What is the scale of the drawing? Answer: 1 inch = 2.4 feet 3/4

Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? 4/4 model height actual height Using the scale given, write a ratio 1 inch 2.5 feet Write the second ratio with data given in problem model height actual height 8 feet Define variable What is the length of the statue’s index finger on the model x inches Write a proportion using the 2 ratios 1 inch 2.5 feet = x inches 8 feet

Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? 4/4 Cross multiply the numbers 1 inch 2.5 feet = x inches 8 feet 2.5x2.5x = 1(8) Bring down 2.5x = 2.5x = Multiply 1  8 2.5x = 8 Ask “what is being done to the variable?” The variable is being multiplied by 2.5

Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? 4/4 2.5x = 8 Do the inverse on each side of the equal sign Bring down the 2.5x = 8 2.5x = 8 Using the fraction bar, divide both sides by Combine “like” terms Bring down = Combine “like” terms 1  x1  x =  x =

Example 6-4a STATUE OF LIBERTY The Statue of Liberty is a 152-foot statue that stands in New York Harbor. John made a model that was only 21 inches tall. What is the length of the statue’s index finger on the model, which is 8 feet long on the actual statue if the scale is 1 inch = 2.5 feet? 4/4 2.5x = 8 Use the Identify Property to multiply 1  x 2.5x =  x1  x =  x = x = Bring down = 3.2 x = 3.2 Add dimensional analysis x = 3.2 inches Answer: x = 3.2 inches

Example 6-4d STATUE Marnie created a model of her town’s statue of Jebediah Springfield. Her model was 6 inches high. The actual statue is 27 feet tall. What is the length of the statue’s mustache on the model, which is 3 feet long on the actual statue. Use the scale 1 inch = 1.25 feet Answer: x = 2.4 inches * 4/4

End of Lesson 6 Assignment Lesson 4:6 Scale Drawings & Models All