Proportions – Cross Products C1 What is a cross-­‐
product? Name: Class: Date: A CROSS PRODUCT is generated when you multiply the denominator of one ratio by the numerator of the other ratio. The Multiplication Property of Equality says that the CROSS PRODUCTS of the proportion are always _____________: Consider this proportion: Example: 6
8
= 9 12
Show that its CROSS PRODUCTS are equal: 6×12 = 8×9 72 = 72 Testing If the cross products are EQUAL then you have a proportion! proportionality using cross products Ex. 1 Are these ratios proportional? 9 27
, 10 30
YES Ex. 2 Are these ratios proportional? 72 7
, 81 9
NO Completing You can use CROSS PRODUCTS to fill in a missing part of a proportion. Proportions using Cross Products Ex. 3 Complete the proportion using cross products: 12 𝑥
= 4
5
Proportions – Cross Products C1 Scale Drawings Name: Class: Date: Ex. 4 Use a proportion to solve: A student buys 6 pencils for $3.90. How much will she have to pay for 10 pencils? You can use PROPORTIONS to make a SCALE drawing. Scale drawings have been PROPORTIONALLY ENLARGED or REDUCED from their original size. They are not too tall and skinny nor too short and wide, compared to the original object. A SCALE is the RATIO that COMPARES a length in the drawing to the length in the original object. It can also compare WIDTHS. You write a scale in SIMPLEST form. Architects and builders use BLUEPRINTS to design houses. Blueprints are SCALE DRAWINGS of the actual house. Ex. 5 A library in a mansion is 40 feet wide. In the blueprint, the room measures 2 inches wide. What is the scale? 40 feet
2 inches
scale = 20 feet : 1 inch Ex. 6 In the same blueprint, the library is 55 feet long. Using the scale that you found, how wide would the room be on the blueprint? 20 feet 55 feet
=
1 inch
𝑥
20𝑥 = 55 ∙ 1 𝑥 = 2.75 𝑖𝑛𝑐ℎ𝑒𝑠 Proportions – Cross Products C1 What is a cross-­‐
product? Name: Class: Date: A ____________ _______________ is generated when you multiply the denominator of one ratio by the numerator of the other ratio. The Multiplication Property of Equality says the ________ ____________ of the proportion are always ________: Consider this proportion: Example: Show that its __________ ____________ are equal: Testing If the cross products are ____________ then you have a proportion! proportionality using cross products Ex. 1 Are these ratios proportional? 9 27
, 10 30
Ex. 2 Are these ratios proportional? 72 7
, 81 9
Completing You can use _________ _____________ to fill in a missing part of a Proportions using proportion. Cross Products Ex. 3 Complete the proportion using cross products: 12 𝑥
= 4
5
Proportions – Cross Products C1 Scale Drawings Name: Class: Date: Ex. 4 Use a proportion to solve: A student buys 6 pencils for $3.90. How much will she have to pay for 10 pencils? You can use _________________ to make a ____________ drawing. Scale drawings have been _______________ __________or _________ from their original size. They are not too tall and skinny nor too short and wide, compared to the original object. A ________ is the __________ that __________ a length in the drawing to the length in the original object. It can also compare ___________. You write a scale in _______________ form. Architects and builders use _______________ to design houses. Blueprints are __________ ________________ of the actual house. Ex. 5 A library in a mansion is 40 feet wide. In the blueprint, the room measures 2 inches wide. What is the scale? scale = _________:_________ Ex. 6 In the same blueprint, the library is 55 feet long. Using the scale that you found, how wide would the room be on the blueprint?