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3,[object Object],?,[object Object],=,[object Object],5.,[object Object],10,[object Object],20,[object Object],3,[object Object],6,[object Object],ANSWER,[object Object],=,[object Object],10,[object Object],20,[object Object],32,[object Object],8,[object Object],=,[object Object],24,[object Object],6,[object Object],?,[object Object],8,[object Object],6.,[object Object],=,[object Object],24,[object Object],6,[object Object],ANSWER,[object Object],Copy and complete the statement to write an equivalent ratio.,[object Object]
Learning Target:Students will learn how to write proportions and solve proportions using cross products property.,[object Object]
Proportion: an equation that shows two ratios are equivalent. a : b = c : d,[object Object]
Cross Product Property:- The cross products of a proportion are equal.If            , then a  d = b  c. ,[object Object]
?,[object Object],=,[object Object],EXAMPLE 1,[object Object],Use cross products to decide whether the ratios form a proportion.,[object Object],3,[object Object],12,[object Object],a.,[object Object],5,[object Object],18,[object Object]
Answer:3   18 = 5   1254 = 6054 does not equal 60 therefore the ratio is NOT a proportion. ,[object Object]
?,[object Object],=,[object Object],EXAMPLE 1,[object Object],Use cross products to decide whether the ratios form a proportion.,[object Object],8,[object Object],20,[object Object],b.,[object Object],10,[object Object],25,[object Object]
Answer:10  20 = 8   25 200 = 200200  does equals 200 therefore the ratio is a proportion.,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object],4,[object Object],12,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object],4      5,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object],4      5,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object],4      5,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object],12      5,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object],4      5,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object],12      5,[object Object],12      5  =  60,  so x  =  60.,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 1  Use equivalent ratios.,[object Object],4      5,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object],12      5,[object Object],12      5  =  60,  so x  =  60.,[object Object],The solution is 60.,[object Object],ANSWER,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 2  Use cross products.,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 2  Use cross products.,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 2  Use cross products.,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object],4x  =  240,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 2  Use cross products.,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object],4x  =  240,[object Object]
EXAMPLE 2,[object Object],4,[object Object],20,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],x,[object Object],12,[object Object],METHOD 2  Use cross products.,[object Object],4,[object Object],20,[object Object],=,[object Object],x,[object Object],12,[object Object],4x  =  240,[object Object],x  =  60,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],=,[object Object],3,[object Object],1.4,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],6.3 =1.4x,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],They are equal.,[object Object],6.3 =1.4x,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],They are equal.,[object Object],6.3 =1.4x,[object Object],6.3      1.4 = x,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],They are equal.,[object Object],6.3 =1.4x,[object Object],6.3 1.4 = x,[object Object],Write the related division equation.,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],They are equal.,[object Object],6.3 =1.4x,[object Object],6.3       1.4 = x,[object Object],Write the related division equation.,[object Object],4.5 = x,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],They are equal.,[object Object],6.3 =1.4x,[object Object],6.3       1.4 = x,[object Object],Write the related division equation.,[object Object],4.5 = x,[object Object],Divide.,[object Object]
EXAMPLE 4,[object Object],2.1,[object Object],x,[object Object],.,[object Object],=,[object Object],Solve the proportion,[object Object],3,[object Object],1.4,[object Object],SOLUTION,[object Object],2.1,[object Object],x,[object Object],Write the cross products.,[object Object],=,[object Object],3,[object Object],1.4,[object Object],They are equal.,[object Object],6.3 =1.4x,[object Object],6.3        1.4 = x,[object Object],Write the related division equation.,[object Object],4.5 = x,[object Object],Divide.,[object Object],The solution is 4.5.,[object Object],ANSWER,[object Object]
GUIDED PRACTICE,[object Object],for Example 4,[object Object],Write the related equation. Use it to solve the proportion.,[object Object],22.5,[object Object],30,[object Object],a,[object Object],50,[object Object],9.,[object Object],8.,[object Object],=,[object Object],=,[object Object],6,[object Object],60,[object Object],6,[object Object],y,[object Object],ANSWER,[object Object],ANSWER,[object Object],1800  =  50y,[object Object],135  =  6a,[object Object],1800,[object Object],135,[object Object],y,[object Object],a,[object Object],=,[object Object],=,[object Object],50,[object Object],6,[object Object],a  =  22.5,[object Object],y  =  36,[object Object]
EXAMPLE 3,[object Object],Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object]
EXAMPLE 3,[object Object],Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],SOLUTION,[object Object],Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.,[object Object]
EXAMPLE 3,[object Object],Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],SOLUTION,[object Object],Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.,[object Object],Write a verbal model.,[object Object]
EXAMPLE 3,[object Object],Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],SOLUTION,[object Object],Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.,[object Object],Distance traveled,[object Object],Total distance,[object Object],Write a verbal model.,[object Object],=,[object Object],Time traveled,[object Object],Total time,[object Object]
EXAMPLE 3,[object Object],Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],SOLUTION,[object Object],Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.,[object Object],Distance traveled,[object Object],Total distance,[object Object],Write a verbal model.,[object Object],=,[object Object],Time traveled,[object Object],Total time,[object Object],Substitutevalues.,[object Object]
EXAMPLE 3,[object Object],Boating You are on a riverboat trip. You travel 5 miles in 3 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],SOLUTION,[object Object],Use a proportion. Let t represent the total time, in hours, of the 20 mile trip.,[object Object],Distance traveled,[object Object],Total distance,[object Object],Write a verbal model.,[object Object],=,[object Object],Time traveled,[object Object],Total time,[object Object],20 mi,[object Object],5 mi,[object Object],Substitutevalues.,[object Object],=,[object Object],t h,[object Object],3 h,[object Object]
EXAMPLE 3,[object Object],Write the cross products.,[object Object]
EXAMPLE 3,[object Object],20,[object Object],5,[object Object],Write the cross products.,[object Object],=,[object Object],t,[object Object],3,[object Object]
EXAMPLE 3,[object Object],20,[object Object],5,[object Object],Write the cross products.,[object Object],=,[object Object],t,[object Object],3,[object Object],They are equal.,[object Object]
EXAMPLE 3,[object Object],20,[object Object],5,[object Object],Write the cross products.,[object Object],=,[object Object],t,[object Object],3,[object Object],5t,[object Object],60,[object Object],=,[object Object],They are equal.,[object Object]
EXAMPLE 3,[object Object],20,[object Object],5,[object Object],Write the cross products.,[object Object],=,[object Object],t,[object Object],3,[object Object],5t,[object Object],60,[object Object],=,[object Object],They are equal.,[object Object],Solve using mental math.,[object Object]
EXAMPLE 3,[object Object],20,[object Object],5,[object Object],Write the cross products.,[object Object],=,[object Object],t,[object Object],3,[object Object],5t,[object Object],60,[object Object],=,[object Object],They are equal.,[object Object],t = 12,[object Object],Solve using mental math.,[object Object]
EXAMPLE 3,[object Object],20,[object Object],5,[object Object],Write the cross products.,[object Object],=,[object Object],t,[object Object],3,[object Object],5t,[object Object],60,[object Object],=,[object Object],They are equal.,[object Object],t = 12,[object Object],Solve using mental math.,[object Object],It will take you 12 hours to travel 20 miles.,[object Object],ANSWER,[object Object]
GUIDED PRACTICE,[object Object],for Examples 1, 2, and 3,[object Object],7.	What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object]
GUIDED PRACTICE,[object Object],for Examples 1, 2, and 3,[object Object],7.	What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],ANSWER,[object Object]
GUIDED PRACTICE,[object Object],for Examples 1, 2, and 3,[object Object],7.	What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],ANSWER,[object Object],20 mi,[object Object],4 mi,[object Object],=,[object Object],t h,[object Object],2 h,[object Object]
GUIDED PRACTICE,[object Object],for Examples 1, 2, and 3,[object Object],7.	What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],ANSWER,[object Object],20 mi,[object Object],4 mi,[object Object],=,[object Object],t h,[object Object],2 h,[object Object],20,[object Object],4,[object Object],=,[object Object],t,[object Object],2,[object Object]
GUIDED PRACTICE,[object Object],for Examples 1, 2, and 3,[object Object],7.	What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],ANSWER,[object Object],20 mi,[object Object],4 mi,[object Object],=,[object Object],t h,[object Object],2 h,[object Object],20,[object Object],4,[object Object],=,[object Object],t,[object Object],2,[object Object],4t,[object Object],40,[object Object],=,[object Object]
GUIDED PRACTICE,[object Object],for Examples 1, 2, and 3,[object Object],7.	What If? In Example 3, suppose you travel 4 miles in 2 hours. At that same rate, how long will it take you to travel 20 miles?,[object Object],ANSWER,[object Object],20 mi,[object Object],4 mi,[object Object],=,[object Object],t h,[object Object],2 h,[object Object],20,[object Object],4,[object Object],=,[object Object],t,[object Object],2,[object Object],4t,[object Object],40,[object Object],=,[object Object],t = 10h,[object Object]
Can you write proportions and solve proportions using cross products property.,[object Object]

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