we looked at how we could use a double number line to find percentages. At the end of the lesson, this was the problem we left you with. A large bottle of juice contains 500 mL of juice. A medium bottle contains 70% as much juice as the large bottle. You'll notice how I started by labeling 500 mL as 100%. Because 500 mL represents the full amount of juice in a large bottle. Now, t 70% of the large bottle. And I know 70% is a multiple of 10. So I saw I need to divide 100% divided by 10 to get to 10%. If I do so, I have to divide 500 mL by 10 as well. This shows me that 10% of the large bottle represents 50 mL. And using my 10% intervals on the number line, I can skip count or multiply to see that 70% is 350 mL of juice, which is the full amount of the medium bottle. Like what if we wanted to find 5% of the orange juice bottle, or 33% . I started by labeling 250 people and 100%, since 250 was the total people who attended the concert. Next I saw I need to find 30% of 250 people in order to find the attendance at the basketball game. Similar to our juice problem, I can divide 250 people by 10 in order to find the value of 10% of the people. Since 250 divided by 10 is 25, I know 10% of the people who attended the concert represents 25 people. And now I can skip count or multiply by 3 to find out what 30% represents. 10% times 3 is 30. So 25 times 3 would be 75. The 75 represents 30% of the people at the concert and also represents the total number of people who attended the basketball game. Next I need to find 140% of 250 in order to find attendance at the drama play. Now, I notice that, because I already know what 100% represents -- which is 250 people -- and 140% is 100% plus an additional 40%. I know that 10% of the people at the play represented 25 people. And so knowing this, I can see 40% of the people is equal to 4 times 25, or 100. Here's how it would look on my diagram. And now I can add this 40%, or 100 people, to the 100%, or 250 people, to see that 140% of the people who attended the concert represents -- 100 plus 250 -- 350 people, all of whom attended the drama play. I would have to add 100 tick marks here in my number line. Even using my intervals of 10, 44 would be really difficult to represent. So in cases like this, I can use a table and find what 1% of 250 represents. 250 people represents 100% of the people who attended the concert. Now, in order to find the number of people represented by 1%, I can divide each row by 100 or multiply by 1 over 100. And 250 times 1 over 100 shows me 1% represents 2.5 people. I can then add a row to find out how many people 44% people represents. And to go from 1% to 44%, I need to multiply by 44. When I multiply my percentage by 44 and my number of people times 44, I can see 44% of the people who attended the concert represents 110 people. I know 80 over 100 in decimals is 0.8. And I can multiply 0.8 times 4 -- times my original price -- to find out the sale price. Which, in this case, would be $3.20. We found 80% of several values. Devonte's process was to make a table, to write the original price and 100%, divide each side by 100 to find 1% of the price. And then to multiply each side by 80 to find 80% of the price. Let's say I want to know, what is 80% of $55. This approach would have us multiply 80 over 100 times the price, which is $55. Here's how I can set this up. I know 80 over 100 can be represented as a decimal as 0.8. I want to multiply this quantity times the original price, which was $55. And so I could do 0.8 times 55. When I multiply this, I would see that 0.8 times 55 is $44. $44 represents 80% of the original price, which was $55. Wow, that was definitely more efficient than drawing our table. Now it's your turn to try this approach with another item. Remember, multiply the original price by the percentage -- in this case, that's 80%. Remember, during the sale, every item is 80% of its regular price. The regular price of our next item is $120. 80% of the original cost is $96. If you wanted to know what's 32% of 500, it would simply be 32 over 100 times 500.
