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Lesson 4: Ratio application

# Part to whole ratio word problem using tables

Discover how to solve ratio problems with a real-life example involving indoor and outdoor playtimes. Learn to use ratios to determine the number of indoor and outdoor playtimes in a class with a 2:3 ratio and 30 total playtimes. Created by Sal Khan.

## Want to join the conversation?

• Total Students is 65, On the Formula at the begin, should be ask for the sum of girls and boys (13) or not? •  Hi Annet. You need to find the sum to be able to find the ratio. Example:

The ratio of girls to boys in a school is (5:6). If there are 33 students, how many boys are there and girls are there?

1. 5 + 6 = 11
2. 6/11 = boy part of the school/total students
3. 11 x ? = 33, so 6 x ? = ? boys
4. 11 x 3 = 33, so 6 x 3 = ?
5. 6 x 3 = 18
6. 18 boys

Now the second part of the question:

7. 18 boys, 33 students, ? girls
8. 33 - 18 = ? girls
9. 15 girls

There are 18 boys and 15 girls.

Check:
10. 18 + 15 = 33 students
• Hey I just want to say if you are doing this course as a review don't skip over lessons you think you already know. You probably haven't mastered everything and there's still room to go. I got this from personal experience :) • what in the world? this isvery difficult can someone explain please:( • Sure, I can help you! The basic concept of part to whole ratios, is that instead of comparing data to another piece of data in the question, you're comparing to the total amount of data. I hope I'm explaining this clearly; it is a bit of a difficult thing to understand. I struggled at first, too. Here's an example:

There are 5 apples, 4 bananas, and 6 oranges. What is the ratio of apples to total fruit?

First, you would want to add the total amount of fruit together - 5 + 4 + 6 = 15. The total amount of fruit is 15.

Since there are 5 apples, the ratio of apples to total fruits would be 5 : 15, or you could simplify to 1 : 3 (divide both sides of the ratio by 5 to simplify).

To try to explain further, instead of comparing one part to another part - for example, apples to bananas - you are instead comparing one part to the whole - which would be apples to all fruit -.

Let's do another example. Say you had ten pairs of blue socks, fifteen pairs of red socks, five pairs of black socks, and nine pairs of purple socks. What is the ratio of black socks to all socks?

First, you would want to add the number of all your socks together, which would be 10 + 15 + 5 + 9, equaling 39. You have 39 total pairs of socks.

Next, you would want to know how many black socks you had - which we know, you have 5 pairs. And then you can do the ratio of black socks to all socks.

Therefore, the ratio of black socks to all socks is 5 : 39.

I know this isn't specific to this particular problem in this video, but I hope these examples help you know how to solve part to whole ratio problems.

Let me know if you'd like me to explain the problem Sal does in this video for you.

Hope this helped! :)
• where did the 13 come from in the problem? like how did he get 13? • DUDE. Where were you when I was in middle school?? and high school? and College? • How is his hand writing so nice when he is doing that on a computer im jeoulous • How can you solve this question in an easier way, like in a way of understanding more about part to whole ratio word problems. If there is no easier way, please comment to help me understand. • What you need to do in any word problem involving the ratios is exactly the same. Take the entire amount and divide it by the sum of the ratios. This will give you the number you need to multiply both ratios by. So the entire amount of playtimes is 30, and the sum of the ratios is 2+3, which is 5. Divide 30 by 5, which is 6. Then multiply each ratio by 6, and you get (2*6 and 3*6). And the sum of the new ratio should equal the whole or 30, even as the sum of 2 and 3 equals 5. In this case, 12 + 18 equals 30. So we’re good

For a more complicated one, let’s say that you have a candy machine with a ratio of red gum balls to blue gum balls to be 4:6 and the amount of gum ballls in the machine is 1060. We solve it in the exact same way. First sum the ratios. 4 +6 is 10. Then divide the full amount by 10 to get the number you need to times each of the ratios. 1060/10 is 106. Now times 4 and 6 by 106 and you will get 424 and 636, respectively. Therefore, there are 424 red gumballs and 636 blue gumballs in the machine. Added together, 424 and 636 equals 1060, which is the total we knew was in the machine.

The reasons that the calculations work is because you’re taking the whole amount and dividing it up into equal smaller amounts based on the ratio. The ratio 2:3 tells us that for any group of 5 there are 2 of one thing and 3 of the other, regardless if the full amount is 30 or 300 or 57,255.88, even as the ratio of 4:6 tells is that in any group of 10, there are 4 of one thing and 6 of another. So all you need to know is how many groups of 5 or 10 you’re working with, which you get by dividing the entire amount by the size of the group, or 30/5 = 6 and 1060/10. Since the ratio of 2:3 tells us that there are two of something in each group of 5 and we know that there are 6 groups pf 5, since 6 times 5 is 30, therefore the total of the 2 of something would also be 2 times 6. Ditto with the 3. And ditto with my example, as the ratio of 4:6 means we’re dividing the whole amount up into groups of 10 and there are 106 groups of ten in 1060. Hope that helps.   