Main content

# 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?(14 votes)
- 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

Answer:

There are 18 boys and 15 girls.

Check:

10. 18 + 15 = 33 students(42 votes)

- what in the world? this isvery difficult can someone explain please:((7 votes)
- 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! :)(22 votes)

- DUDE. Where were you when I was in middle school?? and high school? and College?(16 votes)
- This comment was 9 years ago. Next year will make it about 10 years.(1 vote)

- where did the 13 come from in the problem? like how did he get 13?(5 votes)
- He added 8 and 5.(3 votes)

- How is his hand writing so nice when he is doing that on a computer im jeoulous(6 votes)
- He's using a stylus pen, I also used one during online learning.(7 votes)

- 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.(2 votes)
- 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 get12:18(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.(12 votes)

- can someone help give me an explanation(4 votes)
- Hi vallonvullo!

You can under stand in this way:`the ratio of 🍔to🧋is`

3🍔:2🧋

there are five food in total

how many 🧋and🍔do I have each?

their is 3🍔for 2🧋

so in five food their is 3🍔and2🧋

3+2=5

if 3🍔+2🧋=a combo

I have 2 combo

it will be6🍔:4🧋

hope it's help!(6 votes)

- Dude, when he wrote Original, he dotted the 'i' and then dotted the 'r' for no reason. I think he wasn't looking at the 'r' so that's super weird.(6 votes)
- he dotted the O...

WHY SAL W H YYYYY(5 votes)

## Video transcript

- [Instructor] We're told that one month, the ratio of indoor to outdoor play times for Yousef's class was two to three. They had 30 total play times. How many of the play times were indoors? How many were outdoors? Pause this video and see
if you can figure that out. Alright, now let's work
through this together. And I'm going to figure this out by setting up a little bit of a table. So we have our indoor, indoor play times. I'll write it out. Play times. We have our outdoor play times. Outdoor play times. Then we have our total play times. Total play times. And then, let me set up
a table here as promised, and then, I'm going to
set up two columns here. So the first column is going to concern
itself with the ratios. So this is the original, original ratio, and here, we're going to
put the actual counts. Actual counts. So what information do we know? We know that the ratio of indoor
to outdoor is two to three. So the ratio of indoor to
outdoor is two to three. And then we could also think about what would be the ratio of either of these to total play times? Well, for every two indoor play times, there are three outdoor play times. That means for every
two indoor play times, there are five total play times, or for every three outdoor play times, there are five total play times. And now, let's think about what we know about the actual counts. They tell us that there was
a 30 total actual play times. So this is the actual number is 30. Now this is useful because
now we can think about how do we go from the original
ratios to the actual counts? If we take the total, we notice that we are multiplying by six. So to maintain the ratios, we would want to multiply
everything by six. So if you multiply this by six, you're going to have 12
actual indoor play times. And if you multiply this by six, you're going to have 18
actual outdoor play times. And notice, the ratio still holds up. Two is to three as 12 is to 18 or two is to five as 12 is to 30. And so, there we have it. We know how many of the
play times were indoors, 12, and how many were outdoors, 18.