Part to whole ratio word problem using tables
About this video
The ratio of indoor to outdoor play times is 2:3, and there are 30 play times in total. The video sets up a table with the original ratio (2 indoor, 3 outdoor, 5 total) and the actual counts. Because 5 times 6 is 30, every part is multiplied by 6, giving 12 indoor and 18 outdoor play times.
You'll be able to
- find the total part of a ratio by adding its parts (2:3 means 5 in total).
- use a table to go from a ratio to actual counts.
- find the scale factor from the total and multiply every part by it.
- check an answer by making sure the ratio still holds.
Key words
- ratio
- A comparison of two quantities, like 2 indoor play times for every 3 outdoor ones.
- part-to-whole ratio
- A ratio comparing one part to the total, like 2 indoor play times for every 5 total.
- actual counts
- The real numbers in the situation, as opposed to the numbers in the ratio.
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.
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