The simplified or reduced ratio " 3 to 4 " tells us only that, for every three men, there are four women. These relationships and reasoning are what we use to solve many word problems:. By "representative group", I mean a group which has the same ratio of students as are in the entire class. I can figure out the size of this group by using the ratio they've given me.
The size of the representative group will be the sum of its parts:. So the representative group has 12 students in it, of which 7 passed and 5 failed. In particular, the fraction of the group that failed is given by dividing the number of flunking students by the total number of students in the representative group. That is:. This means that I can now find the number of students in the entire class that flunked this exercise is depressing! So, of the class of 36 students, the class was not passed by:.
The ratio from a representative group can also be used to provide percentage information. I already know that the representative group contains 12 students, of which 7 passed the class. Converting this to a percentage by dividing, and then moving the decimal point, as explained here , I get:. I can use this fraction from the representative group to find the answer for the entire group:. Generally, ratio problems will just be a matter of stating ratios or simplifying them.
For instance:. This exercise wants me to write the ratio as a reduced fraction. So first I'll form the fraction, and then I'll do the cancelling that leads to "simplest form". The dollar signs cancelled off, too, because they were the same, top and bottom, in the ratio's fractional form.
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He climbs 50 meters per hour for 8 hours per day. How many days will it be before he reaches the peak? Now divide by the daily rate to find the number of days it will take him to reach the top.
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Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Example 1: A punch recipe calls for 6 ounces of lime juice, 21 ounces of apricot juice, and 21 ounces of pineapple juice.
Example 2: In the recipe above, what is the ratio of apricot juice to the total amount of punch? Luckily for us, going from down to is quite easy. We just divide the denominator by 3, and then also divide the numerator by 3.
What we end up with is the fact that Once we find out the number of carpentry students per students, we automatically have our percentage. Step 1 : Put the numbers into an equation that we can work with. In this case, put the numbers into a fraction. Now calculate the percentage of plumbing apprentices. Check the video to see if your answer is correct. The next step actually makes the whole process of finding percentages easier.
In this section, we skip that whole procedure and just take the numbers we have and work with them as they are. We could go back to our old ways and get to a fraction with a denominator of , or we could simply divide the 57 by the Now take the 0. This moves the decimal point 2 spots to the right and leaves us with a whole number. Using the same method we just used with the carpentry apprentices, find the percentage of plumbing students in the trades college. Step 2 : Work this out in your head.
Just kidding: grab your calculator and plug the numbers in. Try these practice questions. You can either change each number into a fraction with a denominator of , or you can divide one number by the other.
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