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Proportions - Problem 1
A proportion is two equal fractions, or two equal ratios. Since the fractions are equal to each other, the variable must have a value that would make the two fractions equivalent. If you know what the two numerators are, think about what you need to multiply the first numerator to get the second. Whatever that value is, multiply it by the known denominator to find the unknown. Use the same process if one of the numerators is unknown by thinking about what number you need to multiply the first denominator by to get the second.
This problem is a proportion. They didn't officially call it that but I know because a proportion is two equal fractions. So when you're given a proportion, there are two equal fractions, there is a couple different ways you might want to think about solving it. One way is to look for what number you're multiplying the first fraction by to get the second.
Another method you might try is cross multiplying and a third method you might try is using your solving techniques. Like for example if I wanted to get t all by itself using solving techniques, t is being divided by -8, the opposite of dividing is multiplying. So one way I could solve this would be to multiplying both sides by -8. The way I'm going to do it is by looking at what number I'm multiplying by to get from the first fraction to the second and in this problem I chose to use that method because I can tell pretty quickly 2 time -4 gives me the answer -8. So that means -5 times -4 gives me my answer for t, -5 times -4 is 20. That's my answer for t. The way I did that was by looking at what number I'm multiplying this first fraction by in order to get the second.
In particular I looked at the denominators here. So this is a way you guys might want to use to solve proportions. You could also use cross multiplying or solving, it's totally up to you. Just be really careful whenever you have negative signs like in this situation.