which of the following is equal to 200% of 12?​

Question

which of the following is equal to 200% of 12?​

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4 weeks 2021-08-17T09:18:59+00:00 2 Answers 0 views 0

5 is 5% of 100. 12 is 12% of 100. 250 is 250% of 100.

For, a percent is a number of hundredths. 5 is 5 hundredths — 5% — of 100. That is the ratio of 5 to 100. For a percent expresses a ratio, a relationship, between two numbers. What ratio has 6 to 12? 6 is half of 12, or, in the language of percent, 6 is 50% of 12.

When the percent is less than or equal to 100%, then we can say “out of” 100. 25% is 25 out of 100. But 250% cannot mean 250 out of 100 — that makes no sense. It means 250 for each 100, which is two and a half times. (Lesson 16.)

Example 1. $42.10 is what percent of$42.10?

The method of proportions

What percent?

24 out of 100 is 24%. Equivalently, 24 is 24% of 100.

But what percent is 24 out of 200? 24 is what percent of 200?

Answer. Percent is how many out of 100. But if there are 24 out of 200 —

What percent? What percent?

— then out of each 100 there are half as many: 12.

24 is 12% of 200.

Since percents are ratios, then as a proportion problem, we must find the missing term:

24 out of 200 is equal to ____ out of 100?

When we say “24 out of 200,” then the Base — the number that follows “of” — is 200. But with percent, the Base must be 100. What must we do then to 200 to make it 100? We must take half of it or, equivalently, divide it by 2. Therefore we must also divide 24 by 2.

24 out of 200 is equal to 12 out of 100.

But 12 out of 100 is 12%. Therefore, 24 out of 200 is also 12%.

Example 3. What percent is 24 out of 50? Equivalently, 24 is what percent of 50?

Answer. Again, percent is how many out of 100. But if there are 24 out of 50 —

What percent?

— then out of 100, there are two 24’s: 48.

24 is 48% of 50.

Proportionally,

24 for each 50 is equal to 48 for each 100.

Now without even having to write that, the student should see that to go from base 50 to base 100, we have to multiply by 2. Therefore we must multiply 24 by 2, also.

An all too common method these days is to make this an algebra problem.

24

50 = x

100

The student is taught to cross-multiply and solve for x