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what value is the largest a. 3/8 b.0.45 c. 42% d. 12/25

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2 Answers

3/8, .45, 42%, 12/25

turn all fractions and percents into decimal.

3/8 = .375

.45

42% = .42

12/25 = .48

we see .48 is the largest. So, 12/25 is the largest.

 

Hi Leslie,

For this question, all of the given options should be converted into the same form to make it much easier to determine which is largest. In this case, let's convert all of the options into a simple fraction. To do this, we must find the least common denominator among all four values. At first glance, it appears that 100 may be a suitable choice, since b. 0.45 and c. 42% are already written out of 100 and d. 12/25 goes into 100 evenly 4 times. But, a. 3/8 does not divide into 100 evenly, so we must use 200 as our least common denominator (8 divides into 200 evenly 25 times). 

b. is written as a decimal, 0.45. This simply means "45/100." To get this value out of 200, all we do is multiply the whole fraction by 2. We're left with 90/200 (45 * 2 = 90; 100 * 2 = 200).

c. is given as a percent, which simply means "out of 100." So, 42% can be written as 42 out of 100, or 42/100. As we did in b., we multiply the whole fraction by 2 to get a denominator of 200, and we're left with 84/200 (42 * 2 = 84; 100 * 2 = 200).

d. is given as a simple fraction, 12/25. Now that we have our least common denominator of 200, we must convert this simple fraction into something/200 to be able to compare it with the rest. Luckily, 25 goes into 200 eight times, so we multiply the simple fraction by 8. We're left with 96/200 (12 * 8 = 96; 25 * 8 = 200).

a. is also given as a simple fraction, 3/8. As we did in d., we multiply the whole fraction by the factor that gives us a denominator of 200. In this case, it is 25 because 8 goes into 200 evenly 25 times. Multiplying the whole fraction by 25 gives us 75/200 (3 * 25 = 75; 8 * 25 = 200).

Now that we have all four values in the same form, we can compare them very easily. In fact, we can ignore the denominator in all of them since they are exactly equal (200). 

So, 75 < 84 < 90 < 96; and d. is largest.

 

This can be solved several different ways, and it's a tricky one to explain through text, but I hope you get the gist of it all!