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Comparing Quantities

We are familiar with comparing fractions and comparing decimals .

But what if we have to compare a fraction with a decimal? For example, is 5 7 greater or less than 0.6 ? Or, what if we have to compare a percent with a fraction? For example, is 25 % greater or less than 2 9 ?

The best way to do this is to convert both quantities to the same form. That is, convert both the quantities into a decimal or fraction or percent, and compare them.

Example 1:

Which number among 1 4 and 0.3 is greater?

Here, one number is a fraction and the other is a decimal.

To make the comparison easier, convert the fraction into a decimal. Divide the numerator by the denominator.

So, 1 4 = 0.25 .

Thus, we have two decimals, 0.25 and 0.3 . Since 0.3 > 0.25 , the decimal 0.3 is greater than the fraction 1 4 .

Example 2:

Fill in the blanks with < , >  or  = .

0.4 _ 45 %

Here, one number is a decimal and the other is a percent.

To make the comparison easier, convert the percent into a decimal.

Remember that a percent is really just a special way of expressing a fraction as a number out of 100 . Then, 45 % = 45 100 = 0.45 .

So, 45 % = 0.45 .

Thus, we have two decimals, 0.45 and 0.4 . Since 0.4 < 0.45 , 0.4 < 45 % .

Example 3:

Jordan finished 3 out of 8 homework problems. Kate is done with 40 % of her homework problems. Who has done a greater percentage of homework?

Here, one number is a fraction and the other is a decimal.

To make the comparison easier, convert the fraction into percent. First, divide the numerator by the denominator.

So, 3 8 = 0.375 . Now, to convert to percent , multiply the decimal by 100 .

0.375 × 100 = 37.5

That is, 3 8 = 37.5 % .

Since 40 % > 37.5 % , Kate has done a greater percentage of homework.