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Article Summary: "When you go to the store and something costs $3 and you hand the clerk a $5 bill you will receive $2 in return. This is pretty easy to keep account of as the two one dollar bills are whole numbers. But which price savings would you rather have 25% off, 1/4 off, or only pay 0.75 the cost? They are all the same, but somehow look a little different."

Home > Math Tips > Fractions, Decimals, and Percents: How do they relate and how do they differ?

Fractions, Decimals, and Percents: How do they relate and how do they differ?

When you go to the store and something costs $3 and you hand the clerk a $5 bill you will receive $2 in return. This is pretty easy to keep account of as the two one dollar bills are whole numbers. But what if 10% sales tax was added to the $2 purchase? Then, you would have to pay an increase of 1/10 to your purchase. You change would no longer be $3 but $2.80. Yes, simply making a slight change to a whole number brings you right into the world of fractions, decimals and percents. Fractions, decimals and percents are everywhere and you simply can not avoid them even if you tried. One would believe that the commonality of these three values would lead to people understanding them better but many are still a little bit in the dark as to their value. So, it becomes important to understand what they are and how they differ from one another.

A fraction refers to "part" of a whole number. For example, 1 is a whole number and if you were to cut it in half you would be left with the fraction of 1/2 A fraction is made up of two separate whole numbers a numerator and a common denominator. In 1/2, the number two is known as the common denominator and the 1 is the numerator.

The relationship between fractions, decimals and percents is clear when you look at the fraction �. When you divide the numerator by the common denominator you get a decimal. That is seen in the following: 1 divided by 2 equals .5. This relates to a percentage in the sense that .5 is a half and half is represented in percents as 50%. So, if .5 = 50% and 1/2= .5 then 1/2= 50%. Making a fraction into a percent is easy as you simply place the percentage over the whole number 100 and then reduce it. So, 50% becomes 50/100 which is reduced to 1/2. 50% becomes a decimal by then dividing the whole number by a common denominator. 1/2 becomes 2 divided by 1 which equals .5 So, the relationship between fractions, decimals and percents is that they are simply different numerical expressions of the same value.

This is commonly known as a mixed number which is the result of an improper fraction. Improper fractions (colloquially called a 'top heavy' fraction) are fractions that have a numerator that is greater than the common denominator. For example, 33 1/3 would appear as the following fraction 10/3. When reducing the fraction the result is the improper number .333 with the threes going on into infinity. Interestingly, fractions never appear in decimals, however, as 33 1/3% would be reflected as .333.

But, once again, while they look different they simply express the same values through different representations. For example, did you know, however, that there is a method of telling time known as the decimal method? When we look at the clock - even a digital clock - we are looking at fractions based on 24 hours in the day. (Actually 12 hours but we realize that the same time slots are repeated during AM or PM) The decimal system, however, bases its ability to tell time on using decimals and the power of ten. This is commonly called military time and is ranges from 0000 to 2400 hours. Both methods are designed to express the passage of 24 hours and both do so accurately. They simply do it in a different representational method.

So, you can say that fractions, percents and decimals are two sides of the proverbial same coin with each having their own unique traits.