It’s possible to calculate 0.375 as a fraction, and put it in its simplest form, with only a few quick calculations. The simplest form of the fraction you get from 0.375 is ⅜, but let’s take a closer look at how you would convert the decimal to a fraction and then reduce the fraction down to its simplest form.
The first thing that you need to do to convert a decimal into the simplest form of a fraction is to convert the decimal you have into a fraction. Any fraction will do for this initial conversion. It will help know some things regarding the properties of decimals and fractions. If you know the relationship between decimals and fractions you should be able to easily convert a decimal to a fraction.
Converting A Decimal To A Fraction
Let’s take a look at a quick example of converting a decimal to a fraction. You should remember that decimals are simply used to represent portions of whole numbers. So this means that the numbers that come after the decimal point have number places (columns) just like whole numbers have number places. The tenth place is the first column after the decimal point while the hundredths place is the second column after the decimal point, and so on.
The number 0.75 isn’t a whole number, it means there’s 75% of a whole number. The number 1 will always be equivalent to 100% so to convert a decimal to a percentage, just take the decimal in the hundredths place and move it over two spaces to the right and then put the position of the last column under the new number.
If you have the decimal 0.412, you can convert it to a fraction by noticing that the 2 is the thousandths column, meaning that 0.412 is equivalent to 412/1000. To convert the decimal into a fraction we simply count the number of columns after the decimal point and then moved the decimal point over that many spaces. We then added the value of the last column (the thousands column = one thousand) to the number as the denominator.
The Greatest Common Factor
As far as fractions go, 412/100 is fairly unwieldy. It could be substantially smaller. How would one go about finding the smallest, or simplest, form of the fraction? Finding the smallest/simplest form of a fraction is what we refer to as putting a fraction in its simplest terms, or reducing the fraction. In order to do this, one needs to find something called the greatest common factor or greatest common divisor (GCF or GCD).
The greatest common factor is the largest number which evenly divides into the numerator and the denominator of the fraction. In this case, if you have the fraction 412/1000 and want to put it in its simplest form, know that the greatest common factor of 412/100 is 4. Reducing this down to its simplest form would give us 103/250.
Let’s take a look at another example. Let’s say you have the decimal 0.875. In order to convert it into a fraction, let’s count the columns, move the decimal place over three spaces, and put one thousand underneath it. This gives us 875/1000. The greatest common factor of 875/1000 is 125, and if you divide 125 into the numerator and denominator, you’ll get ⅞.
Finding The GCF
For the two previous examples we looked at, we provided you with the greatest common factor for the fraction. Usually though when trying to determine a fraction’s GCF, you’ll need to do some calculations. To determine the greatest common factor of a fraction, you can use several different methods. One of the ways of determining the GCF is the Prime Factorization method, where you multiply out the prime factors found in both numbers.
For example, let’s look at the fraction 18/24. Prime factors are factors which can only be multiplied by one and itself.
The prime factors of 18 are the numbers 2 and 3 (2 x 3 x 3 = 18), or the smallest numbers you could multiply together to get 18.
The prime factors of 24 are also 2 and 3 (2 x 2 x 2 x 3 = 24). Now if you multiply 2 and 3 together you get 6, which you divide into 18/24 to get ¾.
You could also just list out the common factors between two numbers. For example, if you had 180/210, you could write out the factors of both 180 and 210 and find the great common factor that way.
Factors of 180 (other than one): 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20
Factors of 210 (other than one): 2, 3, 5, 6, 7, 10, 14, 15, 21
The two numbers share the factors 2, 3, 5, 6, 10 and 15. In this case, the largest common factor listed here is 15, and when multiplied by two this creates 30.
30 does indeed happen to be the GCF for 180/210. (Note that you could have also found 30 by multiplying 2, 3, and 5 together). If you divided 30 into 180/210, you get ⅞.
If you had kept going and listed out all the factors, you would have found that 30 was the GCF eventually, but this can take quite a bit of time when compared to using the prime factorization method. There’s another method you can use to find the GCF as well, the Division Method.
The division method is an alternate method of finding the GCF. This method entails dividing the numerator and denominator of the fraction into smaller and smaller chunk until they can’t be divided anymore. Every time the numbers still have common factors that they can be divided by, divide them until you can’t divide them anymore.
As an example, let’s look at the fraction 144/280. Dividing 280 and 144 by 2 gives you the numbers 140 and 72. 140 and 72 can now be divided by 2 again, giving us the numbers 70 and 36.
70 and 36 still have even more common factors between them, so that they still be divided even further. Dividing them by 2 again gives us 35 and 18.
These two numbers don’t have any common factors between them besides 1. Let’s stop here and multiply the numbers we divide them by together: 2 x 2 x 2 gives us 8. If we divide 8 into 144/280 we get 18/35.
To Sum Up
Remember how easy it is to turn a fraction into a decimal, all you need to do is shift the decimal point over to the right until you hit zero. Then you need to count how many columns you moved the decimal point over. If the last number was in the thousandths column, you put 1000 as the denominator of the fraction.
In order to put a fraction into its simplest form, all you need to do is find the GCF. You can find the GCF with one of several different methods:
Listing the primes of the respective numbers and then multiplying together the common prime factors.
Listing out all the factors of the numbers and then selecting the two largest factors the numbers have in common.
Divide the two numbers by common factors until they no long have any common factors between them, then multiply the numbers you divided by together.