Fraction Calculator

Sometimes math problems include the word "of," as in What is 1/3 of 3/8? Of means you should multiply so you need to solve 1/3 3/8. To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator.

This calculator performs the reducing calculation faster than other calculators you might find. The primary reason is that it utilizes Euclid's Algorithm for reducing fractions which can be found on The Math Forum.

Fraction Calculator

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Below are multiple fraction calculators capable of addition, subtraction, multiplication, division, simplification, and conversion between fractions and decimals. Fields above the solid black line represent the numerator, while fields below represent the denominator.

In mathematics, a fraction is a number that represents a part of a whole. It consists of a numerator and a denominator. The numerator represents the number of equal parts of a whole, while the denominator is the total number of parts that make up said whole. For example, in the fraction of 38, the numerator is 3, and the denominator is 8. A more illustrative example could involve a pie with 8 slices. 1 of those 8 slices would constitute the numerator of a fraction, while the total of 8 slices that comprises the whole pie would be the denominator. If a person were to eat 3 slices, the remaining fraction of the pie would therefore be 58 as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.

Unlike adding and subtracting integers such as 2 and 8, fractions require a common denominator to undergo these operations. One method for finding a common denominator involves multiplying the numerators and denominators of all of the fractions involved by the product of the denominators of each fraction. Multiplying all of the denominators ensures that the new denominator is certain to be a multiple of each individual denominator. The numerators also need to be multiplied by the appropriate factors to preserve the value of the fraction as a whole. This is arguably the simplest way to ensure that the fractions have a common denominator. However, in most cases, the solutions to these equations will not appear in simplified form (the provided calculator computes the simplification automatically). Below is an example using this method.

This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem.

An alternative method for finding a common denominator is to determine the least common multiple (LCM) for the denominators, then add or subtract the numerators as one would an integer. Using the least common multiple can be more efficient and is more likely to result in a fraction in simplified form. In the example above, the denominators were 4, 6, and 2. The least common multiple is the first shared multiple of these three numbers.

The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators.

Fraction subtraction is essentially the same as fraction addition. A common denominator is required for the operation to occur. Refer to the addition section as well as the equations below for clarification.

Multiplying fractions is fairly straightforward. Unlike adding and subtracting, it is not necessary to compute a common denominator in order to multiply fractions. Simply, the numerators and denominators of each fraction are multiplied, and the result forms a new numerator and denominator. If possible, the solution should be simplified. Refer to the equations below for clarification.

The process for dividing fractions is similar to that for multiplying fractions. In order to divide fractions, the fraction in the numerator is multiplied by the reciprocal of the fraction in the denominator. The reciprocal of a number a is simply 1a . When a is a fraction, this essentially involves exchanging the position of the numerator and the denominator. The reciprocal of the fraction 34 would therefore be 43. Refer to the equations below for clarification.

It is often easier to work with simplified fractions. As such, fraction solutions are commonly expressed in their simplified forms. 220440 for example, is more cumbersome than 12. The calculator provided returns fraction inputs in both improper fraction form as well as mixed number form. In both cases, fractions are presented in their lowest forms by dividing both numerator and denominator by their greatest common factor.

Converting from decimals to fractions is straightforward. It does, however, require the understanding that each decimal place to the right of the decimal point represents a power of 10; the first decimal place being 101, the second 102, the third 103, and so on. Simply determine what power of 10 the decimal extends to, use that power of 10 as the denominator, enter each number to the right of the decimal point as the numerator, and simplify. For example, looking at the number 0.1234, the number 4 is in the fourth decimal place, which constitutes 104, or 10,000. This would make the fraction 123410000, which simplifies to 6175000, since the greatest common factor between the numerator and denominator is 2.

Similarly, fractions with denominators that are powers of 10 (or can be converted to powers of 10) can be translated to decimal form using the same principles. Take the fraction 12 for example. To convert this fraction into a decimal, first convert it into the fraction of 510. Knowing that the first decimal place represents 10-1, 510 can be converted to 0.5. If the fraction were instead 5100, the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division.

The Fraction Calculator will reduce a fraction to its simplest form. You can also add, subtract, multiply, and divide fractions, as well as, convert to a decimal and work with mixed numbers and reciprocals. We also offer step by step solutions. Step 2:

Just wanted to share my latest find on the goggle app store. A fraction calculator. It makes my life so much easier. I am sure there are a lot of other people in this community who struggle when it comes to fractions.

If you're open to using a small third-party script, you could take a look at fraction.js. As per @Zyberzero's answer, it calculates the greatest common divisor of a non-integer and returns it as the lowest fraction it can make as a string:

If the result is an integer, it will return the same integer. If the result contains an integer, it will return in the format int d/n; so if you want just the fraction, you can split around the space.

It depends how low you want to go, though; there are certain decimal values that notionally represent fractions, but can't be divided to the 'lowest' fraction that you might want. For example, 0.3333333333... ostensibly represents one third, but fractions.js would (correctly) return 33/100. In my most recent use-case, I wanted particular low fractions like 1/3, 1/9, 2/3 etc. (based on decimal values like 0.33, 0.11, 0.66) so I wrote a quick & dirty if/else to give me the lower fractions I was after:

According to Math Through the Ages: A Gentle History for Teachers and Others, the Egyptians were one of the first to devise a form of fraction as early as 1800 B.C. Their concept was mainly limited to parts, otherwise known as unit fractions. Unit fractions use 1 as its numerator.

Parts were expressed as sums of unit fractions. However, the system did not allow unit fractions to be repeated in this sequence, making it difficult to do calculations. To resolve the problem, Egyptians created extensive table listings that supplied the double values of various parts.

Babylonians organized fractions in groups of 60 (base 60). Today, we usually organize numbers in groups of 10. But for calculations like angles and minutes for time, we also use base 60. The system grouped fractions in 10s and used two symbols, one for unit and another for 10.

In Greece, the practice of using fractional values as sumsof unit fractions was fairly common until the Middle Ages. For example, LiberAbbaci by Italian mathematician Fibonacci is anotable 13th century text. It made extensive use of fractions, describingdifferent ways of converting other fractions into sums of unit fraction.

According to Math Through the Ages, it contained most of the usual rules for calculating with fractions, such as how to add, divide and multiply fractions, as well as reduce a fraction to its lowest terms.

Before 1000 B.C., Hindu mantras during the early Vedic period would invoke powers of ten from a hundred, even up to a trillion, according to resource site, The Story of Mathematics. This is evidence that early Indian civilization used complex mathematical operations, including fractions, squares, cubes and roots.

The Indian system wrote fractions by placing one value on top of another, just like how the numerator is written above the denominator today. However, they did not place a line in between it. For instance, the fraction 4/5 would look like this:

Later on, the system was used by the Arabs while trading with the Indians. It was the Arabs who drew a line to distinguish the top number from the lower number in the fraction. This eventually led to the way we write fractions in the modern age.

Moreover, keeping the measurements in one unit allows us to add, subtract, multiply and divide fractions easily. This eliminates the problem of conversion, which is not possible if a measurement is between two different units.

While decimals provide an alternative way of indicatingfractions (and an easier way to calculate fractions using a calculator), it isimperative to understand traditional fractions and how their values affect awhole number. ff782bc1db