What Is A Fraction Reciprocal

Visual Fraction Calculator

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Welcome to the Fraction Calculator

This page hosts a fraction computer that can perform improver, subtraction multiplication or partition of two fractions. The values for the calculation tin can be simple or mixed fractions, or consist of but wholes. Input of improper fractions is allowed. Enter the values direct into the corresponding locations in the fraction calculator and the answer will be updated in real time. A visualization of the operand fractions and the answer fraction is shown in the panel underneath where the values are entered.

Consummate steps for solving each blazon of fraction operation will exist listed in a version of the fraction calculator coming soon! This office of the fraction computer is designed to illustrate not only the answers, but provide a learning tool so you can see how the bug were solved.

If you wish to save the fraction calculator showing the problem y'all're working on, the "Share this Calculation" link can be copied and pasted into an e-mail, your browser bookmarks or a web page. It will return to the fraction estimator and show the problem exactly as you see it.

Don't just apply this fraction calculator to race through your homework! Solve the problems on your own, and employ the computer to bank check your piece of work or come across how to work a trouble you don't understand. This fraction reckoner is a useful tool, simply it'south non a substitute for a powerful mathematical mind! At that place is no substitute for developing a solid set up of concepts, and this lesson provides an interesting introduction to fractions if you are looking for some other approach.

When nosotros learn the bones math operations, we start by dealing with the operations on integers. But the world is total of partial amounts of things… A half cup of carbohydrate in a recipe or six tenths of amile or a quarter dollar. All of these represent a portion of a whole, and that'southward exactly what a fraction is. We deal with fractional amounts every day, so these ideas are familiar even if the way we have to work with them in math at first seems a little intimidating. Don't worry! We'll make it piece of cake!

Real-World Uses for the Fraction Calculator

A fraction is a way to correspond in mathematical terms a smaller role of a whole of something. Then in our pizza instance, if the whole pizza is cut into eight equal slices, and y'all eat three slices, yous would accept eaten three out of the eight parts of the whole. We represent this as a fraction as 3/8 and we say, "three eighths" when we read it aloud.

There are special terms for the numbers that make up a fraction. The number on the bottom is called the denominator. This is how many parts the whole is divided into. In our pizza instance, the whole is divided into 8 parts, then this fraction has a denominator of eight. The give-and-take denominator is a fancy word that simply means "the thing that divides." Sometimes instead of denominator you may see the word divisor, just it's the same thing.

Another way to think about a denominator is to understand it tells yous how large each fractional slice is, and so for instance if our pizza is sliced into eight pieces, you lot tin motion picture in your mind roughly how big each one is. If our pizza is sliced into 20 slices, yous can imagine that each piece is going to be much smaller. This can be a stumbling block… Equally the denominator gets larger, each fractional part of the whole is actually smaller. This can exist confusing when yous are first learning near fractions because we are used to larger numbers corresponding to significant larger real-world values, but in this example a larger value in the divisor may actually brand the value of the entire fraction smaller. For example, 1/8 is actually a bigger value (a bigger slice of pizza) than 1/20.

The peak number in a fraction is chosen the numerator, which is just another fancy for that means "the thing that counts." This represents the bodily value in terms of how many parts of the whole are being represented by the fraction. In our pizza case, when you were really hungry and ate three slices, we represented that equally the fraction 3/8. The numerator is three in this example and represents the three of the viii parts that make up the whole.

That's actually as complicated as it gets. A unproblematic fraction merely has two parts, the numerator on summit and the denominator on the bottom. The denominator tells us how many pieces a whole is existence divided into, and the numerator tells us how many of those pieces the fraction is meant to represent.

If this however seems a fleck fuzzy, here'due south another great clarification of fraction concepts with a few illustrations.

Mixed Fractions and Improper Fractions with the Fraction Calculator

Mixed fractions stand for some number of wholes, likewise as a fractional part. Three and a half cups of sugar would be an instance of something that you would represent with a mixed fraction.

Sometimes working with fractions in the steps you calculate a numerator larger than the denominator. This is chosen an "improper fraction." An example would exist something similar 9/eight, which means nine parts of a whole, where each whole is divided into viii parts. If the devisor is telling us a whole is divided into eight parts, if we have nine parts we take enough for a complete whole with one part left over. So this ways 9/8 is the same as one whole plus one part, or the mixed fraction i/8.

When you lot are using the fraction calculator on this page, you can enter either improper fractions or mixed fractions and it will calculate the results for you appropriately, simply the answer volition always be given as a proper fraction.

Reducing Equivalent Fractions with the Fraction Calculator

If you're really thinking about fractions work, you might meet that you lot can stand for the aforementioned fractional amount with dissimilar fractions that have different denominators. If nosotros go back to visualizing our pizza, if a whole is divided into 4 parts, half is going to be two slices. Yet, if the whole is divided instead into eight parts, half of the pizza would be four slices. In these examples, two/4 and four/viii are both the aforementioned corporeality of the whole. ii/four, 4/8 and i/2 are all equivalent fractions because the represent the same real-world corporeality of a whole value.

Of course, the simplest style to represent any of those values is simple to say, "one half" and the fraction in simplest form that represents this is obviously 1/2. The ii in this case is the smallest divisor possible that represents the fraction. Getting to the smallest possible devisor is called "reducing fractions" to their simplest class. This fraction reckoner automatically reduces fractions in the answers.

Adding Fractions with the Fraction Calculator

The process of adding fractions is straightforward if the denominators are the same. Simply add together the numerators, and the resulting fraction has the same denominator. So one slice of pizza (ane/eight) plus another (1/eight) equals two slices of pizza (2/eight). That fraction could be reduced to 1/4, and mentally that makes sense because those 2 slices stand for 1 quarter of the whole.

If you start with two fractions with different denominators, you need to find the least mutual denominator. This is the smallest denominator that will piece of work to make equivalent fractions for each of the fractions y'all are attempting to add together. For example, if nosotros were trying to add 3/16 and 1/viii, we could turn the one/8 into the equivalent fraction 2/sixteen. Now we are adding iii/sixteen and ii/xvi which equals 5/sixteen.

You can find more virtually common denominators in full general at WikiPedia but this link provides another good description of actually finding least mutual denominators at Quick and Dirty Tips.

Fifty-fifty though 2/16 is not a reduced fraction, for purposes of computing the answer it'due south okay to create not-reduced fractions or even improper fractions. We just desire to return the fractions in proper reduced form when we provide an answer at the end.

Again, this fraction calculator does all of these steps for you, so if you demand to run across more examples, try a problem out and see how it works! Noticing that when you lot are adding fractions, the visual preview in the fraction figurer shows how the two original fractions might combine to form the answer fraction.

Subtracting Fractions with the Fraction Computer

Subtracting fractions works much the same as calculation fractions. Yous need to insure the fractions have a common denominator, then simply subtract the numerators and reduce the answer fraction.

Simply like with addition, if you are starting with a mixed fraction, you may need to convert the fraction to improper form to subtract the numerators. This is the opposite of the procedure we used to create proper fractions. To create an improper fraction, multiply the wholes past the denominator and add it to the numerator value. And so 1 and one/8 is the aforementioned every bit one whole plus one part, or viii parts plus one part, or a total of nine parts. And so the proper mixed fraction one 1/8 as an improper fraction is 9/viii.

When subtracting fractions, if y'all take a larger fraction away from a smaller fraction, yous will be left with a negative corporeality. You'll show the resulting fraction with negative sign on either the whole amount or the numerator. A negative fraction should simply take one negative sign. A mutual mistake is to think you need to put brand both the numerator and the denominator negative if you take a negative reply. Don't do this! If your respond is negative, you should only see one negative sign on the resulting fraction.

Multiplying Fractions with the Fraction Calculator

Multiplying fractions is in some means less complicated than calculation or subtracting fractions considering y'all don't need a common denominator. However, a good showtime footstep is to see if the one or both of the fractions being multiplied can be reduced. This will make the calculations a little easier.

If either of the fractions are mixed, turn them into improper fractions using as described above. If you are multiplying a fraction by a whole value, plow the whole into a fraction with a denominator of one, so for case the whole three is turned into the fraction iii/i for the sake of doing the multiplication.

Next, to become the numerator for the answer, multiply the two numerators of the fractions you are starting with. To get the denominator, exercise the same thing, multiply the two denominators and write the upshot as the denominator in the answer fraction.

There's a good likelihood that the resulting fraction is improper or could be reduced. You lot should always reduce your answer and put it in proper form. Once more, if y'all need help with this, try a fraction multiplication problem using the fraction calculator on this page and information technology will show you lot an example. This fraction calculator volition ever simplify fractions in the respond.

Dividing Fractions with the Fraction Reckoner

The procedure for dividing fractions is similar to multiplying fractions with one additional pace. Start post-obit the steps for multiplying fractions. As soon as you have the 2 fractions in improper class and you're ready to multiply the numerators and denominators, yous do ane more step showtime. On the second fraction, swap the numerator and the denominator. So the old denominator goes on peak and becomes the numerator, and the old numerator goes on bottom and becomes the denominator. Then, finish the procedure for multiplying fractions… Multiply straight across, reduce and but.

When yous swap the numerator and denominator of a fraction, the result is something chosen a reciprocal. This procedure is sometimes called "inverting" or "taking the reciprocal" of a fraction. A reciprocal of a fraction has an interesting feature. If you multiply a fraction and a reciprocal of that fraction, the result will take the same number on the in the numerator and the denominator, which means information technology will reduce to one. Attempt it out in the fraction calculator by multiplying 2/3 by 3/two and run into.

Multiplying Fraction Calculator

Simplify Fractions Calculator

This fraction calculator will automatically simplify results. If you need to simplify fractions, this fraction calculator can do the work for you lot by entering a regular fraction, mixed fraction or improper fraction so multiply the value by 1. The fraction computer will simply the reply for you lot. For example, if you enter four/32 x 1 in the fraction calculator, the simplified product is i/eight.

Simplify Fraction Calculator

Mixed Fraction Calculator

This faction calculator handles mixed fractions for all operations and will return the event in simplest grade. When the fraction calculator deals with mixed fractions, the procedure is almost e'er easier if the whole number is multipied by the denominator and added to the numerator to create an improper fraction. This conversion from mixed numbers to improper fractions allows fraction issues to be treated just as though the whole numbers were not involved.

The fraction figurer does this internally to solve mixed fraction bug.

For adding fractions or subtracting fractions, the fraction calculator still needs to make up one's mind a common denominator. Then, later completing the operation, if the resulting fraction is still improper the fraction calculator converts information technology back to a mixed fraction for use as the reply.

Even once the fraction figurer factors a whole number out of an improper fraction, the resulting mixed fraction may not nevertheless be in simplest class. If the fraction can be reduced, the fraction figurer will find a common divisor of both the numerator and the denominator and so divide both components to simplify the final fraction.

You lot're Ready for Fractions with Our Online Fraction Calculator

This page has given a very cursory overview of fractions, and provided a number of examples that you can attempt in the fraction calculator. Nosotros covered adding fractions, subtracting fractions, multiplying fractions and dividing fractions, plus how to create a proper fraction from an improper fraction (and vice-versa), reducing fractions, finding a least common denominator, plus how have a reciprocal of a fraction. You've seen how to utilize the fraction estimator to simplify improper fractions, and how to utilise the fraction estimator to reduce fractions. You can try all of these concepts in the fraction calculator, report the results and you lot'll discover you're a fraction rock star in no time!

When you're gear up for more, endeavour out the fractions worksheets below for exercise and share this fraction computer with your friends!

Online Fraction Calculator

Fraction Calculator Updates

Date	Description
03/30/2022	Native Vue.js version of the Fraction Calculator.
01/07/2018	Modified loading of JavaScript files so that the fraction calculator executes earlier on the folio, making the calculator appear before during the page load.
10/24/2016	When multiplying fractions, the fraction reckoner displayed some mixed fractions inconsistently. Added instructions for how to simply fractions using the fraction calculator past multiplying.
10/09/2016	Corrected mal-formed HTML in the fraction estimator instructions.
09/27/2016	I received some outstanding advice from my friend Maria Miller on the preview portion of the fraction figurer. The previews for adding fractions and subtracting fractions at present show small mixed fractions with the wholes component as diagrams instead of numbers. For multiplying fractions, the kickoff multiplicand is shown every bit a numeric mixed fraction to reinforce the idea that the 2nd fraction is repeated. Similarly, for dividing fractions, the fraction calculator shows the divisor is shown equally a mixed fraction to reinforce the thought of the dividend being dissever upwards that many times to yield the quotient.