Calculator Fractions
Roselee Kruppa
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.
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.
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.
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.
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:
If you click the MODE key, you will be greeted with a menu that shows you the settings of the calculator. Scroll down until you find the Exact/Approx option and select the one you wish. Exact -- with fractions, Approx -- no fractions.
Added
Or how about a simpler example like 2.5 or 5.125 So, a fractional part that can be represented in binary? So for 2.5 that calc should show 010.10 or 1.10*2^3. Or for 5.125 the calc should show 0101.001 or 1.01001*2^5 Can the windows calculator show that?
Your number 0.21 is stored in memory as 1.6799999475479126 * 2^(-3) which is equivalent to 0.20999999344348907470703125 (windows calculator shows this as 0.209999993443489075 when calculating manually)
Any calculator that utilises this standard will store numbers in the same format (if it doesn't, excluding different endianness, it probably has a different way of storing floating point numbers, so when passing values from one piece of software/hardware to another, translation must happen, but this is a different topic altogether).
Now, to answer your question, while Windows calculator stores the numbers in this form, it hasn't been designed to show you the intermediate/raw values in the memory. If you really felt like it, you could use a memory viewing tool and spy on values as you type them in the calculator, but again, that is a different topic...
@Keltari Generally, fraction value CAN be represented in binary, using kind of "binary point" (counterpart of decimal point). In fact, that is how real/double numbers are represented in computers (although usually binary point position is stored, instead of the "point character"). But remember: not all decimal fractions can be represented in binary form exactly - some rounding must be applied then, especially if only limited count of bits can be used (which is always true in real computer science world).
BTW Usually count of bits used to represent data in computers is power of 2 - 8, 16, 32, 64, sometimes 48, etc. In such a case, you can simply use faster "multipling by 2" method in the calculator, suggested by you in comment below (*(2^n)).
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.
Some calculators can show a decimal as a fraction if applicable. eg. 1.333333 -> 1r1r3 on my calculator (hardware) representing \$1 \frac13\$. Can the built in calculator do that? If not which (software) can?
I've been having troubles trying to get my fractional calculator to work. I'm trying to get the simplifying to work, it works correctly simplifiyng positive fractions, but if I were to put a negative fraction it won't simplify it, I'm not sure what I'm doing wrong and I've read over it numerous times (the Gcd and Reduce functions).
In a routine clinical environment, it can be difficult to determine the most effective fractionation for a patient undergoing treatment. Biological Effective Dose (BED) and Equivalent Dose in 2Gy Fractions (EQD2) are often used to quantify radiobiological concepts into concrete interpretable values. Here, we present a BED/EQD2 calculator and a brief background on the topic and its applications.
However, you can enhance the type of mathematical equations you're able to conduct by tilting your iPhone's Calculator sideways to access a scientific-calculator layout in landscape mode, allowing you to perform mathematical formulas like fractions or square roots.
3. When you are ready to compute fractions, input the number you wish to convert into a fraction. Then, you can press the 1/x button to put that number in the denominator (the numerator will be 1), and get your fraction value.
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.
760c119bf3