Inputs data - fraction, which you're going to explore

Enter fraction here

Results - informations about your fraction

Simple conversions

Fraction you entered

5	12
	16

Equal improper fraction
(top-heavy fraction)

Equal proper fraction

5	12
	16

Equal proper simplest fraction

5	12 :4
	16 :4

5	3
	4

Factorization of numerator and denominator

Factors

5	2 × 2 × 3
	2 × 2 × 2 × 2

Factors grouped

5	2² × 3
	2⁴

Reductions (simplyfing)

Simplest

5	12 :4
	16 :4

5	3
	4

Reductions step-by-step

5	12 :2
	16 :2

5	6 :2
	8 :2

5	3
	4

Some facts

Fractions let you express part of a whole, eg. half of the cake can be written as 1/2, and a quarter of chocolate as a 1/4.
Fractions consists of two numbers separated by a hyphen. Number listed above the line is called numerator, and under line denominator.
Fractions where numerator is greater than denominator e.g. 5/4 are correct too. These type of fractions represent number greater than one. They are called improper fractions or heavy top fractions.
Fractions with numerator less than denominator e.g. 1/2 are called proper fractions.
Fraction slash can be replaced by a division sign.

How to use this tool

This calculator can help you in many common fraction related excersises, for example:

Convert fraction into improper form (top-heavy) - to do this, enter wholes, numerator and denomintator of your fraction and then go to simple conversions → equal improper fraction section. Your fraction converted into improper form should be there.
Quick reminder:
- Numerator of top-heavy fraction (improper fraction) is always greater than it's denominator.
- To convert fraction from proper into top-heavy one you should include wholes part into numerator using below formula:
  
  $C \times \frac{a}{b} = \frac{C \times b + a}{b}$
- Improper fraction (top-heavy) is always greater than one. For example 3/2 of bar of chocolate is the same as 1 and 1/2 bar, so it's more than one bar.
Convert improper fraction into mixed (proper) form - to do this, enter numerator (greater than denominator) and denominator of your fraction and then go to simple conversion → equal proper fraction section. Your fraction converted into proper form should be there.
Quick reminder:
- We say that fraction is given in proper form if it's numerator is lower than denominator.
- To convert improper fraction (top-heavy) into proper one you should factor out wholes part before fraction bar e.g. 3/2 = 1 1/2.
- The fractional part of proper fractions is always lower than one.
Reduction (finding of the simplest form) - to do this enter numerator, denominator and optionally the wholes part of your fraction and then go to reduction section. You should see your fraction in the simplest form and steps showing how to find it on your own here..
Quick reminder:
- Reduction does not change fraction value - it's still the same fraction (it's the same amount, the same value), but presented in alternative form e.g. 6/8 and 3/4 are the same number.
- To reduce your fraction you should divide numerator and denominator by their common division.
- We say that fraction is given in the simplest form if there is no common divisors of it's numerator and denominator. In this case fraction is reduced as much as possible and there is no way to reduce it more.
- It often happens that the same fraction can be reduced more than one time by searching for the next and then again for the next numerator and denominator divisors. It means that there could be more than one way to found the simplest form of your fraction.
Factorization of numerator and/or denominator - to do this enter numerator, denominator and optionally wholes part of your fraction and then go to factorization of numerator and denominator section. You should see your fraction with numerator and denominator presented as product of prime numbers (factorized).
Quick reminder:
- Factorization is converting given number into product of prime numbers.
- Prime numbers have only two divisors: one number and self.
- Factorization of numerator and denominator can be helpful during reducing the fraction, beacuse it makes easier to see common numerator and denominator divisors, which would be used to reduce it.

What is the meaning of each calculator field ?

Inputs data - fraction, which you're going to explore - simply enter your fraction in any form you have (proper, improper etc.) here.
Quick reminder: the fraction consists of numerator (part "above fraction mark"), denominator (part "below fraction mark") and - optional, in case of mixed fractions - wholes part (number "before fraction").
Results - informations about your fraction - here you can see your fraction after various transformations, it means that your fraction still has the same numerical value, but it's presented in different, alternative form.
- Simple conversions:
  - Fraction you entered - simply your fraction in original form once again.
  - Equal improper fraction (top-heavy fraction) - your fraction converted into improper form i.e. after including wholes into numerator. Fraction presented here will be different from original one, only if your input fraction contains wholes part. The specific thing of top heavy fractions is that their numerator is greater than denominator.
  - Equal proper fraction - your fraction converted into proper form i.e. after moving wholes before the fraction. Fraction presented here will look different from original one, only if your input fraction is given in improper form i.e. if it's numerator is greater than denominator.
  - Equal proper simplest fraction - as above - your fraction converted into proper form, but after reducing numerator and denominator by common divisor if possible.
- Factorization of numerator and denominator:
  - Factors - your fraction after numerator and denominator factorized i.e. presented as product of prime numbers.
  - Factors grouped - as above, but after grouping repetitive factors and converting them into powers.
- Reductions (simplyfing):
  - Simplest - your fraction after reduction (as much as possible), it's the simplest form of your fraction.
  - Reductions step-by-step - as above, but you can see step-by-step how we found the simplest form of your fraction.

Tags and links to this website

Tags:

fraction · simplifying_fractions · extending_fractions

Tags to Polish version:

ulamek · ulamki · skracanie_ulamkow · rozszerzanie_ulamkow

What tags this calculator has

CALCULATOR · MATH · A -> Z (all)

Permalink

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http://calculla.com/fraction?inFraction=$fract(p,5,12,16)

Links to external sites (leaving Calculla?)

wikipedia: fraction

Ancient version of this site - links

"Calculla v1" version of this calculatorIn December 2016 the Calculla website has been republished using new technologies and all calculators have been rewritten. Old version of the Calculla is still available through this link: v1.calculla.com. We left the version 1 of Calculla untouched for archival purposes.
Direct link to the old version:

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