23/29 - 32/1,613 + 38 - 31/23 = ? Adding Ordinary (Simple, Common) Math Fractions Calculator, Addition Explained Step by Step

23/29 - 32/1,613 + 38 - 31/23 = ?

Reduce (simplify) fractions to their lowest terms equivalents:

To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.

Fraction: 23/29 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
23 is a prime number;
29 is a prime number;
gcf (23; 29) = 1;


Fraction: - 32/1,613 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
32 = 25;
1,613 is a prime number;
gcf (25; 1,613) = 1;


Fraction: - 31/23 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
31 is a prime number;
23 is a prime number;
gcf (31; 23) = 1;

Reduce (simplify) fractions to their simplest form, online calculator


Rewrite the improper fractions:

Fraction: - 31/23


- 31 ÷ 23 = - 1 and remainder = - 8 => - 31 = - 1 × 23 - 8


- 31/23 = ( - 1 × 23 - 8)/23 = ( - 1 × 23)/23 - 8/23 = - 1 - 8/23;



Rewrite the equivalent simplified operation:

38 + 23/29 - 32/1,613 - 31/23 =


38 + 23/29 - 32/1,613 - 1 - 8/23 =


37 + 23/29 - 32/1,613 - 8/23

To operate fractions, build up their denominators the same.

Calculate LCM, the least common multiple of the denominators of the fractions:

LCM will be the common denominator of the fractions that we work with.

The prime factorization of the denominators:


29 is a prime number;


1,613 is a prime number;


23 is a prime number;


Multiply all the unique prime factors, by the largest exponents:


LCM (29; 1,613; 23) = 23 × 29 × 1,613 = 1,075,871


Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction:

Divide LCM by the numerator of each fraction.


For fraction: 23/29 is 1,075,871 ÷ 29 = (23 × 29 × 1,613) ÷ 29 = 37,099;


For fraction: - 32/1,613 is 1,075,871 ÷ 1,613 = (23 × 29 × 1,613) ÷ 1,613 = 667;


For fraction: - 8/23 is 1,075,871 ÷ 23 = (23 × 29 × 1,613) ÷ 23 = 46,777;


Build up the fractions to the same denominator:

Expand each fraction - multiply the numerator and denominator by the expanding number.


Then work with the numerators of the fractions.


37 + 23/29 - 32/1,613 - 8/23 =


37 + (37,099 × 23)/(37,099 × 29) - (667 × 32)/(667 × 1,613) - (46,777 × 8)/(46,777 × 23) =


37 + 853,277/1,075,871 - 21,344/1,075,871 - 374,216/1,075,871 =


37 + (853,277 - 21,344 - 374,216)/1,075,871 =


37 + 457,717/1,075,871


Reduce (simplify) the fraction to its lowest terms equivalent:

To reduce a fraction: divide the numerator and denominator by their greatest common factor, GCF.

457,717/1,075,871 already reduced to the lowest terms.


The numerator and denominator have no common prime factors.


Their prime factorization:


457,717 = 13 × 137 × 257;


1,075,871 = 23 × 29 × 1,613;


gcf (13 × 137 × 257; 23 × 29 × 1,613) = 1;


Reduce (simplify) fractions to their simplest form, online calculator


Rewrite the expression:

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.


Proper fraction = numerator smaller than denominator.


37 + 457,717/1,075,871 = 37 457,717/1,075,871

As a positive improper fraction (numerator >= denominator):

37 + 457,717/1,075,871 =


(37 × 1,075,871)/1,075,871 + 457,717/1,075,871 =


(37 × 1,075,871 + 457,717)/1,075,871 =


40,264,944/1,075,871

As a decimal number:

37 + 457,717/1,075,871 =


37 + 457,717 ÷ 1,075,871 ≈


37.425438551648 ≈


37.43

As a percentage:

37.425438551648 =


37.425438551648 × 100/100 =


(37.425438551648 × 100)/100 =


3,742.543855164792/100 =


3,742.543855164792% ≈


3,742.54%

>> Convert fractions to percentages, online calculator


The final answer:
:: written in four ways ::

As a mixed number (also called a mixed fraction):
23/29 - 32/1,613 + 38 - 31/23 = 37 457,717/1,075,871

As a positive improper fraction (numerator >= denominator):
23/29 - 32/1,613 + 38 - 31/23 = 40,264,944/1,075,871

As a decimal number:
23/29 - 32/1,613 + 38 - 31/23 ≈ 37.43

As a percentage:
23/29 - 32/1,613 + 38 - 31/23 ≈ 3,742.54%

More operations of this kind:

How to add the ordinary fractions:
- 30/37 + 41/1,623 - 45/6 - 37/29


Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case);

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation;

Add ordinary fractions, online calculator

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see more... added fractions

How to: Adding ordinary (simple, common) math fractions. Steps.

There are two cases regarding the denominators when we add ordinary fractions:

A. How to add ordinary fractions that have like denominators?

An example of adding ordinary fractions that have like denominators, with explanations

B. To add fractions with different denominators (unlike denominators), build up the fractions to the same denominator. How is it done?


>> Read the rest of this article, here: How to add ordinary (common) fractions?

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers