Add fractions: 26/53 + 19/40 = ? Addition of ordinary (simple, common) math fractions, result explained

The executed operation (with ordinary fractions):
26/53 + 19/40

Reduce (simplify) fractions to their lowest terms equivalents:

Fraction: 26/53 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
26 = 2 × 13;
53 is a prime number;


Fraction: 19/40 already reduced to the lowest terms.
The numerator and the denominator have no common prime factors.
Their prime factorization:
19 is a prime number;
40 = 23 × 5;

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


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 compared fractions

The prime factorization of the denominators:


53 is a prime number;


40 = 23 × 5;


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


LCM (53; 40) = 23 × 5 × 53 = 2,120


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: 26/53 is 2,120 ÷ 53 = (23 × 5 × 53) ÷ 53 = 40;


For fraction: 19/40 is 2,120 ÷ 40 = (23 × 5 × 53) ÷ (23 × 5) = 53;

Build up the fractions to the same denominator: expand each fraction - multiply the numerator and the denominator by the expanding number; then work with the numerators:

26/53 + 19/40 =


(40 × 26)/(40 × 53) + (53 × 19)/(53 × 40) =


1,040/2,120 + 1,007/2,120 =


(1,040 + 1,007)/2,120 =


2,047/2,120

Reduce (simplify) fraction to its lowest terms equivalent:

2,047/2,120 already reduced to the lowest terms.


The numerator and the denominator have no common prime factors.


Their prime factorization:


2,047 = 23 × 89;


2,120 = 23 × 5 × 53;

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


Rewrite the fraction

As a decimal number:

2,047/2,120 =


2,047 ÷ 2,120 ≈


0.965566037736 ≈


0.97

As a percentage:

0.965566037736 =


0.965566037736 × 100/100 =


(0.965566037736 × 100)/100 =


96.556603773585/100


96.556603773585% ≈


96.56%

>> Convert fractions to percentages, online calculator


The final answer:
:: written in three ways ::

As a positive proper fraction (numerator < denominator):
26/53 + 19/40 = 2,047/2,120

As a decimal number:
26/53 + 19/40 ≈ 0.97

As a percentage:
26/53 + 19/40 ≈ 96.56%

How to add the ordinary fractions:
32/65 + 27/51

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;

Subtract ordinary fractions, online calculator

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

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

  • A. the fractions have like denominators;
  • B. the fractions have unlike denominators.

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

  • Simply subtract the numerators of the fractions.
  • The denominator of the resulting fraction will be the common denominator of the fractions.
  • Reduce the resulting fraction.

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

  • 3/18 + 4/18 - 5/18 = (3 + 4 - 5)/18 = 2/18;

  • We simply subtracted the numerators of the fractions: 3 + 4 - 5 = 2;
  • The denominator of the resulting fraction is: 18;
  • The resulting fraction is being reduced as: 2/18 = (2 ÷ 2)/(18 ÷ 2) = 1/9.

  • How to reduce (simplify) the common fraction 2/18?

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

  • 1. Reduce the fractions to the lowest terms (simplify them).

  • 2. Calculate the least common multiple, LCM, of all the fractions' new denominators:

    • LCM is going to be the common denominator of the added fractions, also called the lowest common denominator (the least common denominator).
    • Factor all the new denominators of the reduced fractions (run the prime factorization).
    • The least common multiple, LCM, is the product of all the unique prime factors of the denominators, multiplied by the largest exponents.
    • Calculate LCM, the least common multiple of numbers, online.

  • 3. Calculate each fraction's expanding number:

    • The expanding number is the non-zero number that will be used to multiply both the numerator and the denominator of each fraction, in order to build all the fractions up to the same common denominator.
    • Divide the least common multiple, LCM, calculated above, by the denominator of each fraction, in order to calculate each fraction's expanding number.
  • 4. Expand each fraction:

    • Multiply each fraction's both numerator and denominator by the expanding number.
    • At this point, fractions are built up to the same denominator.
  • 5. Subtract the fractions:

    • In order to subtract all the fractions simply subtract all the fractions' numerators.
    • The end fraction will have as a denominator the least common multiple, LCM, calculated above.
  • 6. Reduce the end fraction to the lowest terms, if needed.

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

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