51/20 - 34/49 = ? Subtracting ordinary (common) fractions, online calculator, subtraction operation explained step by step. The answer, written in four ways. As a positive improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage.

51/20 - 34/49 = ?

Simplify the operation

Reduce (simplify) the fractions to their lowest terms equivalents:

To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.


* Why do we try to reduce (simplify) the fractions?


By reducing the values of the numerators and the denominators of the fractions the calculations are easier to make.


A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

* * *

The fraction: 51/20 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
51 = 3 × 17
20 = 22 × 5
GCF (3 × 17; 22 × 5) = 1


The fraction: - 34/49 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
34 = 2 × 17
49 = 72
GCF (2 × 17; 72) = 1



Rewrite the improper fractions:

An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.

A proper fraction: the value of the numerator is smaller than the value of the denominator.


Each improper fraction will be rewritten as a whole number and a proper fraction, both having the same sign: divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below.


Why do we rewrite the improper fractions?

By reducing the value of the numerator of a fraction the calculations are getting easier to perform.

* * *

The fraction: 51/20


51 ÷ 20 = 2 and the remainder = 11 => 51 = 2 × 20 + 11


51/20 = (2 × 20 + 11)/20 = (2 × 20)/20 + 11/20 = 2 + 11/20



Rewrite the equivalent simplified operation:

51/20 - 34/49 =


2 + 11/20 - 34/49

Perform the operation of calculating the fractions.

To add or subtract fractions we need them to have equal denominators (the same common denominator).

To calculate the fractions' operation we have to:


1) find their common denominator


2) then calculate the expanding number of each fraction


3) then build up their denominators the same by expanding the fractions to equivalent forms, which all have equal denominators (the same denominator)


* The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.


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


1) Find the common denominator
Calculate the LCM of the denominators:

The prime factorization of the denominators:


20 = 22 × 5


49 = 72


Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).


LCM (20; 49) = 22 × 5 × 72 = 980



2) Calculate the expanding number of each fraction:

Divide the LCM by the denominator of each fraction.


11/20 : 980 ÷ 20 = (22 × 5 × 72) ÷ (22 × 5) = 49


- 34/49 : 980 ÷ 49 = (22 × 5 × 72) ÷ 72 = 20


3) Build up the fractions to the same common denominator:

Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above. This way all the fractions will have the same denominator.


Then keep the common denominator and work only with the numerators of the fractions.


2 + 11/20 - 34/49 =


2 + (49 × 11)/(49 × 20) - (20 × 34)/(20 × 49) =


2 + 539/980 - 680/980 =


2 + (539 - 680)/980 =


2 - 141/980


Fully reduce (simplify) the fraction to its lowest terms equivalent:

To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.


A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.


- 141/980 is already reduced to the lowest terms.


The numerator and denominator have no common prime factors.


Their prime factorization:

141 = 3 × 47

980 = 22 × 5 × 72


GCF (3 × 47; 22 × 5 × 72) = 1



Rewrite the intermediate result

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

An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.


2 - 141/980 =


(2 × 980)/980 - 141/980 =


(2 × 980 - 141)/980 =


1,819/980

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

A mixed number: a whole number and a proper fraction, both having the same sign.


A proper fraction: the value of the numerator is smaller than the value of the denominator.


Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:


1,819 ÷ 980 = 1 and the remainder = 839 =>


1,819 = 1 × 980 + 839 =>


1,819/980 =


(1 × 980 + 839)/980 =


(1 × 980)/980 + 839/980 =


1 + 839/980 =


1 839/980

As a decimal number:

Simply divide the numerator by the denominator, without a remainder, as shown below:


1 + 839/980 =


1 + 839 ÷ 980 ≈


1.85612244898 ≈


1.86

As a percentage:

A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.


To do that, multiply the number by the fraction 100/100.


The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.


1.85612244898 =


1.85612244898 × 100/100 =


(1.85612244898 × 100)/100 =


185.612244897959/100


185.612244897959% ≈


185.61%



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

As a positive improper fraction:
(the numerator >= the denominator)
51/20 - 34/49 = 1,819/980

As a mixed number (also called a mixed fraction):
51/20 - 34/49 = 1 839/980

As a decimal number:
51/20 - 34/49 ≈ 1.86

As a percentage:
51/20 - 34/49 ≈ 185.61%

How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

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Subtract common ordinary fractions, online calculator:

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

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

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

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

B. To subtract 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 subtract ordinary (common) fractions

More on ordinary (common) fractions / theory:

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


(2) Changing the form of fractions, by expanding or reducing (simplifying)


(3) How to reduce fractions (simplifying). The greatest common factor, GCF


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


(5) How to sort out fractions in ascending order


(6) Adding common (ordinary) fractions


(7) Subtracting common (ordinary) fractions


(8) Multiplying common (ordinary) fractions


(9) Fractions as rational numbers