Multiplying the common ordinary fractions: - 58/30 × 38/65 = ? The multiplication process explained. The result written: As a negative improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage

- 58/30 × 38/65 = ?

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.


* 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.


* In order to easily reduce a fraction, factor its numerator and denominator. This way all the common prime factors are easily identified and crossed out, without calculating the GCF.


58/30 =


(2 × 29)/(2 × 3 × 5) =


((2 × 29) ÷ 2)/((2 × 3 × 5) ÷ 2) =


(2 ÷ 2 × 29)/(2 ÷ 2 × 3 × 5) =


(1 × 29)/(1 × 3 × 5) =


29/15


38/65 is already reduced to the lowest terms.


The numerator and denominator have no common prime factors.


Their prime factorization:
38 = 2 × 19
65 = 5 × 13



Rewrite the equivalent simplified operation:

- 58/30 × 38/65 =


- 29/15 × 38/65

Perform the operation of calculating the fractions

Multiply the fractions:

1) Multiply the numerators, that is, all the numbers above the fractions bars, separately.


2) Multiply the denominators, that is, all the numbers below the fractions bars, separately.


* Factor all the numerators and all the denominators in order to easily reduce (simplify) the end fraction.

External link » Factor (decompose) composite numbers into prime factors, online calculator


- 29/15 × 38/65 =


- (29 × 38) / (15 × 65) =


- (29 × 2 × 19) / (3 × 5 × 5 × 13) =


- (2 × 19 × 29) / (3 × 52 × 13)

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

Calculate the greatest common factor, GCF,
of the numerator and denominator of the fraction:

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.


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


* To calculate the GCF, we need to factor the numerator and the denominator of the fraction into prime factors.


Then multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).


But the numerator and the denominator have no common prime factors:

GCF (2 × 19 × 29; 3 × 52 × 13) = 1



Divide the numerator and the denominator by their GCF:

The numerator and the denominator of the fraction are coprime numbers (there are no common prime factors, the GCF = 1). The end fraction can no longer be shortened, it already has the smallest possible numerator and denominator, it is an irreducible fraction.


- (2 × 19 × 29) / (3 × 52 × 13) =


- 1,102/975

Rewrite the fraction

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:


- 1,102 ÷ 975 = - 1 and the remainder = - 127 ⇒


- 1,102 = - 1 × 975 - 127 ⇒


- 1,102/975 =


( - 1 × 975 - 127)/975 =


( - 1 × 975)/975 - 127/975 =


- 1 - 127/975 =


- 1 127/975

As a decimal number:

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


- 1 - 127/975 =


- 1 - 127 ÷ 975 ≈


- 1.130256410256 ≈


- 1.13

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.


- 1.130256410256 =


- 1.130256410256 × 100/100 =


( - 1.130256410256 × 100)/100 =


- 113.025641025641/100 =


- 113.025641025641% ≈


- 113.03%


The final answer:
written in four ways

As a negative improper fraction:
(the numerator >= the denominator)
- 58/30 × 38/65 = - 1,102/975

As a mixed number (also called a mixed fraction):
- 58/30 × 38/65 = - 1 127/975

As a decimal number:
- 58/30 × 38/65 ≈ - 1.13

As a percentage:
- 58/30 × 38/65 ≈ - 113.03%

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.

Other similar operations

How to multiply the common ordinary fractions:
- 68/37 × 45/70

Multiply common ordinary fractions, online calculator:

The latest common ordinary fractions that have been multiplied

Multiplying fractions. How to multiply ordinary math fractions? Steps. Example.

How to multiply two fractions?

When we multiply ordinary fractions, the end fraction will have:

  • as a numerator, the result of multiplying all the numerators of the fractions,
  • as a denominator, the result of multiplying all the denominators of the fractions.
  • a/b × c/d = (a × c) / (b × d)
  • a, b, c, d are integer numbers;
  • if the pairs (a × c) and (b × d) are not coprime (they have common prime factors) the end fraction should be reduced (simplified) to lower terms.

How to multiply ordinary fractions? Steps.


Internal link > Read the rest of the article, here: How to multiply common ordinary fractions?

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