Multiply fractions: - 39/30 × - 36/53 × - 31/141 = ? Multiplication result of the ordinary (simple, common) fractions explained

- 39/30 × - 36/53 × - 31/141 = ?

Rewrite the equivalent simplified operation:

Combine the signs of the fractions into a single one, placed in front of the expression.

The sign of the multiplication: + 1 × + 1 = + 1; + 1 × - 1 = - 1; - 1 × - 1 = + 1.

- 39/30 × - 36/53 × - 31/141 =


- 39/30 × 36/53 × 31/141

Reduce (simplify) fractions to their lowest terms equivalents:

Factor all the numbers in order to easily reduce (simplify) the end fraction.

Fraction: 39/30 =


(3 × 13)/(2 × 3 × 5) =


((3 × 13) ÷ 3)/((2 × 3 × 5) ÷ 3) =


(3 ÷ 3 × 13)/(2 × 3 ÷ 3 × 5) =


(1 × 13)/(2 × 1 × 5) =


13/10;


Fraction: 36/53 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
36 = 22 × 32;
53 is a prime number, it cannot be factored into other prime factors;


Fraction: 31/141 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
31 is a prime number, it cannot be factored into other prime factors;
141 = 3 × 47;


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


Rewrite the equivalent simplified operation:

- 39/30 × 36/53 × 31/141 =


- 13/10 × 36/53 × 31/141

Multiply the numerators and denominators of the fractions separately:

Factor all the numbers in order to easily reduce (simplify) the end fraction.

- 13/10 × 36/53 × 31/141 =


- (13 × 36 × 31) / (10 × 53 × 141) =


- (13 × 22 × 32 × 31) / (2 × 5 × 53 × 3 × 47) =


- (22 × 32 × 13 × 31) / (2 × 3 × 5 × 47 × 53)

>> Calculate the prime factors of numbers, online calculator


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

Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.


gcf(22 × 32 × 13 × 31; 2 × 3 × 5 × 47 × 53) = 2 × 3

>> Calculate the greatest common factor, GCF, online calculator


Divide the numerator and denominator by GCF.

- (22 × 32 × 13 × 31) / (2 × 3 × 5 × 47 × 53) =


- ((22 × 32 × 13 × 31) ÷ (2 × 3)) / ((2 × 3 × 5 × 47 × 53) ÷ (2 × 3)) =


- (22 ÷ 2 × 32 ÷ 3 × 13 × 31)/(2 ÷ 2 × 3 ÷ 3 × 5 × 47 × 53) =


- (2(2 - 1) × 3(2 - 1) × 13 × 31)/(1 × 1 × 5 × 47 × 53) =


- (21 × 31 × 13 × 31)/(1 × 1 × 5 × 47 × 53) =


- (2 × 3 × 13 × 31)/(1 × 1 × 5 × 47 × 53) =


- (2 × 3 × 13 × 31)/(5 × 47 × 53) =


- 2,418/12,455;

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


Rewrite the fraction

As a decimal number:

- 2,418/12,455 =


- 2,418 ÷ 12,455 ≈


- 0.19413890004 ≈


- 0.19

As a percentage:

- 0.19413890004 =


- 0.19413890004 × 100/100 =


( - 0.19413890004 × 100)/100 =


- 19.413890004014/100


- 19.413890004014% ≈


- 19.41%

>> Convert fractions to percentages, online calculator


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

As a negative proper fraction (numerator < denominator):
- 39/30 × - 36/53 × - 31/141 = - 2,418/12,455

As a decimal number:
- 39/30 × - 36/53 × - 31/141 ≈ - 0.19

As a percentage:
- 39/30 × - 36/53 × - 31/141 ≈ - 19.41%

More operations of this kind:

How to multiply the ordinary fractions:
46/39 × - 44/59 × - 36/147


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;

Multiply ordinary fractions, online calculator

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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:

How to multiply ordinary fractions? Steps.


>> Read the rest of this article, here: How to multiply 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