Multiplying the common ordinary fractions: - 13/27 × 15/27 × - 20/29 × - 117/119 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 13/27 × 15/27 × - 20/29 × - 117/119 = ?
Simplify the operation
Rewrite the equivalent simplified operation:
Combine the signs of the fractions into a single one, placed in front of the expression. If the sign is + then it is usually not written.
The sign of a multiplication operation:
+ 1 × + 1 = + 1
+ 1 × - 1 = - 1
- 1 × - 1 = + 1
- 13/27 × 15/27 × - 20/29 × - 117/119 =
- 13/27 × 15/27 × 20/29 × 117/119
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.
13/27 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
13 is a prime number (it cannot be factored into other prime factors)
27 = 33
15/27 =
(3 × 5)/33 =
((3 × 5) ÷ 3)/(33 ÷ 3) =
(3 ÷ 3 × 5)/(33 ÷ 3) =
(1 × 5)/3(3 - 1) =
(1 × 5)/32 =
5/9
20/29 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
20 = 22 × 5
29 is a prime number (it cannot be factored into other prime factors)
117/119 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
117 = 32 × 13
119 = 7 × 17
Rewrite the equivalent simplified operation:
- 13/27 × 15/27 × 20/29 × 117/119 =
- 13/27 × 5/9 × 20/29 × 117/119
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.
- 13/27 × 5/9 × 20/29 × 117/119 =
- (13 × 5 × 20 × 117) / (27 × 9 × 29 × 119) =
- (13 × 5 × 22 × 5 × 32 × 13) / (33 × 32 × 29 × 7 × 17) =
- (22 × 32 × 52 × 132) / (35 × 7 × 17 × 29)
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).
GCF (22 × 32 × 52 × 132; 35 × 7 × 17 × 29) = 32
Divide the numerator and the denominator by their GCF:
- (22 × 32 × 52 × 132) / (35 × 7 × 17 × 29) =
- ((22 × 32 × 52 × 132) ÷ 32) / ((35 × 7 × 17 × 29) ÷ 32) =
- (22 × 32 ÷ 32 × 52 × 132)/(35 ÷ 32 × 7 × 17 × 29) =
- (22 × 3(2 - 2) × 52 × 132)/(3(5 - 2) × 7 × 17 × 29) =
- (22 × 30 × 52 × 132)/(33 × 7 × 17 × 29) =
- (22 × 1 × 52 × 132)/(33 × 7 × 17 × 29) =
- (22 × 52 × 132)/(33 × 7 × 17 × 29) =
- (4 × 25 × 169)/(27 × 7 × 17 × 29) =
- 16,900/93,177
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 16,900/93,177 =
- 16,900 ÷ 93,177 ≈
- 0.181375232085 ≈
- 0.18
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.
- 0.181375232085 =
- 0.181375232085 × 100/100 =
( - 0.181375232085 × 100)/100 =
- 18.137523208517/100 ≈
- 18.137523208517% ≈
- 18.14%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 13/27 × 15/27 × - 20/29 × - 117/119 = - 16,900/93,177
As a decimal number:
- 13/27 × 15/27 × - 20/29 × - 117/119 ≈ - 0.18
As a percentage:
- 13/27 × 15/27 × - 20/29 × - 117/119 ≈ - 18.14%
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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