Multiplying the common ordinary fractions: - 71/129 × 60/106 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 71/129 × 60/106 = ?
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.
71/129 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
71 is a prime number (it cannot be factored into other prime factors)
129 = 3 × 43
60/106 =
(22 × 3 × 5)/(2 × 53) =
((22 × 3 × 5) ÷ 2)/((2 × 53) ÷ 2) =
(22 ÷ 2 × 3 × 5)/(2 ÷ 2 × 53) =
(2(2 - 1) × 3 × 5)/(1 × 53) =
(21 × 3 × 5)/(1 × 53) =
(2 × 3 × 5)/(1 × 53) =
30/53
Rewrite the equivalent simplified operation:
- 71/129 × 60/106 =
- 71/129 × 30/53
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.
- 71/129 × 30/53 =
- (71 × 30) / (129 × 53) =
- (71 × 2 × 3 × 5) / (3 × 43 × 53) =
- (2 × 3 × 5 × 71) / (3 × 43 × 53)
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 (2 × 3 × 5 × 71; 3 × 43 × 53) = 3
Divide the numerator and the denominator by their GCF:
- (2 × 3 × 5 × 71) / (3 × 43 × 53) =
- ((2 × 3 × 5 × 71) ÷ 3) / ((3 × 43 × 53) ÷ 3) =
- (2 × 3 ÷ 3 × 5 × 71)/(3 ÷ 3 × 43 × 53) =
- (2 × 1 × 5 × 71)/(1 × 43 × 53) =
- (2 × 5 × 71)/(43 × 53) =
- 710/2,279
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 710/2,279 =
- 710 ÷ 2,279 ≈
- 0.311540149188 ≈
- 0.31
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.
- 0.311540149188 =
- 0.311540149188 × 100/100 =
( - 0.311540149188 × 100)/100 =
- 31.154014918824/100 =
- 31.154014918824% ≈
- 31.15%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 71/129 × 60/106 = - 710/2,279
As a decimal number:
- 71/129 × 60/106 ≈ - 0.31
As a percentage:
- 71/129 × 60/106 ≈ - 31.15%
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
Multiply common ordinary fractions, online calculator: