Multiplying the common ordinary fractions: 82/114 × 76/119 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
82/114 × 76/119 = ?
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.
82/114 =
(2 × 41)/(2 × 3 × 19) =
((2 × 41) ÷ 2)/((2 × 3 × 19) ÷ 2) =
(2 ÷ 2 × 41)/(2 ÷ 2 × 3 × 19) =
(1 × 41)/(1 × 3 × 19) =
41/57
76/119 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
76 = 22 × 19
119 = 7 × 17
Rewrite the equivalent simplified operation:
82/114 × 76/119 =
41/57 × 76/119
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.
41/57 × 76/119 =
(41 × 76) / (57 × 119) =
(41 × 22 × 19) / (3 × 19 × 7 × 17) =
(22 × 19 × 41) / (3 × 7 × 17 × 19)
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 × 19 × 41; 3 × 7 × 17 × 19) = 19
Divide the numerator and the denominator by their GCF:
(22 × 19 × 41) / (3 × 7 × 17 × 19) =
((22 × 19 × 41) ÷ 19) / ((3 × 7 × 17 × 19) ÷ 19) =
(22 × 19 ÷ 19 × 41)/(3 × 7 × 17 × 19 ÷ 19) =
(22 × 1 × 41)/(3 × 7 × 17 × 1) =
(22 × 41)/(3 × 7 × 17) =
(4 × 41)/(3 × 7 × 17) =
164/357
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
164/357 =
164 ÷ 357 ≈
0.459383753501 ≈
0.46
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.
0.459383753501 =
0.459383753501 × 100/100 =
(0.459383753501 × 100)/100 =
45.93837535014/100 =
45.93837535014% ≈
45.94%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
82/114 × 76/119 = 164/357
As a decimal number:
82/114 × 76/119 ≈ 0.46
As a percentage:
82/114 × 76/119 ≈ 45.94%
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
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