Multiplying the common ordinary fractions: 188/89 × 87/242 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
188/89 × 87/242 = ?
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.
188/89 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
188 = 22 × 47
89 is a prime number (it cannot be factored into other prime factors)
87/242 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
87 = 3 × 29
242 = 2 × 112
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.
188/89 × 87/242 =
(188 × 87) / (89 × 242) =
(22 × 47 × 3 × 29) / (89 × 2 × 112) =
(22 × 3 × 29 × 47) / (2 × 112 × 89)
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 × 3 × 29 × 47; 2 × 112 × 89) = 2
Divide the numerator and the denominator by their GCF:
(22 × 3 × 29 × 47) / (2 × 112 × 89) =
((22 × 3 × 29 × 47) ÷ 2) / ((2 × 112 × 89) ÷ 2) =
(22 ÷ 2 × 3 × 29 × 47)/(2 ÷ 2 × 112 × 89) =
(2(2 - 1) × 3 × 29 × 47)/(1 × 112 × 89) =
(21 × 3 × 29 × 47)/(1 × 112 × 89) =
(2 × 3 × 29 × 47)/(1 × 112 × 89) =
(2 × 3 × 29 × 47)/(112 × 89) =
(2 × 3 × 29 × 47)/(121 × 89) =
8,178/10,769
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
8,178/10,769 =
8,178 ÷ 10,769 ≈
0.759401987185 ≈
0.76
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.
0.759401987185 =
0.759401987185 × 100/100 =
(0.759401987185 × 100)/100 =
75.940198718544/100 ≈
75.940198718544% ≈
75.94%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
188/89 × 87/242 = 8,178/10,769
As a decimal number:
188/89 × 87/242 ≈ 0.76
As a percentage:
188/89 × 87/242 ≈ 75.94%
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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