Multiplying the common ordinary fractions: - 73/126 × - 87/137 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 73/126 × - 87/137 = ?
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
- 73/126 × - 87/137 =
73/126 × 87/137
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.
73/126 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
73 is a prime number (it cannot be factored into other prime factors)
126 = 2 × 32 × 7
87/137 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
87 = 3 × 29
137 is a prime number (it cannot be factored into other prime factors)
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.
73/126 × 87/137 =
(73 × 87) / (126 × 137) =
(73 × 3 × 29) / (2 × 32 × 7 × 137) =
(3 × 29 × 73) / (2 × 32 × 7 × 137)
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 (3 × 29 × 73; 2 × 32 × 7 × 137) = 3
Divide the numerator and the denominator by their GCF:
(3 × 29 × 73) / (2 × 32 × 7 × 137) =
((3 × 29 × 73) ÷ 3) / ((2 × 32 × 7 × 137) ÷ 3) =
(3 ÷ 3 × 29 × 73)/(2 × 32 ÷ 3 × 7 × 137) =
(1 × 29 × 73)/(2 × 3(2 - 1) × 7 × 137) =
(1 × 29 × 73)/(2 × 31 × 7 × 137) =
(1 × 29 × 73)/(2 × 3 × 7 × 137) =
(29 × 73)/(2 × 3 × 7 × 137) =
2,117/5,754
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
2,117/5,754 =
2,117 ÷ 5,754 ≈
0.367917970108 ≈
0.37
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.
0.367917970108 =
0.367917970108 × 100/100 =
(0.367917970108 × 100)/100 =
36.791797010775/100 ≈
36.791797010775% ≈
36.79%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 73/126 × - 87/137 = 2,117/5,754
As a decimal number:
- 73/126 × - 87/137 ≈ 0.37
As a percentage:
- 73/126 × - 87/137 ≈ 36.79%
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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