Multiplying the common ordinary fractions: 33/52 × 109/156 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
33/52 × 109/156 = ?
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.
33/52 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
33 = 3 × 11
52 = 22 × 13
109/156 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
109 is a prime number (it cannot be factored into other prime factors)
156 = 22 × 3 × 13
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.
33/52 × 109/156 =
(33 × 109) / (52 × 156) =
(3 × 11 × 109) / (22 × 13 × 22 × 3 × 13) =
(3 × 11 × 109) / (24 × 3 × 132)
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 × 11 × 109; 24 × 3 × 132) = 3
Divide the numerator and the denominator by their GCF:
(3 × 11 × 109) / (24 × 3 × 132) =
((3 × 11 × 109) ÷ 3) / ((24 × 3 × 132) ÷ 3) =
(3 ÷ 3 × 11 × 109)/(24 × 3 ÷ 3 × 132) =
(1 × 11 × 109)/(24 × 1 × 132) =
(11 × 109)/(24 × 132) =
(11 × 109)/(16 × 169) =
1,199/2,704
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
1,199/2,704 =
1,199 ÷ 2,704 ≈
0.443417159763 ≈
0.44
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.
0.443417159763 =
0.443417159763 × 100/100 =
(0.443417159763 × 100)/100 =
44.341715976331/100 ≈
44.341715976331% ≈
44.34%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
33/52 × 109/156 = 1,199/2,704
As a decimal number:
33/52 × 109/156 ≈ 0.44
As a percentage:
33/52 × 109/156 ≈ 44.34%
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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