Multiplying the common ordinary fractions: 15/32 × 16/27 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
15/32 × 16/27 = ?
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.
15/32 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
15 = 3 × 5
32 = 25
16/27 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
16 = 24
27 = 33
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.
15/32 × 16/27 =
(15 × 16) / (32 × 27) =
(3 × 5 × 24) / (25 × 33) =
(24 × 3 × 5) / (25 × 33)
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 (24 × 3 × 5; 25 × 33) = 24 × 3
Divide the numerator and the denominator by their GCF:
(24 × 3 × 5) / (25 × 33) =
((24 × 3 × 5) ÷ (24 × 3)) / ((25 × 33) ÷ (24 × 3)) =
(24 ÷ 24 × 3 ÷ 3 × 5)/(25 ÷ 24 × 33 ÷ 3) =
(2(4 - 4) × 1 × 5)/(2(5 - 4) × 3(3 - 1)) =
(20 × 1 × 5)/(2 × 32) =
(1 × 1 × 5)/(2 × 32) =
5/(2 × 32) =
5/(2 × 9) =
5/18
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
5/18 =
5 ÷ 18 ≈
0.277777777778 ≈
0.28
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.
0.277777777778 =
0.277777777778 × 100/100 =
(0.277777777778 × 100)/100 =
27.777777777778/100 ≈
27.777777777778% ≈
27.78%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
15/32 × 16/27 = 5/18
As a decimal number:
15/32 × 16/27 ≈ 0.28
As a percentage:
15/32 × 16/27 ≈ 27.78%
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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