Multiplying the common ordinary fractions: 11/24 × 15/36 × 16/21 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
11/24 × 15/36 × 16/21 = ?
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.
11/24 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
11 is a prime number (it cannot be factored into other prime factors)
24 = 23 × 3
15/36 =
(3 × 5)/(22 × 32) =
((3 × 5) ÷ 3)/((22 × 32) ÷ 3) =
(3 ÷ 3 × 5)/(22 × 32 ÷ 3) =
(1 × 5)/(22 × 3(2 - 1)) =
(1 × 5)/(22 × 31) =
(1 × 5)/(22 × 3) =
5/12
16/21 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
16 = 24
21 = 3 × 7
Rewrite the equivalent simplified operation:
11/24 × 15/36 × 16/21 =
11/24 × 5/12 × 16/21
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.
11/24 × 5/12 × 16/21 =
(11 × 5 × 16) / (24 × 12 × 21) =
(11 × 5 × 24) / (23 × 3 × 22 × 3 × 3 × 7) =
(24 × 5 × 11) / (25 × 33 × 7)
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 × 5 × 11; 25 × 33 × 7) = 24
Divide the numerator and the denominator by their GCF:
(24 × 5 × 11) / (25 × 33 × 7) =
((24 × 5 × 11) ÷ 24) / ((25 × 33 × 7) ÷ 24) =
(24 ÷ 24 × 5 × 11)/(25 ÷ 24 × 33 × 7) =
(2(4 - 4) × 5 × 11)/(2(5 - 4) × 33 × 7) =
(20 × 5 × 11)/(21 × 33 × 7) =
(1 × 5 × 11)/(2 × 33 × 7) =
(5 × 11)/(2 × 33 × 7) =
(5 × 11)/(2 × 27 × 7) =
55/378
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
55/378 =
55 ÷ 378 ≈
0.145502645503 ≈
0.15
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.
0.145502645503 =
0.145502645503 × 100/100 =
(0.145502645503 × 100)/100 =
14.550264550265/100 ≈
14.550264550265% ≈
14.55%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
11/24 × 15/36 × 16/21 = 55/378
As a decimal number:
11/24 × 15/36 × 16/21 ≈ 0.15
As a percentage:
11/24 × 15/36 × 16/21 ≈ 14.55%
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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