Multiplying the common ordinary fractions: 9/14 × 3/13 × 8/12 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
9/14 × 3/13 × 8/12 = ?
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.
9/14 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
9 = 32
14 = 2 × 7
3/13 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
3 is a prime number (it cannot be factored into other prime factors)
13 is a prime number (it cannot be factored into other prime factors)
8/12 =
23/(22 × 3) =
(23 ÷ 22)/((22 × 3) ÷ 22) =
(23 ÷ 22)/(22 ÷ 22 × 3) =
2(3 - 2)/(2(2 - 2) × 3) =
21/(20 × 3) =
2/(1 × 3) =
2/3
Rewrite the equivalent simplified operation:
9/14 × 3/13 × 8/12 =
9/14 × 3/13 × 2/3
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 3/13 × 2/3 = 2/13
Rewrite the equivalent simplified operation:
9/14 × 3/13 × 2/3 =
9/14 × 2/13
Simplify the operation
Reduce (simplify) the new 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.
* 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.
2/13 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
2 is a prime number (it cannot be factored into other prime factors)
13 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.
9/14 × 2/13 =
(9 × 2) / (14 × 13) =
(32 × 2) / (2 × 7 × 13) =
(2 × 32) / (2 × 7 × 13)
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 (2 × 32; 2 × 7 × 13) = 2
Divide the numerator and the denominator by their GCF:
(2 × 32) / (2 × 7 × 13) =
((2 × 32) ÷ 2) / ((2 × 7 × 13) ÷ 2) =
(2 ÷ 2 × 32)/(2 ÷ 2 × 7 × 13) =
(1 × 32)/(1 × 7 × 13) =
32/(7 × 13) =
9/(7 × 13) =
9/91
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
9/91 =
9 ÷ 91 ≈
0.098901098901 ≈
0.1
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.
0.098901098901 =
0.098901098901 × 100/100 =
(0.098901098901 × 100)/100 =
9.89010989011/100 ≈
9.89010989011% ≈
9.89%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
9/14 × 3/13 × 8/12 = 9/91
As a decimal number:
9/14 × 3/13 × 8/12 ≈ 0.1
As a percentage:
9/14 × 3/13 × 8/12 ≈ 9.89%
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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