Multiplying the common ordinary fractions: 13/18 × 9/30 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
13/18 × 9/30 = ?
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.
13/18 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
13 is a prime number (it cannot be factored into other prime factors)
18 = 2 × 32
9/30 =
32/(2 × 3 × 5) =
(32 ÷ 3)/((2 × 3 × 5) ÷ 3) =
(32 ÷ 3)/(2 × 3 ÷ 3 × 5) =
3(2 - 1)/(2 × 1 × 5) =
31/(2 × 1 × 5) =
3/(2 × 1 × 5) =
3/10
Rewrite the equivalent simplified operation:
13/18 × 9/30 =
13/18 × 3/10
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.
13/18 × 3/10 =
(13 × 3) / (18 × 10) =
(13 × 3) / (2 × 32 × 2 × 5) =
(3 × 13) / (22 × 32 × 5)
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 × 13; 22 × 32 × 5) = 3
Divide the numerator and the denominator by their GCF:
(3 × 13) / (22 × 32 × 5) =
((3 × 13) ÷ 3) / ((22 × 32 × 5) ÷ 3) =
(3 ÷ 3 × 13)/(22 × 32 ÷ 3 × 5) =
(1 × 13)/(22 × 3(2 - 1) × 5) =
(1 × 13)/(22 × 31 × 5) =
(1 × 13)/(22 × 3 × 5) =
13/(22 × 3 × 5) =
13/(4 × 3 × 5) =
13/60
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
13/60 =
13 ÷ 60 ≈
0.216666666667 ≈
0.22
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.
0.216666666667 =
0.216666666667 × 100/100 =
(0.216666666667 × 100)/100 =
21.666666666667/100 ≈
21.666666666667% ≈
21.67%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
13/18 × 9/30 = 13/60
As a decimal number:
13/18 × 9/30 ≈ 0.22
As a percentage:
13/18 × 9/30 ≈ 21.67%
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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