Multiplying the common ordinary fractions: 30/359 × 20/32 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
30/359 × 20/32 = ?
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.
30/359 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
30 = 2 × 3 × 5
359 is a prime number (it cannot be factored into other prime factors)
20/32 =
(22 × 5)/25 =
((22 × 5) ÷ 22)/(25 ÷ 22) =
(22 ÷ 22 × 5)/(25 ÷ 22) =
(2(2 - 2) × 5)/2(5 - 2) =
(20 × 5)/23 =
(1 × 5)/23 =
5/8
Rewrite the equivalent simplified operation:
30/359 × 20/32 =
30/359 × 5/8
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.
30/359 × 5/8 =
(30 × 5) / (359 × 8) =
(2 × 3 × 5 × 5) / (359 × 23) =
(2 × 3 × 52) / (23 × 359)
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 × 3 × 52; 23 × 359) = 2
Divide the numerator and the denominator by their GCF:
(2 × 3 × 52) / (23 × 359) =
((2 × 3 × 52) ÷ 2) / ((23 × 359) ÷ 2) =
(2 ÷ 2 × 3 × 52)/(23 ÷ 2 × 359) =
(1 × 3 × 52)/(2(3 - 1) × 359) =
(1 × 3 × 52)/(22 × 359) =
(3 × 52)/(22 × 359) =
(3 × 25)/(4 × 359) =
75/1,436
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
75/1,436 =
75 ÷ 1,436 ≈
0.052228412256 ≈
0.05
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.
0.052228412256 =
0.052228412256 × 100/100 =
(0.052228412256 × 100)/100 =
5.222841225627/100 ≈
5.222841225627% ≈
5.22%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
30/359 × 20/32 = 75/1,436
As a decimal number:
30/359 × 20/32 ≈ 0.05
As a percentage:
30/359 × 20/32 ≈ 5.22%
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
Multiply common ordinary fractions, online calculator: