Multiplying the common ordinary fractions: 16/66 × 18/32 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
16/66 × 18/32 = ?
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.
16/66 =
24/(2 × 3 × 11) =
(24 ÷ 2)/((2 × 3 × 11) ÷ 2) =
(24 ÷ 2)/(2 ÷ 2 × 3 × 11) =
2(4 - 1)/(1 × 3 × 11) =
23/(1 × 3 × 11) =
8/33
18/32 =
(2 × 32)/25 =
((2 × 32) ÷ 2)/(25 ÷ 2) =
(2 ÷ 2 × 32)/(25 ÷ 2) =
(1 × 32)/2(5 - 1) =
(1 × 32)/24 =
9/16
Rewrite the equivalent simplified operation:
16/66 × 18/32 =
8/33 × 9/16
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.
8/33 × 9/16 =
(8 × 9) / (33 × 16) =
(23 × 32) / (3 × 11 × 24) =
(23 × 32) / (24 × 3 × 11)
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 (23 × 32; 24 × 3 × 11) = 23 × 3
Divide the numerator and the denominator by their GCF:
(23 × 32) / (24 × 3 × 11) =
((23 × 32) ÷ (23 × 3)) / ((24 × 3 × 11) ÷ (23 × 3)) =
(23 ÷ 23 × 32 ÷ 3)/(24 ÷ 23 × 3 ÷ 3 × 11) =
(2(3 - 3) × 3(2 - 1))/(2(4 - 3) × 1 × 11) =
(20 × 31)/(2 × 1 × 11) =
(1 × 3)/(2 × 1 × 11) =
3/(2 × 11) =
3/22
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
3/22 =
3 ÷ 22 ≈
0.136363636364 ≈
0.14
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.
0.136363636364 =
0.136363636364 × 100/100 =
(0.136363636364 × 100)/100 =
13.636363636364/100 ≈
13.636363636364% ≈
13.64%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
16/66 × 18/32 = 3/22
As a decimal number:
16/66 × 18/32 ≈ 0.14
As a percentage:
16/66 × 18/32 ≈ 13.64%
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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