Multiplying the common ordinary fractions: - 30/248 × 27/55 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 30/248 × 27/55 = ?
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.
30/248 =
(2 × 3 × 5)/(23 × 31) =
((2 × 3 × 5) ÷ 2)/((23 × 31) ÷ 2) =
(2 ÷ 2 × 3 × 5)/(23 ÷ 2 × 31) =
(1 × 3 × 5)/(2(3 - 1) × 31) =
(1 × 3 × 5)/(22 × 31) =
15/124
27/55 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
27 = 33
55 = 5 × 11
Rewrite the equivalent simplified operation:
- 30/248 × 27/55 =
- 15/124 × 27/55
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.
- 15/124 × 27/55 =
- (15 × 27) / (124 × 55) =
- (3 × 5 × 33) / (22 × 31 × 5 × 11) =
- (34 × 5) / (22 × 5 × 11 × 31)
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 (34 × 5; 22 × 5 × 11 × 31) = 5
Divide the numerator and the denominator by their GCF:
- (34 × 5) / (22 × 5 × 11 × 31) =
- ((34 × 5) ÷ 5) / ((22 × 5 × 11 × 31) ÷ 5) =
- (34 × 5 ÷ 5)/(22 × 5 ÷ 5 × 11 × 31) =
- (34 × 1)/(22 × 1 × 11 × 31) =
- 34/(22 × 11 × 31) =
- 81/(4 × 11 × 31) =
- 81/1,364
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 81/1,364 =
- 81 ÷ 1,364 ≈
- 0.059384164223 ≈
- 0.06
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.
- 0.059384164223 =
- 0.059384164223 × 100/100 =
( - 0.059384164223 × 100)/100 =
- 5.938416422287/100 ≈
- 5.938416422287% ≈
- 5.94%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 30/248 × 27/55 = - 81/1,364
As a decimal number:
- 30/248 × 27/55 ≈ - 0.06
As a percentage:
- 30/248 × 27/55 ≈ - 5.94%
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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