Multiplying the common ordinary fractions: - 8/13 × 12/16 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 8/13 × 12/16 = ?
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.
8/13 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
8 = 23
13 is a prime number (it cannot be factored into other prime factors)
12/16 =
(22 × 3)/24 =
((22 × 3) ÷ 22)/(24 ÷ 22) =
(22 ÷ 22 × 3)/(24 ÷ 22) =
(2(2 - 2) × 3)/2(4 - 2) =
(20 × 3)/22 =
(1 × 3)/22 =
3/4
Rewrite the equivalent simplified operation:
- 8/13 × 12/16 =
- 8/13 × 3/4
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.
- 8/13 × 3/4 =
- (8 × 3) / (13 × 4) =
- (23 × 3) / (13 × 22) =
- (23 × 3) / (22 × 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 (23 × 3; 22 × 13) = 22
Divide the numerator and the denominator by their GCF:
- (23 × 3) / (22 × 13) =
- ((23 × 3) ÷ 22) / ((22 × 13) ÷ 22) =
- (23 ÷ 22 × 3)/(22 ÷ 22 × 13) =
- (2(3 - 2) × 3)/(2(2 - 2) × 13) =
- (21 × 3)/(20 × 13) =
- (2 × 3)/(1 × 13) =
- (2 × 3)/13 =
- 6/13
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 6/13 =
- 6 ÷ 13 ≈
- 0.461538461538 ≈
- 0.46
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.
- 0.461538461538 =
- 0.461538461538 × 100/100 =
( - 0.461538461538 × 100)/100 =
- 46.153846153846/100 ≈
- 46.153846153846% ≈
- 46.15%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 8/13 × 12/16 = - 6/13
As a decimal number:
- 8/13 × 12/16 ≈ - 0.46
As a percentage:
- 8/13 × 12/16 ≈ - 46.15%
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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