Multiplying the common ordinary fractions: - 725/456 × - 12/30 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 725/456 × - 12/30 = ?
Simplify the operation
Rewrite the equivalent simplified operation:
Combine the signs of the fractions into a single one, placed in front of the expression. If the sign is + then it is usually not written.
The sign of a multiplication operation:
+ 1 × + 1 = + 1
+ 1 × - 1 = - 1
- 1 × - 1 = + 1
- 725/456 × - 12/30 =
725/456 × 12/30
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.
725/456 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
725 = 52 × 29
456 = 23 × 3 × 19
12/30 =
(22 × 3)/(2 × 3 × 5) =
((22 × 3) ÷ (2 × 3))/((2 × 3 × 5) ÷ (2 × 3)) =
(22 ÷ 2 × 3 ÷ 3)/(2 ÷ 2 × 3 ÷ 3 × 5) =
(2(2 - 1) × 1)/(1 × 1 × 5) =
(2 × 1)/(1 × 1 × 5) =
2/5
Rewrite the equivalent simplified operation:
725/456 × 12/30 =
725/456 × 2/5
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.
725/456 × 2/5 =
(725 × 2) / (456 × 5) =
(52 × 29 × 2) / (23 × 3 × 19 × 5) =
(2 × 52 × 29) / (23 × 3 × 5 × 19)
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 × 52 × 29; 23 × 3 × 5 × 19) = 2 × 5
Divide the numerator and the denominator by their GCF:
(2 × 52 × 29) / (23 × 3 × 5 × 19) =
((2 × 52 × 29) ÷ (2 × 5)) / ((23 × 3 × 5 × 19) ÷ (2 × 5)) =
(2 ÷ 2 × 52 ÷ 5 × 29)/(23 ÷ 2 × 3 × 5 ÷ 5 × 19) =
(1 × 5(2 - 1) × 29)/(2(3 - 1) × 3 × 1 × 19) =
(1 × 51 × 29)/(22 × 3 × 1 × 19) =
(1 × 5 × 29)/(22 × 3 × 1 × 19) =
(5 × 29)/(22 × 3 × 19) =
(5 × 29)/(4 × 3 × 19) =
145/228
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
145/228 =
145 ÷ 228 ≈
0.635964912281 ≈
0.64
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.
0.635964912281 =
0.635964912281 × 100/100 =
(0.635964912281 × 100)/100 =
63.59649122807/100 ≈
63.59649122807% ≈
63.6%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 725/456 × - 12/30 = 145/228
As a decimal number:
- 725/456 × - 12/30 ≈ 0.64
As a percentage:
- 725/456 × - 12/30 ≈ 63.6%
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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