Multiplying the common ordinary fractions: - 120/156 × 134/152 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 120/156 × 134/152 = ?
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.
120/156 =
(23 × 3 × 5)/(22 × 3 × 13) =
((23 × 3 × 5) ÷ (22 × 3))/((22 × 3 × 13) ÷ (22 × 3)) =
(23 ÷ 22 × 3 ÷ 3 × 5)/(22 ÷ 22 × 3 ÷ 3 × 13) =
(2(3 - 2) × 1 × 5)/(2(2 - 2) × 1 × 13) =
(2 × 1 × 5)/(20 × 1 × 13) =
(2 × 1 × 5)/(1 × 1 × 13) =
10/13
134/152 =
(2 × 67)/(23 × 19) =
((2 × 67) ÷ 2)/((23 × 19) ÷ 2) =
(2 ÷ 2 × 67)/(23 ÷ 2 × 19) =
(1 × 67)/(2(3 - 1) × 19) =
(1 × 67)/(22 × 19) =
67/76
Rewrite the equivalent simplified operation:
- 120/156 × 134/152 =
- 10/13 × 67/76
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.
- 10/13 × 67/76 =
- (10 × 67) / (13 × 76) =
- (2 × 5 × 67) / (13 × 22 × 19) =
- (2 × 5 × 67) / (22 × 13 × 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 × 5 × 67; 22 × 13 × 19) = 2
Divide the numerator and the denominator by their GCF:
- (2 × 5 × 67) / (22 × 13 × 19) =
- ((2 × 5 × 67) ÷ 2) / ((22 × 13 × 19) ÷ 2) =
- (2 ÷ 2 × 5 × 67)/(22 ÷ 2 × 13 × 19) =
- (1 × 5 × 67)/(2(2 - 1) × 13 × 19) =
- (1 × 5 × 67)/(21 × 13 × 19) =
- (1 × 5 × 67)/(2 × 13 × 19) =
- (5 × 67)/(2 × 13 × 19) =
- 335/494
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 335/494 =
- 335 ÷ 494 ≈
- 0.678137651822 ≈
- 0.68
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.
- 0.678137651822 =
- 0.678137651822 × 100/100 =
( - 0.678137651822 × 100)/100 =
- 67.813765182186/100 ≈
- 67.813765182186% ≈
- 67.81%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 120/156 × 134/152 = - 335/494
As a decimal number:
- 120/156 × 134/152 ≈ - 0.68
As a percentage:
- 120/156 × 134/152 ≈ - 67.81%
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: