Multiplying the common ordinary fractions: 84/113 × - 65/118 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
84/113 × - 65/118 = ?
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
84/113 × - 65/118 =
- 84/113 × 65/118
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.
84/113 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
84 = 22 × 3 × 7
113 is a prime number (it cannot be factored into other prime factors)
65/118 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
65 = 5 × 13
118 = 2 × 59
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.
- 84/113 × 65/118 =
- (84 × 65) / (113 × 118) =
- (22 × 3 × 7 × 5 × 13) / (113 × 2 × 59) =
- (22 × 3 × 5 × 7 × 13) / (2 × 59 × 113)
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 (22 × 3 × 5 × 7 × 13; 2 × 59 × 113) = 2
Divide the numerator and the denominator by their GCF:
- (22 × 3 × 5 × 7 × 13) / (2 × 59 × 113) =
- ((22 × 3 × 5 × 7 × 13) ÷ 2) / ((2 × 59 × 113) ÷ 2) =
- (22 ÷ 2 × 3 × 5 × 7 × 13)/(2 ÷ 2 × 59 × 113) =
- (2(2 - 1) × 3 × 5 × 7 × 13)/(1 × 59 × 113) =
- (21 × 3 × 5 × 7 × 13)/(1 × 59 × 113) =
- (2 × 3 × 5 × 7 × 13)/(1 × 59 × 113) =
- (2 × 3 × 5 × 7 × 13)/(59 × 113) =
- 2,730/6,667
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 2,730/6,667 =
- 2,730 ÷ 6,667 ≈
- 0.409479526024 ≈
- 0.41
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.
- 0.409479526024 =
- 0.409479526024 × 100/100 =
( - 0.409479526024 × 100)/100 =
- 40.94795260237/100 ≈
- 40.94795260237% ≈
- 40.95%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
84/113 × - 65/118 = - 2,730/6,667
As a decimal number:
84/113 × - 65/118 ≈ - 0.41
As a percentage:
84/113 × - 65/118 ≈ - 40.95%
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: