Multiplying the common ordinary fractions: 78/109 × - 55/90 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
78/109 × - 55/90 = ?
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
78/109 × - 55/90 =
- 78/109 × 55/90
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.
78/109 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
78 = 2 × 3 × 13
109 is a prime number (it cannot be factored into other prime factors)
55/90 =
(5 × 11)/(2 × 32 × 5) =
((5 × 11) ÷ 5)/((2 × 32 × 5) ÷ 5) =
(5 ÷ 5 × 11)/(2 × 32 × 5 ÷ 5) =
(1 × 11)/(2 × 32 × 1) =
11/18
Rewrite the equivalent simplified operation:
- 78/109 × 55/90 =
- 78/109 × 11/18
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.
- 78/109 × 11/18 =
- (78 × 11) / (109 × 18) =
- (2 × 3 × 13 × 11) / (109 × 2 × 32) =
- (2 × 3 × 11 × 13) / (2 × 32 × 109)
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 × 3 × 11 × 13; 2 × 32 × 109) = 2 × 3
Divide the numerator and the denominator by their GCF:
- (2 × 3 × 11 × 13) / (2 × 32 × 109) =
- ((2 × 3 × 11 × 13) ÷ (2 × 3)) / ((2 × 32 × 109) ÷ (2 × 3)) =
- (2 ÷ 2 × 3 ÷ 3 × 11 × 13)/(2 ÷ 2 × 32 ÷ 3 × 109) =
- (1 × 1 × 11 × 13)/(1 × 3(2 - 1) × 109) =
- (1 × 1 × 11 × 13)/(1 × 31 × 109) =
- (1 × 1 × 11 × 13)/(1 × 3 × 109) =
- (11 × 13)/(3 × 109) =
- 143/327
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 143/327 =
- 143 ÷ 327 ≈
- 0.437308868502 ≈
- 0.44
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.
- 0.437308868502 =
- 0.437308868502 × 100/100 =
( - 0.437308868502 × 100)/100 =
- 43.730886850153/100 ≈
- 43.730886850153% ≈
- 43.73%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
78/109 × - 55/90 = - 143/327
As a decimal number:
78/109 × - 55/90 ≈ - 0.44
As a percentage:
78/109 × - 55/90 ≈ - 43.73%
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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