Multiplying the common ordinary fractions: 65/96 × - 70/111 × 62/107 × 83/111 × - 78/109 × - 76/95 × - 84/113 × - 70/105 × 72/106 × - 102/81 × 112/72 × - 77/105 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
65/96 × - 70/111 × 62/107 × 83/111 × - 78/109 × - 76/95 × - 84/113 × - 70/105 × 72/106 × - 102/81 × 112/72 × - 77/105 = ?
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
65/96 × - 70/111 × 62/107 × 83/111 × - 78/109 × - 76/95 × - 84/113 × - 70/105 × 72/106 × - 102/81 × 112/72 × - 77/105 =
- 65/96 × 70/111 × 62/107 × 83/111 × 78/109 × 76/95 × 84/113 × 70/105 × 72/106 × 102/81 × 112/72 × 77/105
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 72/106 × 112/72 = 112/106
Rewrite the equivalent simplified operation:
- 65/96 × 70/111 × 62/107 × 83/111 × 78/109 × 76/95 × 84/113 × 70/105 × 72/106 × 102/81 × 112/72 × 77/105 =
- 65/96 × 70/111 × 62/107 × 83/111 × 78/109 × 76/95 × 84/113 × 70/105 × 112/106 × 102/81 × 77/105
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.
65/96 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
65 = 5 × 13
96 = 25 × 3
70/111 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
70 = 2 × 5 × 7
111 = 3 × 37
62/107 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
62 = 2 × 31
107 is a prime number (it cannot be factored into other prime factors)
83/111 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
83 is a prime number (it cannot be factored into other prime factors)
111 = 3 × 37
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)
76/95 =
(22 × 19)/(5 × 19) =
((22 × 19) ÷ 19)/((5 × 19) ÷ 19) =
(22 × 19 ÷ 19)/(5 × 19 ÷ 19) =
(22 × 1)/(5 × 1) =
4/5
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)
70/105 =
(2 × 5 × 7)/(3 × 5 × 7) =
((2 × 5 × 7) ÷ (5 × 7))/((3 × 5 × 7) ÷ (5 × 7)) =
(2 × 5 ÷ 5 × 7 ÷ 7)/(3 × 5 ÷ 5 × 7 ÷ 7) =
(2 × 1 × 1)/(3 × 1 × 1) =
2/3
112/106 =
(24 × 7)/(2 × 53) =
((24 × 7) ÷ 2)/((2 × 53) ÷ 2) =
(24 ÷ 2 × 7)/(2 ÷ 2 × 53) =
(2(4 - 1) × 7)/(1 × 53) =
(23 × 7)/(1 × 53) =
56/53
102/81 =
(2 × 3 × 17)/34 =
((2 × 3 × 17) ÷ 3)/(34 ÷ 3) =
(2 × 3 ÷ 3 × 17)/(34 ÷ 3) =
(2 × 1 × 17)/3(4 - 1) =
(2 × 1 × 17)/33 =
34/27
77/105 =
(7 × 11)/(3 × 5 × 7) =
((7 × 11) ÷ 7)/((3 × 5 × 7) ÷ 7) =
(7 ÷ 7 × 11)/(3 × 5 × 7 ÷ 7) =
(1 × 11)/(3 × 5 × 1) =
11/15
Rewrite the equivalent simplified operation:
- 65/96 × 70/111 × 62/107 × 83/111 × 78/109 × 76/95 × 84/113 × 70/105 × 112/106 × 102/81 × 77/105 =
- 65/96 × 70/111 × 62/107 × 83/111 × 78/109 × 4/5 × 84/113 × 2/3 × 56/53 × 34/27 × 11/15
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.
- 65/96 × 70/111 × 62/107 × 83/111 × 78/109 × 4/5 × 84/113 × 2/3 × 56/53 × 34/27 × 11/15 =
- (65 × 70 × 62 × 83 × 78 × 4 × 84 × 2 × 56 × 34 × 11) / (96 × 111 × 107 × 111 × 109 × 5 × 113 × 3 × 53 × 27 × 15) =
- (5 × 13 × 2 × 5 × 7 × 2 × 31 × 83 × 2 × 3 × 13 × 22 × 22 × 3 × 7 × 2 × 23 × 7 × 2 × 17 × 11) / (25 × 3 × 3 × 37 × 107 × 3 × 37 × 109 × 5 × 113 × 3 × 53 × 33 × 3 × 5) =
- (212 × 32 × 52 × 73 × 11 × 132 × 17 × 31 × 83) / (25 × 38 × 52 × 372 × 53 × 107 × 109 × 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 (212 × 32 × 52 × 73 × 11 × 132 × 17 × 31 × 83; 25 × 38 × 52 × 372 × 53 × 107 × 109 × 113) = 25 × 32 × 52
Divide the numerator and the denominator by their GCF:
- (212 × 32 × 52 × 73 × 11 × 132 × 17 × 31 × 83) / (25 × 38 × 52 × 372 × 53 × 107 × 109 × 113) =
- ((212 × 32 × 52 × 73 × 11 × 132 × 17 × 31 × 83) ÷ (25 × 32 × 52)) / ((25 × 38 × 52 × 372 × 53 × 107 × 109 × 113) ÷ (25 × 32 × 52)) =
- (212 ÷ 25 × 32 ÷ 32 × 52 ÷ 52 × 73 × 11 × 132 × 17 × 31 × 83)/(25 ÷ 25 × 38 ÷ 32 × 52 ÷ 52 × 372 × 53 × 107 × 109 × 113) =
- (2(12 - 5) × 3(2 - 2) × 5(2 - 2) × 73 × 11 × 132 × 17 × 31 × 83)/(2(5 - 5) × 3(8 - 2) × 5(2 - 2) × 372 × 53 × 107 × 109 × 113) =
- (27 × 30 × 50 × 73 × 11 × 132 × 17 × 31 × 83)/(20 × 36 × 50 × 372 × 53 × 107 × 109 × 113) =
- (27 × 1 × 1 × 73 × 11 × 132 × 17 × 31 × 83)/(1 × 36 × 1 × 372 × 53 × 107 × 109 × 113) =
- (27 × 73 × 11 × 132 × 17 × 31 × 83)/(36 × 372 × 53 × 107 × 109 × 113) =
- (128 × 343 × 11 × 169 × 17 × 31 × 83)/(729 × 1,369 × 53 × 107 × 109 × 113) =
- 3,570,032,642,176/69,710,077,435,707
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 3,570,032,642,176/69,710,077,435,707 =
- 3,570,032,642,176 ÷ 69,710,077,435,707 ≈
- 0.051212576051 ≈
- 0.05
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.
- 0.051212576051 =
- 0.051212576051 × 100/100 =
( - 0.051212576051 × 100)/100 =
- 5.12125760507/100 ≈
- 5.12125760507% ≈
- 5.12%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
65/96 × - 70/111 × 62/107 × 83/111 × - 78/109 × - 76/95 × - 84/113 × - 70/105 × 72/106 × - 102/81 × 112/72 × - 77/105 = - 3,570,032,642,176/69,710,077,435,707
As a decimal number:
65/96 × - 70/111 × 62/107 × 83/111 × - 78/109 × - 76/95 × - 84/113 × - 70/105 × 72/106 × - 102/81 × 112/72 × - 77/105 ≈ - 0.05
As a percentage:
65/96 × - 70/111 × 62/107 × 83/111 × - 78/109 × - 76/95 × - 84/113 × - 70/105 × 72/106 × - 102/81 × 112/72 × - 77/105 ≈ - 5.12%
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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