Multiplying the common ordinary fractions: - 26/34 × - 34/41 × 36/56 × 83/764 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 26/34 × - 34/41 × 36/56 × 83/764 = ?
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
- 26/34 × - 34/41 × 36/56 × 83/764 =
26/34 × 34/41 × 36/56 × 83/764
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 26/34 × 34/41 = 26/41
Rewrite the equivalent simplified operation:
26/34 × 34/41 × 36/56 × 83/764 =
26/41 × 36/56 × 83/764
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.
26/41 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
26 = 2 × 13
41 is a prime number (it cannot be factored into other prime factors)
36/56 =
(22 × 32)/(23 × 7) =
((22 × 32) ÷ 22)/((23 × 7) ÷ 22) =
(22 ÷ 22 × 32)/(23 ÷ 22 × 7) =
(2(2 - 2) × 32)/(2(3 - 2) × 7) =
(20 × 32)/(21 × 7) =
(1 × 32)/(2 × 7) =
9/14
83/764 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)
764 = 22 × 191
Rewrite the equivalent simplified operation:
26/41 × 36/56 × 83/764 =
26/41 × 9/14 × 83/764
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.
26/41 × 9/14 × 83/764 =
(26 × 9 × 83) / (41 × 14 × 764) =
(2 × 13 × 32 × 83) / (41 × 2 × 7 × 22 × 191) =
(2 × 32 × 13 × 83) / (23 × 7 × 41 × 191)
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 × 32 × 13 × 83; 23 × 7 × 41 × 191) = 2
Divide the numerator and the denominator by their GCF:
(2 × 32 × 13 × 83) / (23 × 7 × 41 × 191) =
((2 × 32 × 13 × 83) ÷ 2) / ((23 × 7 × 41 × 191) ÷ 2) =
(2 ÷ 2 × 32 × 13 × 83)/(23 ÷ 2 × 7 × 41 × 191) =
(1 × 32 × 13 × 83)/(2(3 - 1) × 7 × 41 × 191) =
(1 × 32 × 13 × 83)/(22 × 7 × 41 × 191) =
(32 × 13 × 83)/(22 × 7 × 41 × 191) =
(9 × 13 × 83)/(4 × 7 × 41 × 191) =
9,711/219,268
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
9,711/219,268 =
9,711 ÷ 219,268 ≈
0.044288268238 ≈
0.04
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.
0.044288268238 =
0.044288268238 × 100/100 =
(0.044288268238 × 100)/100 =
4.428826823796/100 ≈
4.428826823796% ≈
4.43%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 26/34 × - 34/41 × 36/56 × 83/764 = 9,711/219,268
As a decimal number:
- 26/34 × - 34/41 × 36/56 × 83/764 ≈ 0.04
As a percentage:
- 26/34 × - 34/41 × 36/56 × 83/764 ≈ 4.43%
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.
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