Multiplying the common ordinary fractions: 28/147 × - 28/88 × - 26/70 × 20/58 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
28/147 × - 28/88 × - 26/70 × 20/58 = ?
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
28/147 × - 28/88 × - 26/70 × 20/58 =
28/147 × 28/88 × 26/70 × 20/58
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.
28/147 =
(22 × 7)/(3 × 72) =
((22 × 7) ÷ 7)/((3 × 72) ÷ 7) =
(22 × 7 ÷ 7)/(3 × 72 ÷ 7) =
(22 × 1)/(3 × 7(2 - 1)) =
(22 × 1)/(3 × 71) =
(22 × 1)/(3 × 7) =
4/21
28/88 =
(22 × 7)/(23 × 11) =
((22 × 7) ÷ 22)/((23 × 11) ÷ 22) =
(22 ÷ 22 × 7)/(23 ÷ 22 × 11) =
(2(2 - 2) × 7)/(2(3 - 2) × 11) =
(20 × 7)/(21 × 11) =
(1 × 7)/(2 × 11) =
7/22
26/70 =
(2 × 13)/(2 × 5 × 7) =
((2 × 13) ÷ 2)/((2 × 5 × 7) ÷ 2) =
(2 ÷ 2 × 13)/(2 ÷ 2 × 5 × 7) =
(1 × 13)/(1 × 5 × 7) =
13/35
20/58 =
(22 × 5)/(2 × 29) =
((22 × 5) ÷ 2)/((2 × 29) ÷ 2) =
(22 ÷ 2 × 5)/(2 ÷ 2 × 29) =
(2(2 - 1) × 5)/(1 × 29) =
(21 × 5)/(1 × 29) =
(2 × 5)/(1 × 29) =
10/29
Rewrite the equivalent simplified operation:
28/147 × 28/88 × 26/70 × 20/58 =
4/21 × 7/22 × 13/35 × 10/29
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.
4/21 × 7/22 × 13/35 × 10/29 =
(4 × 7 × 13 × 10) / (21 × 22 × 35 × 29) =
(22 × 7 × 13 × 2 × 5) / (3 × 7 × 2 × 11 × 5 × 7 × 29) =
(23 × 5 × 7 × 13) / (2 × 3 × 5 × 72 × 11 × 29)
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 (23 × 5 × 7 × 13; 2 × 3 × 5 × 72 × 11 × 29) = 2 × 5 × 7
Divide the numerator and the denominator by their GCF:
(23 × 5 × 7 × 13) / (2 × 3 × 5 × 72 × 11 × 29) =
((23 × 5 × 7 × 13) ÷ (2 × 5 × 7)) / ((2 × 3 × 5 × 72 × 11 × 29) ÷ (2 × 5 × 7)) =
(23 ÷ 2 × 5 ÷ 5 × 7 ÷ 7 × 13)/(2 ÷ 2 × 3 × 5 ÷ 5 × 72 ÷ 7 × 11 × 29) =
(2(3 - 1) × 1 × 1 × 13)/(1 × 3 × 1 × 7(2 - 1) × 11 × 29) =
(22 × 1 × 1 × 13)/(1 × 3 × 1 × 71 × 11 × 29) =
(22 × 1 × 1 × 13)/(1 × 3 × 1 × 7 × 11 × 29) =
(22 × 13)/(3 × 7 × 11 × 29) =
(4 × 13)/(3 × 7 × 11 × 29) =
52/6,699
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
52/6,699 =
52 ÷ 6,699 ≈
0.00776235259 ≈
0.01
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.
0.00776235259 =
0.00776235259 × 100/100 =
(0.00776235259 × 100)/100 =
0.776235258994/100 ≈
0.776235258994% ≈
0.78%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
28/147 × - 28/88 × - 26/70 × 20/58 = 52/6,699
As a decimal number:
28/147 × - 28/88 × - 26/70 × 20/58 ≈ 0.01
As a percentage:
28/147 × - 28/88 × - 26/70 × 20/58 ≈ 0.78%
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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