Multiplying the common ordinary fractions: - 52/89 × 52/88 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 52/89 × 52/88 = ?
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.
52/89 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
52 = 22 × 13
89 is a prime number (it cannot be factored into other prime factors)
52/88 =
(22 × 13)/(23 × 11) =
((22 × 13) ÷ 22)/((23 × 11) ÷ 22) =
(22 ÷ 22 × 13)/(23 ÷ 22 × 11) =
(2(2 - 2) × 13)/(2(3 - 2) × 11) =
(20 × 13)/(21 × 11) =
(1 × 13)/(2 × 11) =
13/22
Rewrite the equivalent simplified operation:
- 52/89 × 52/88 =
- 52/89 × 13/22
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.
- 52/89 × 13/22 =
- (52 × 13) / (89 × 22) =
- (22 × 13 × 13) / (89 × 2 × 11) =
- (22 × 132) / (2 × 11 × 89)
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 × 132; 2 × 11 × 89) = 2
Divide the numerator and the denominator by their GCF:
- (22 × 132) / (2 × 11 × 89) =
- ((22 × 132) ÷ 2) / ((2 × 11 × 89) ÷ 2) =
- (22 ÷ 2 × 132)/(2 ÷ 2 × 11 × 89) =
- (2(2 - 1) × 132)/(1 × 11 × 89) =
- (21 × 132)/(1 × 11 × 89) =
- (2 × 132)/(1 × 11 × 89) =
- (2 × 132)/(11 × 89) =
- (2 × 169)/(11 × 89) =
- 338/979
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 338/979 =
- 338 ÷ 979 ≈
- 0.345250255363 ≈
- 0.35
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.
- 0.345250255363 =
- 0.345250255363 × 100/100 =
( - 0.345250255363 × 100)/100 =
- 34.525025536261/100 ≈
- 34.525025536261% ≈
- 34.53%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 52/89 × 52/88 = - 338/979
As a decimal number:
- 52/89 × 52/88 ≈ - 0.35
As a percentage:
- 52/89 × 52/88 ≈ - 34.53%
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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