Multiplying the common ordinary fractions: - 50/88 × - 68/91 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 50/88 × - 68/91 = ?
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
- 50/88 × - 68/91 =
50/88 × 68/91
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.
50/88 =
(2 × 52)/(23 × 11) =
((2 × 52) ÷ 2)/((23 × 11) ÷ 2) =
(2 ÷ 2 × 52)/(23 ÷ 2 × 11) =
(1 × 52)/(2(3 - 1) × 11) =
(1 × 52)/(22 × 11) =
25/44
68/91 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
68 = 22 × 17
91 = 7 × 13
Rewrite the equivalent simplified operation:
50/88 × 68/91 =
25/44 × 68/91
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.
25/44 × 68/91 =
(25 × 68) / (44 × 91) =
(52 × 22 × 17) / (22 × 11 × 7 × 13) =
(22 × 52 × 17) / (22 × 7 × 11 × 13)
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 × 52 × 17; 22 × 7 × 11 × 13) = 22
Divide the numerator and the denominator by their GCF:
(22 × 52 × 17) / (22 × 7 × 11 × 13) =
((22 × 52 × 17) ÷ 22) / ((22 × 7 × 11 × 13) ÷ 22) =
(22 ÷ 22 × 52 × 17)/(22 ÷ 22 × 7 × 11 × 13) =
(2(2 - 2) × 52 × 17)/(2(2 - 2) × 7 × 11 × 13) =
(20 × 52 × 17)/(20 × 7 × 11 × 13) =
(1 × 52 × 17)/(1 × 7 × 11 × 13) =
(52 × 17)/(7 × 11 × 13) =
(25 × 17)/(7 × 11 × 13) =
425/1,001
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
425/1,001 =
425 ÷ 1,001 ≈
0.424575424575 ≈
0.42
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.
0.424575424575 =
0.424575424575 × 100/100 =
(0.424575424575 × 100)/100 =
42.457542457542/100 ≈
42.457542457542% ≈
42.46%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 50/88 × - 68/91 = 425/1,001
As a decimal number:
- 50/88 × - 68/91 ≈ 0.42
As a percentage:
- 50/88 × - 68/91 ≈ 42.46%
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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