Multiplying the common ordinary fractions: - 111/77 × 49/106 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 111/77 × 49/106 = ?
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.
111/77 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
111 = 3 × 37
77 = 7 × 11
49/106 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
49 = 72
106 = 2 × 53
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.
- 111/77 × 49/106 =
- (111 × 49) / (77 × 106) =
- (3 × 37 × 72) / (7 × 11 × 2 × 53) =
- (3 × 72 × 37) / (2 × 7 × 11 × 53)
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 (3 × 72 × 37; 2 × 7 × 11 × 53) = 7
Divide the numerator and the denominator by their GCF:
- (3 × 72 × 37) / (2 × 7 × 11 × 53) =
- ((3 × 72 × 37) ÷ 7) / ((2 × 7 × 11 × 53) ÷ 7) =
- (3 × 72 ÷ 7 × 37)/(2 × 7 ÷ 7 × 11 × 53) =
- (3 × 7(2 - 1) × 37)/(2 × 1 × 11 × 53) =
- (3 × 71 × 37)/(2 × 1 × 11 × 53) =
- (3 × 7 × 37)/(2 × 1 × 11 × 53) =
- (3 × 7 × 37)/(2 × 11 × 53) =
- 777/1,166
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 777/1,166 =
- 777 ÷ 1,166 ≈
- 0.666380789022 ≈
- 0.67
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.
- 0.666380789022 =
- 0.666380789022 × 100/100 =
( - 0.666380789022 × 100)/100 =
- 66.63807890223/100 ≈
- 66.63807890223% ≈
- 66.64%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 111/77 × 49/106 = - 777/1,166
As a decimal number:
- 111/77 × 49/106 ≈ - 0.67
As a percentage:
- 111/77 × 49/106 ≈ - 66.64%
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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