Multiplying the common ordinary fractions: - 33/27 × - 43/143 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 33/27 × - 43/143 = ?
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
- 33/27 × - 43/143 =
33/27 × 43/143
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.
33/27 =
(3 × 11)/33 =
((3 × 11) ÷ 3)/(33 ÷ 3) =
(3 ÷ 3 × 11)/(33 ÷ 3) =
(1 × 11)/3(3 - 1) =
(1 × 11)/32 =
11/9
43/143 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
43 is a prime number (it cannot be factored into other prime factors)
143 = 11 × 13
Rewrite the equivalent simplified operation:
33/27 × 43/143 =
11/9 × 43/143
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.
11/9 × 43/143 =
(11 × 43) / (9 × 143) =
(11 × 43) / (32 × 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 (11 × 43; 32 × 11 × 13) = 11
Divide the numerator and the denominator by their GCF:
(11 × 43) / (32 × 11 × 13) =
((11 × 43) ÷ 11) / ((32 × 11 × 13) ÷ 11) =
(11 ÷ 11 × 43)/(32 × 11 ÷ 11 × 13) =
(1 × 43)/(32 × 1 × 13) =
43/(32 × 13) =
43/(9 × 13) =
43/117
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
43/117 =
43 ÷ 117 ≈
0.367521367521 ≈
0.37
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.
0.367521367521 =
0.367521367521 × 100/100 =
(0.367521367521 × 100)/100 =
36.752136752137/100 ≈
36.752136752137% ≈
36.75%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 33/27 × - 43/143 = 43/117
As a decimal number:
- 33/27 × - 43/143 ≈ 0.37
As a percentage:
- 33/27 × - 43/143 ≈ 36.75%
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
Multiply common ordinary fractions, online calculator: