Multiplying the common ordinary fractions: 27/21 × - 22/30 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
27/21 × - 22/30 = ?
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
27/21 × - 22/30 =
- 27/21 × 22/30
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.
27/21 =
33/(3 × 7) =
(33 ÷ 3)/((3 × 7) ÷ 3) =
(33 ÷ 3)/(3 ÷ 3 × 7) =
3(3 - 1)/(1 × 7) =
32/(1 × 7) =
9/7
22/30 =
(2 × 11)/(2 × 3 × 5) =
((2 × 11) ÷ 2)/((2 × 3 × 5) ÷ 2) =
(2 ÷ 2 × 11)/(2 ÷ 2 × 3 × 5) =
(1 × 11)/(1 × 3 × 5) =
11/15
Rewrite the equivalent simplified operation:
- 27/21 × 22/30 =
- 9/7 × 11/15
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.
- 9/7 × 11/15 =
- (9 × 11) / (7 × 15) =
- (32 × 11) / (7 × 3 × 5) =
- (32 × 11) / (3 × 5 × 7)
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 (32 × 11; 3 × 5 × 7) = 3
Divide the numerator and the denominator by their GCF:
- (32 × 11) / (3 × 5 × 7) =
- ((32 × 11) ÷ 3) / ((3 × 5 × 7) ÷ 3) =
- (32 ÷ 3 × 11)/(3 ÷ 3 × 5 × 7) =
- (3(2 - 1) × 11)/(1 × 5 × 7) =
- (31 × 11)/(1 × 5 × 7) =
- (3 × 11)/(1 × 5 × 7) =
- (3 × 11)/(5 × 7) =
- 33/35
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 33/35 =
- 33 ÷ 35 ≈
- 0.942857142857 ≈
- 0.94
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.
- 0.942857142857 =
- 0.942857142857 × 100/100 =
( - 0.942857142857 × 100)/100 =
- 94.285714285714/100 ≈
- 94.285714285714% ≈
- 94.29%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
27/21 × - 22/30 = - 33/35
As a decimal number:
27/21 × - 22/30 ≈ - 0.94
As a percentage:
27/21 × - 22/30 ≈ - 94.29%
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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