Multiplying the common ordinary fractions: 54/120 × - 84/46 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
54/120 × - 84/46 = ?
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
54/120 × - 84/46 =
- 54/120 × 84/46
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.
54/120 =
(2 × 33)/(23 × 3 × 5) =
((2 × 33) ÷ (2 × 3))/((23 × 3 × 5) ÷ (2 × 3)) =
(2 ÷ 2 × 33 ÷ 3)/(23 ÷ 2 × 3 ÷ 3 × 5) =
(1 × 3(3 - 1))/(2(3 - 1) × 1 × 5) =
(1 × 32)/(22 × 1 × 5) =
9/20
84/46 =
(22 × 3 × 7)/(2 × 23) =
((22 × 3 × 7) ÷ 2)/((2 × 23) ÷ 2) =
(22 ÷ 2 × 3 × 7)/(2 ÷ 2 × 23) =
(2(2 - 1) × 3 × 7)/(1 × 23) =
(21 × 3 × 7)/(1 × 23) =
(2 × 3 × 7)/(1 × 23) =
42/23
Rewrite the equivalent simplified operation:
- 54/120 × 84/46 =
- 9/20 × 42/23
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.
- 9/20 × 42/23 =
- (9 × 42) / (20 × 23) =
- (32 × 2 × 3 × 7) / (22 × 5 × 23) =
- (2 × 33 × 7) / (22 × 5 × 23)
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 (2 × 33 × 7; 22 × 5 × 23) = 2
Divide the numerator and the denominator by their GCF:
- (2 × 33 × 7) / (22 × 5 × 23) =
- ((2 × 33 × 7) ÷ 2) / ((22 × 5 × 23) ÷ 2) =
- (2 ÷ 2 × 33 × 7)/(22 ÷ 2 × 5 × 23) =
- (1 × 33 × 7)/(2(2 - 1) × 5 × 23) =
- (1 × 33 × 7)/(21 × 5 × 23) =
- (1 × 33 × 7)/(2 × 5 × 23) =
- (33 × 7)/(2 × 5 × 23) =
- (27 × 7)/(2 × 5 × 23) =
- 189/230
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 189/230 =
- 189 ÷ 230 ≈
- 0.821739130435 ≈
- 0.82
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.
- 0.821739130435 =
- 0.821739130435 × 100/100 =
( - 0.821739130435 × 100)/100 =
- 82.173913043478/100 ≈
- 82.173913043478% ≈
- 82.17%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
54/120 × - 84/46 = - 189/230
As a decimal number:
54/120 × - 84/46 ≈ - 0.82
As a percentage:
54/120 × - 84/46 ≈ - 82.17%
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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