Multiplying the common ordinary fractions: 25/36 × - 8/23 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
25/36 × - 8/23 = ?
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
25/36 × - 8/23 =
- 25/36 × 8/23
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.
25/36 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
25 = 52
36 = 22 × 32
8/23 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
8 = 23
23 is a prime number (it cannot be factored into other prime factors)
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.
- 25/36 × 8/23 =
- (25 × 8) / (36 × 23) =
- (52 × 23) / (22 × 32 × 23) =
- (23 × 52) / (22 × 32 × 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 (23 × 52; 22 × 32 × 23) = 22
Divide the numerator and the denominator by their GCF:
- (23 × 52) / (22 × 32 × 23) =
- ((23 × 52) ÷ 22) / ((22 × 32 × 23) ÷ 22) =
- (23 ÷ 22 × 52)/(22 ÷ 22 × 32 × 23) =
- (2(3 - 2) × 52)/(2(2 - 2) × 32 × 23) =
- (21 × 52)/(20 × 32 × 23) =
- (2 × 52)/(1 × 32 × 23) =
- (2 × 52)/(32 × 23) =
- (2 × 25)/(9 × 23) =
- 50/207
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 50/207 =
- 50 ÷ 207 ≈
- 0.24154589372 ≈
- 0.24
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.
- 0.24154589372 =
- 0.24154589372 × 100/100 =
( - 0.24154589372 × 100)/100 =
- 24.154589371981/100 ≈
- 24.154589371981% ≈
- 24.15%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
25/36 × - 8/23 = - 50/207
As a decimal number:
25/36 × - 8/23 ≈ - 0.24
As a percentage:
25/36 × - 8/23 ≈ - 24.15%
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: