Multiplying the common ordinary fractions: - 15/32 × 40/61 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 15/32 × 40/61 = ?
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.
15/32 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
15 = 3 × 5
32 = 25
40/61 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
40 = 23 × 5
61 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.
- 15/32 × 40/61 =
- (15 × 40) / (32 × 61) =
- (3 × 5 × 23 × 5) / (25 × 61) =
- (23 × 3 × 52) / (25 × 61)
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 × 3 × 52; 25 × 61) = 23
Divide the numerator and the denominator by their GCF:
- (23 × 3 × 52) / (25 × 61) =
- ((23 × 3 × 52) ÷ 23) / ((25 × 61) ÷ 23) =
- (23 ÷ 23 × 3 × 52)/(25 ÷ 23 × 61) =
- (2(3 - 3) × 3 × 52)/(2(5 - 3) × 61) =
- (20 × 3 × 52)/(22 × 61) =
- (1 × 3 × 52)/(22 × 61) =
- (3 × 52)/(22 × 61) =
- (3 × 25)/(4 × 61) =
- 75/244
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 75/244 =
- 75 ÷ 244 ≈
- 0.30737704918 ≈
- 0.31
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.
- 0.30737704918 =
- 0.30737704918 × 100/100 =
( - 0.30737704918 × 100)/100 =
- 30.737704918033/100 ≈
- 30.737704918033% ≈
- 30.74%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 15/32 × 40/61 = - 75/244
As a decimal number:
- 15/32 × 40/61 ≈ - 0.31
As a percentage:
- 15/32 × 40/61 ≈ - 30.74%
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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