Multiplying the common ordinary fractions: 40/63 × 47/64 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
40/63 × 47/64 = ?
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.
40/63 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
40 = 23 × 5
63 = 32 × 7
47/64 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
47 is a prime number (it cannot be factored into other prime factors)
64 = 26
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.
40/63 × 47/64 =
(40 × 47) / (63 × 64) =
(23 × 5 × 47) / (32 × 7 × 26) =
(23 × 5 × 47) / (26 × 32 × 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 (23 × 5 × 47; 26 × 32 × 7) = 23
Divide the numerator and the denominator by their GCF:
(23 × 5 × 47) / (26 × 32 × 7) =
((23 × 5 × 47) ÷ 23) / ((26 × 32 × 7) ÷ 23) =
(23 ÷ 23 × 5 × 47)/(26 ÷ 23 × 32 × 7) =
(2(3 - 3) × 5 × 47)/(2(6 - 3) × 32 × 7) =
(20 × 5 × 47)/(23 × 32 × 7) =
(1 × 5 × 47)/(23 × 32 × 7) =
(5 × 47)/(23 × 32 × 7) =
(5 × 47)/(8 × 9 × 7) =
235/504
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
235/504 =
235 ÷ 504 ≈
0.46626984127 ≈
0.47
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.
0.46626984127 =
0.46626984127 × 100/100 =
(0.46626984127 × 100)/100 =
46.626984126984/100 ≈
46.626984126984% ≈
46.63%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
40/63 × 47/64 = 235/504
As a decimal number:
40/63 × 47/64 ≈ 0.47
As a percentage:
40/63 × 47/64 ≈ 46.63%
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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