Multiplying the common ordinary fractions: 17/35 × 21/43 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
17/35 × 21/43 = ?
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.
17/35 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
17 is a prime number (it cannot be factored into other prime factors)
35 = 5 × 7
21/43 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
21 = 3 × 7
43 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.
17/35 × 21/43 =
(17 × 21) / (35 × 43) =
(17 × 3 × 7) / (5 × 7 × 43) =
(3 × 7 × 17) / (5 × 7 × 43)
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 (3 × 7 × 17; 5 × 7 × 43) = 7
Divide the numerator and the denominator by their GCF:
(3 × 7 × 17) / (5 × 7 × 43) =
((3 × 7 × 17) ÷ 7) / ((5 × 7 × 43) ÷ 7) =
(3 × 7 ÷ 7 × 17)/(5 × 7 ÷ 7 × 43) =
(3 × 1 × 17)/(5 × 1 × 43) =
(3 × 17)/(5 × 43) =
51/215
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
51/215 =
51 ÷ 215 ≈
0.237209302326 ≈
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.
0.237209302326 =
0.237209302326 × 100/100 =
(0.237209302326 × 100)/100 =
23.720930232558/100 ≈
23.720930232558% ≈
23.72%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
17/35 × 21/43 = 51/215
As a decimal number:
17/35 × 21/43 ≈ 0.24
As a percentage:
17/35 × 21/43 ≈ 23.72%
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.
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