Multiplying the common ordinary fractions: 32/40 × 15/20 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
32/40 × 15/20 = ?
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.
32/40 =
25/(23 × 5) =
(25 ÷ 23)/((23 × 5) ÷ 23) =
(25 ÷ 23)/(23 ÷ 23 × 5) =
2(5 - 3)/(2(3 - 3) × 5) =
22/(20 × 5) =
22/(1 × 5) =
4/5
15/20 =
(3 × 5)/(22 × 5) =
((3 × 5) ÷ 5)/((22 × 5) ÷ 5) =
(3 × 5 ÷ 5)/(22 × 5 ÷ 5) =
(3 × 1)/(22 × 1) =
3/4
Rewrite the equivalent simplified operation:
32/40 × 15/20 =
4/5 × 3/4
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 4/5 × 3/4 = 3/5
Simplify the operation
Reduce (simplify) the new 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.
* 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.
3/5 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
3 is a prime number (it cannot be factored into other prime factors)
5 is a prime number (it cannot be factored into other prime factors)
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
3/5 =
3 ÷ 5 =
0.6
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.
0.6 =
0.6 × 100/100 =
(0.6 × 100)/100 =
60/100 =
60%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
32/40 × 15/20 = 3/5
As a decimal number:
32/40 × 15/20 = 0.6
As a percentage:
32/40 × 15/20 = 60%
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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