Multiplying the common ordinary fractions: - 21/8 × - 8/31 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 21/8 × - 8/31 = ?
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
- 21/8 × - 8/31 =
21/8 × 8/31
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 21/8 × 8/31 = 21/31
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.
21/31 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
21 = 3 × 7
31 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:
21/31 =
21 ÷ 31 ≈
0.677419354839 ≈
0.68
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.
0.677419354839 =
0.677419354839 × 100/100 =
(0.677419354839 × 100)/100 =
67.741935483871/100 ≈
67.741935483871% ≈
67.74%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 21/8 × - 8/31 = 21/31
As a decimal number:
- 21/8 × - 8/31 ≈ 0.68
As a percentage:
- 21/8 × - 8/31 ≈ 67.74%
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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