Multiplying the common ordinary fractions: - 31/56 × - 36/62 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 31/56 × - 36/62 = ?
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
- 31/56 × - 36/62 =
31/56 × 36/62
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.
31/56 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
31 is a prime number (it cannot be factored into other prime factors)
56 = 23 × 7
36/62 =
(22 × 32)/(2 × 31) =
((22 × 32) ÷ 2)/((2 × 31) ÷ 2) =
(22 ÷ 2 × 32)/(2 ÷ 2 × 31) =
(2(2 - 1) × 32)/(1 × 31) =
(21 × 32)/(1 × 31) =
(2 × 32)/(1 × 31) =
18/31
Rewrite the equivalent simplified operation:
31/56 × 36/62 =
31/56 × 18/31
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 31/56 × 18/31 = 18/56
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.
18/56 =
(2 × 32)/(23 × 7) =
((2 × 32) ÷ 2)/((23 × 7) ÷ 2) =
(2 ÷ 2 × 32)/(23 ÷ 2 × 7) =
(1 × 32)/(2(3 - 1) × 7) =
(1 × 32)/(22 × 7) =
9/28
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
9/28 =
9 ÷ 28 ≈
0.321428571429 ≈
0.32
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.
0.321428571429 =
0.321428571429 × 100/100 =
(0.321428571429 × 100)/100 =
32.142857142857/100 ≈
32.142857142857% ≈
32.14%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 31/56 × - 36/62 = 9/28
As a decimal number:
- 31/56 × - 36/62 ≈ 0.32
As a percentage:
- 31/56 × - 36/62 ≈ 32.14%
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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