Multiplying the common ordinary fractions: 65/29 × - 63/27 = ? The multiplication process explained. The result written: As a negative improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage
65/29 × - 63/27 = ?
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
65/29 × - 63/27 =
- 65/29 × 63/27
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.
* Why do we try to reduce (simplify) the fractions?
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.
65/29 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization: 65 = 5 × 13 29 is a prime number (it cannot be factored into other prime factors)
Divide the numerator and the denominator by their GCF:
The numerator and the denominator of the fraction are coprime numbers (there are no common prime factors, the GCF = 1). The end fraction can no longer be shortened, it already has the smallest possible numerator and denominator, it is an irreducible fraction.
As a negative improper fraction: (the numerator >= the denominator) 65/29 × - 63/27 = - 455/87
As a mixed number (also called a mixed fraction): 65/29 × - 63/27 = - 5 20/87
As a decimal number: 65/29 × - 63/27 ≈ - 5.23
As a percentage: 65/29 × - 63/27 ≈ - 522.99%
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.
The latest common ordinary fractions that have been multiplied
Above the fraction bar we write the product of all the prime factors of the fractions' numerators, without doing any calculations.
Below the fraction bar we write the product of all the prime factors of the fractions' denominators, without doing any calculations.
Cross out all the common prime factors that appear both above and below the fraction bar.
Multiply the remaining prime factors above the fraction bar - this will be the numerator of the resulted fraction.
Multiply the remaining prime factors below the fraction bar - this will be the denominator of the resulted fraction.
There is no need to reduce (simplify) the resulting fraction, since we have already crossed out all the common prime factors.
If the resulted fraction is an improper one (without considering the sign, the numerator is larger than the denominator), it could be written as a mixed number, consisting of an integer and a proper fraction of the same sign.