Multiplying the common ordinary fractions: 566/12 × - 4,740/12 × 5,503/11 × 17/12 = ? 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

566/12 × - 4,740/12 × 5,503/11 × 17/12 = ?

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


566/12 × - 4,740/12 × 5,503/11 × 17/12 =


- 566/12 × 4,740/12 × 5,503/11 × 17/12

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.


566/12 =


(2 × 283)/(22 × 3) =


((2 × 283) ÷ 2)/((22 × 3) ÷ 2) =


(2 ÷ 2 × 283)/(22 ÷ 2 × 3) =


(1 × 283)/(2(2 - 1) × 3) =


(1 × 283)/(21 × 3) =


(1 × 283)/(2 × 3) =


283/6


4,740/12 =


(22 × 3 × 5 × 79)/(22 × 3) =


((22 × 3 × 5 × 79) ÷ (22 × 3))/((22 × 3) ÷ (22 × 3)) =


(22 ÷ 22 × 3 ÷ 3 × 5 × 79)/(22 ÷ 22 × 3 ÷ 3) =


(2(2 - 2) × 1 × 5 × 79)/(2(2 - 2) × 1) =


(20 × 1 × 5 × 79)/(20 × 1) =


(1 × 1 × 5 × 79)/(1 × 1) =


395/1 =


395


5,503/11 is already reduced to the lowest terms.


The numerator and denominator have no common prime factors.


Their prime factorization:
5,503 is a prime number (it cannot be factored into other prime factors)
11 is a prime number (it cannot be factored into other prime factors)


17/12 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)
12 = 22 × 3



Rewrite the equivalent simplified operation:

- 566/12 × 4,740/12 × 5,503/11 × 17/12 =


- 283/6 × 395 × 5,503/11 × 17/12

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.


- 283/6 × 395 × 5,503/11 × 17/12 =


- (283 × 395 × 5,503 × 17) / (6 × 11 × 12) =


- (283 × 5 × 79 × 5,503 × 17) / (2 × 3 × 11 × 22 × 3) =


- (5 × 17 × 79 × 283 × 5,503) / (23 × 32 × 11)


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).


But the numerator and the denominator have no common prime factors:

GCF(5 × 17 × 79 × 283 × 5,503; 23 × 32 × 11) = 1



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.


- (5 × 17 × 79 × 283 × 5,503) / (23 × 32 × 11) =


- 10,457,598,535/792


Rewrite the fraction

As a mixed number (also called a mixed fraction):

A mixed number: a whole number and a proper fraction, both having the same sign.


A proper fraction: the value of the numerator is smaller than the value of the denominator.


Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:


- 10,457,598,535 ÷ 792 = - 13,204,038 and the remainder = - 439 =>


- 10,457,598,535 = - 13,204,038 × 792 - 439 =>


- 10,457,598,535/792 =


( - 13,204,038 × 792 - 439)/792 =


( - 13,204,038 × 792)/792 - 439/792 =


- 13,204,038 - 439/792 =


- 13,204,038 439/792

As a decimal number:

Simply divide the numerator by the denominator, without a remainder, as shown below:


- 13,204,038 - 439/792 =


- 13,204,038 - 439 ÷ 792 ≈


- 13,204,038.554292929293 ≈


- 13,204,038.55

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.


- 13,204,038.554292929293 =


- 13,204,038.554292929293 × 100/100 =


( - 13,204,038.554292929293 × 100)/100 =


- 1,320,403,855.429292929293/100


- 1,320,403,855.429292929293% ≈


- 1,320,403,855.43%


The final answer:
written in four ways

As a negative improper fraction:
(the numerator >= the denominator)
566/12 × - 4,740/12 × 5,503/11 × 17/12 = - 10,457,598,535/792

As a mixed number (also called a mixed fraction):
566/12 × - 4,740/12 × 5,503/11 × 17/12 = - 13,204,038 439/792

As a decimal number:
566/12 × - 4,740/12 × 5,503/11 × 17/12 ≈ - 13,204,038.55

As a percentage:
566/12 × - 4,740/12 × 5,503/11 × 17/12 ≈ - 1,320,403,855.43%

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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Internal link > Read the rest of the article, here: How to multiply common ordinary fractions?

More on ordinary (common) fractions / theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Changing the form of fractions, by expanding or reducing (simplifying)


(3) How to reduce fractions (simplifying). The greatest common factor, GCF


(4) How to compare two fractions with unlike (different) numerators and denominators


(5) How to sort out fractions in ascending order


(6) Adding common (ordinary) fractions


(7) Subtracting common (ordinary) fractions


(8) Multiplying common (ordinary) fractions


(9) Fractions as rational numbers