Multiplying the common ordinary fractions: 90/47 × - 423/27 = ? The multiplication process explained. The result written: As a negative integer number. As a negative improper fraction (the denominator = 1). As a percentage

90/47 × - 423/27 = ?

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


90/47 × - 423/27 =


- 90/47 × 423/27

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.


* 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.


90/47 is already reduced to the lowest terms.


The numerator and denominator have no common prime factors.


Their prime factorization:
90 = 2 × 32 × 5
47 is a prime number (it cannot be factored into other prime factors)


423/27 =


(32 × 47)/33 =


((32 × 47) ÷ 32)/(33 ÷ 32) =


(32 ÷ 32 × 47)/(33 ÷ 32) =


(3(2 - 2) × 47)/3(3 - 2) =


(30 × 47)/31 =


(1 × 47)/3 =


47/3



Rewrite the equivalent simplified operation:

- 90/47 × 423/27 =


- 90/47 × 47/3

These fractions reduce each other:

They have numerators and denominators of equal values.

The fractions: 90/47 × 47/3 = 90/3

Rewrite the equivalent simplified operation:

- 90/47 × 47/3 =


- 90/3

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.


90/3 =


(2 × 32 × 5)/3 =


((2 × 32 × 5) ÷ 3)/(3 ÷ 3) =


(2 × 32 ÷ 3 × 5)/(3 ÷ 3) =


(2 × 3(2 - 1) × 5)/1 =


(2 × 31 × 5)/1 =


(2 × 3 × 5)/1 =


30/1 =


30



Rewrite the equivalent simplified operation:

- 90/3 =


- 30

Rewrite the intermediate result

As a negative improper fraction:
(the denominator = 1)

An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.

- 30 = - 30/1


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.


- 30 =


- 30 × 100/100 =


( - 30 × 100)/100 =


- 3,000/100 =


- 3,000%



The final answer:
written in three ways

As a negative integer number:
90/47 × - 423/27 = - 30

As a negative improper fraction:
(the denominator = 1)
90/47 × - 423/27 = - 30/1

As a percentage:
90/47 × - 423/27 = - 3,000%

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

How to multiply the common ordinary fractions:
- 101/54 × 430/35

Multiply common ordinary fractions, online calculator:

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Multiplying fractions. How to multiply ordinary math fractions? Steps. Example.

How to multiply two fractions?

When we multiply ordinary fractions, the end fraction will have:

  • as a numerator, the result of multiplying all the numerators of the fractions,
  • as a denominator, the result of multiplying all the denominators of the fractions.
  • a/b × c/d = (a × c) / (b × d)
  • a, b, c, d are integer numbers;
  • if the pairs (a × c) and (b × d) are not coprime (they have common prime factors) the end fraction should be reduced (simplified) to lower terms.

How to multiply ordinary fractions? Steps.


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

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