Multiplying the common ordinary fractions: 20/8 × 32/8 = ? The multiplication process explained. The result written: As a positive integer number. As a positive improper fraction (the denominator = 1). As a percentage

20/8 × 32/8 = ?

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.


20/8 =


(22 × 5)/23 =


((22 × 5) ÷ 22)/(23 ÷ 22) =


(22 ÷ 22 × 5)/(23 ÷ 22) =


(2(2 - 2) × 5)/2(3 - 2) =


(20 × 5)/21 =


(1 × 5)/2 =


5/2


32/8 =


25/23 =


(25 ÷ 23)/(23 ÷ 23) =


2(5 - 3)/2(3 - 3) =


22/20 =


22/1 =


4/1 =


4



Rewrite the equivalent simplified operation:

20/8 × 32/8 =


5/2 × 4

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.


5/2 × 4 =


(5 × 4) / 2 =


(5 × 22) / 2 =


(22 × 5) / 2

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).


GCF (22 × 5; 2) = 2



Divide the numerator and the denominator by their GCF:

(22 × 5) / 2 =


((22 × 5) ÷ 2) / (2 ÷ 2) =


(22 ÷ 2 × 5)/(2 ÷ 2) =


(2(2 - 1) × 5)/1 =


(21 × 5)/1 =


(2 × 5)/1 =


2 × 5 =


10

Rewrite the intermediate result

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

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

10 = 10/1


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.


10 =


10 × 100/100 =


(10 × 100)/100 =


1,000/100 =


1,000%



The final answer:
written in three ways

As a positive integer number:
20/8 × 32/8 = 10

As a positive improper fraction:
(the denominator = 1)
20/8 × 32/8 = 10/1

As a percentage:
20/8 × 32/8 = 1,000%

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:
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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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