Multiplying the common ordinary fractions: 1/2 × 60 = ? The multiplication process explained. The result written: As a positive integer number. As a positive improper fraction (the denominator = 1). As a percentage

1/2 × 60 = ?

Simplify the operation

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.


1/2 × 60 =


60 / 2 =


(22 × 3 × 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 × 3 × 5; 2) = 2



Divide the numerator and the denominator by their GCF:

(22 × 3 × 5) / 2 =


((22 × 3 × 5) ÷ 2) / (2 ÷ 2) =


(22 ÷ 2 × 3 × 5)/(2 ÷ 2) =


(2(2 - 1) × 3 × 5)/1 =


(21 × 3 × 5)/1 =


(2 × 3 × 5)/1 =


2 × 3 × 5 =


30


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.

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 positive integer number:
1/2 × 60 = 30

As a positive improper fraction:
(the denominator = 1)
1/2 × 60 = 30/1

As a percentage:
1/2 × 60 = 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.

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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