Convert the decimal number 45.5. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

Convert 45.5

1. Write the number as a percentage.

Multiply the number by 100/100

Note: 100/100 = 1

The value of the number does not change when multiplying by 100/100


45.5 =


45.5 × 100/100 =


(45.5 × 100)/100 =


4,550/100 =


4,550%


In other words:


Multiply the number by 100...


... And then add the percent sign, %


45.5 = 4,550%



2. Write the number as an improper fraction.

45.5 can be written as an improper fraction.

The numerator is larger than or equal to the denominator.


Write down the number divided by 1, as a fraction:

45.5 = 45.5/1

Turn the top number into a whole number.

Multiply both the top and the bottom by the same number.


This number is: 10.


1 followed by as many 0-s as the number of digits after the decimal point.


45.5/1 =


(45.5 × 10)/(1 × 10) =


455/10


3. Reduce (simplify) the fraction above: 455/10
(to the lowest terms, to its simplest equivalent form, irreducible).

To reduce a fraction divide the numerator and the denominator by their greatest (highest) common factor (divisor), GCF.


Factor both the numerator and the denominator (prime factorization).

455 = 5 × 7 × 13


10 = 2 × 5



Calculate the greatest (highest) common factor (divisor), GCF.

Multiply all the common prime factors by the lowest exponents.

GCF (5 × 7 × 13; 2 × 5) = 5



Divide both the numerator and the denominator by their greatest common factor, GCF.

455/10 =


(5 × 7 × 13)/(2 × 5) =


((5 × 7 × 13) ÷ 5) / ((2 × 5) ÷ 5) =


(7 × 13)/2 =


91/2


4. The fraction is an improper one, rewrite it as a mixed number (mixed fraction):

A mixed number = an integer number and a proper fraction, of the same sign.


Example 1: 2 1/5; Example 2: - 1 3/7.


A proper fraction = the numerator is smaller than the denominator.


91 ÷ 2 = 45, remainder = 1 ⇒


91 = 45 × 2 + 1 ⇒


91/2 =


(45 × 2 + 1) / 2 =


(45 × 2) / 2 + 1/2 =


45 + 1/2 =


45 1/2


91/2: Equivalent fractions.

The above fraction cannot be reduced.


That is, it has the smallest possible numerator and denominator.


By expanding it we can build up equivalent fractions.


Multiply the numerator & the denominator by the same number.


Example 1. By expanding the fraction by 6:

91/2 = (91 × 6)/(2 × 6) = 546/12

Example 2. By expanding the fraction by 8:

91/2 = (91 × 8)/(2 × 8) = 728/16

Of course, the above fractions are reducing...


... to the initial fraction: 91/2



:: Final answer ::
Written in 4 different ways

As a reduced (simplified) positive improper fraction:
45.5 = 91/2

As a mixed number:
45.5 = 45 1/2

As a percentage:
45.5 = 4,550%

As equivalent fractions:
45.5 = 91/2 = 546/12 = 728/16

More operations of this kind

45.6 = ? Convert the decimal number 45.6. Turn it into a reduced (simplified) improper fraction, into a mixed number and write it as a percentage. Calculate other equivalent fractions to the decimal number, by expanding

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Learn how to turn a decimal number into a fraction and a percentage. Steps.

1. How to write the number as a percentage:

  • Multiply the number by 100. Then add the percent sign, %.

2. How to write the number as a fraction:

  • Write down the number divided by 1, as a fraction.
  • Turn the top number into a whole number: multiply both the top and the bottom by the same number.
  • Reduce (simplify) the above fraction to the lowest terms, to its simplest equivalent form, irreducible. To reduce a fraction divide the numerator and the denominator by their greatest (highest) common factor (divisor), GCF.
  • If the fraction is an improper one, rewrite it as a mixed number (mixed fraction).
  • Calculate equivalent fractions. By expanding it we can build up equivalent fractions: multiply the numerator & the denominator by the same number.

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