How to reduce (simplify) the common fraction 33/176 to its simplest equivalent form, irreducible? Result written as a proper fraction, as a decimal number and as a percentage %

How to reduce (simplify) the common fraction: 33/176?
Result written as a proper fraction, as a decimal number and as a percentage.

Detailed calculations and explanations, below

Ordinary fractions. Introduction

The fraction consists of two numbers and a fraction bar: 33/176


The number above the bar is called numerator: 33


The number below the bar is called denominator: 176


The fraction bar means that the two numbers are dividing themselves.


To get fraction's value divide the numerator by the denominator:
Value = 33 ÷ 176



To reduce a fraction:
divide the numerator and denominator by their greatest common factor, GCF

To calculate the greatest common factor, GCF:


1. Build the prime factorizations of the numerator and denominator.


2. Multiply all the common prime factors, by the lowest exponents.


Factor both the numerator and the denominator, break them down to prime factors:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


33 = 3 × 11;
33 is a composite number;


In exponential notation:
176 = 2 × 2 × 2 × 2 × 11 = 24 × 11;
176 is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.

>> Calculate the prime factors of numbers, online calculator


Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.


gcf (3 × 11; 24 × 11) = 11

>> Calculate the greatest common factor, GCF, online calculator


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

33/176 =


(3 × 11)/(24 × 11) =


((3 × 11) ÷ 11) / ((24 × 11) ÷ 11) =


3/24 =


3/16


The fraction is now reduced to the lowest terms.


When it's 1 the denominator can be omitted.


Fraction 3/16 is a positive proper fractions (numerator < denominator).


Rewrite the end result:

As a decimal number:

3/16 =


3 ÷ 16 =


0.1875 ≈


0.19

As a percentage:

'Percent (%)' means 'out of one hundred'.


p% = p 'out of one hundred'.


p% = p/100 = p ÷ 100.


Fraction 100/100 = 100% = 100 ÷ 100 = 1


Multiply a number by the fraction 100/100 and its value doesn't change:

0.1875 =


0.1875 × 100/100 =


18.75/100 =


18.75%

In other words:

Calculate the fraction's value,


Multiply that number by 100,


Add the percent sign % to it.


>> Convert fractions to percentages, online calculator


The final answer:
:: written in three ways ::

As a positive proper fraction
(numerator < denominator):
33/176 = 3/16

As a decimal number:
33/1760.19

As a percentage:
33/176 = 18.75%

>> How to reduce (simplify) the common fraction: 40/179?


Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; two vertical bars surrounding a number, |n|, is the symbol for the absolute value of that number;

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; ≈ approximation; = equal;

Reduce (simplify) ordinary fractions, online calculator

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Fractions reducing to lower terms (simplifying). Equivalent fractions

Let's learn by an example, let's simplify the fraction: 12/16

  • Numerator of the fraction. The number that is above the fraction bar, 12, is called the numerator of the fraction;
  • Denominator of the fraction. The number that is below the fraction bar, 16, is called the denominator of the fraction;
  • The value of the fraction. Fraction 12/16 shows us in how many equal parts the number above the fraction bar, 12, is being divided: into 16 equal parts. Thus, the value of the fraction is calculated as:
  • 12 ÷ 16 = 0.75
  • We notice that the two numbers, the numerator and the denominator, are dividing themselves without any remainder by 2, so we divide them by the same number, 2:
  • 12/16 = (12 ÷ 2)/(16 ÷ 2) = 6/8
  • The value of the fraction 6/8 is calculated as:
  • 6 ÷ 8 = 0.75
  • We notice that the value of the fraction 6/8 is equal to that of the fraction 12/16, namely 0.75
  • Reduced (simplified) fraction, Equivalent fraction. The new fraction, 6/8, is equivalent to the original one, 12/16, that is, it represents the same value or proportion of the whole, and it was calculated out of the original fraction by reducing it (simplifying it): both the numerator and the denominator of the fraction were divided by the number 2.
  • Common factor (divisor). The number 2 that was used to divide the two numbers that make up the fraction is called a common factor or a divisor of the numerator and the denominator of the fraction.
  • Find all the divisors of a number or all the common factors of two numbers, online.
  • The reduced fraction has now a numerator that is equal to 6 and a denominator that is equal to 8.
  • We also notice that the two new numbers, the new numerator and the new denominator, 6 and 8, are also dividing themselves without any remainder by 2 (2 is a common factor of 6 and 8), so we divide them again by 2:
  • 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4
  • The value of the fraction 3/4 is calculated as:
  • 3 ÷ 4 = 0.75
  • The new fraction, 3/4, is a reduced fraction (a simplified fraction) and an equivalent of the fractions 12/16 and 6/8
  • Irreducible fraction. Fraction 3/4 is also called an irreducible fraction, in another words it could no longer be reduced or simplified, it is in its simplest form, the numbers 3 and 4, the numerator and the denominator of the fraction, are coprime numbers (prime to each other), not having any common factors other than 1.
  • Reduce fractions to lower terms (simplify), online, with explanations.

... Read the rest of this article, here: How to reduce (simplify) common fractions?

More on ordinary (common) math fractions theory:

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


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


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


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers