How to reduce (simplify) fraction 394/52 to lowest terms? Write it as an improper fraction, a mixed number, a decimal number, a percentage

Reduce: 394/52

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 394/52

The number above the bar is the numerator: 394

The number below the bar is the denominator: 52

The fraction bar means that the two numbers are dividing themselves:
394/52 = 394 ÷ 52

Divide the numerator by the denominator to get fraction's value:
Value = 394 ÷ 52


Introduction. Percent

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

p% = p 'out of one hundred',

p% = p/100 = p ÷ 100


Note:

The fraction 100/100 = 100 ÷ 100 = 100% = 1

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



To reduce a fraction, divide both its numerator and denominator by their greatest common factor, GCF.

Integer numbers prime factorization:

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

394 = 2 × 197;
394 is not a prime, is a composite number;

52 = 22 × 13;
52 is not a prime, is a composite number;

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

>> Integer numbers prime factorization


Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Multiply all the common prime factors, by the lowest exponents (if any).

gcf, hcf, gcd (394; 52) = 2


>> Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd


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

394/52 =

(2 × 197)/(22 × 13) =

((2 × 197) ÷ 2) / ((22 × 13) ÷ 2) =

197/(2 × 13) =

197/26


The fraction is now reduced to the lowest terms.

197/26 is an improper fraction.

An improper fraction: numerator larger than denominator.


Rewrite the end result, continued below...

Rewrite the fraction:

As a mixed number (mixed fraction):

A mixed number (mixed fraction): a whole number and a proper fraction, of the same sign.

A proper fraction: numerator smaller than denominator.


197 ÷ 26 = 7 and remainder = 15 =>

197 = 7 × 26 + 15 =>

197/26 =

(7 × 26 + 15) / 26 =

(7 × 26) / 26 + 15 / 26 =

7 + 15/26 =

7 15/26


As a decimal number:

7 15/26 =

7 + 15/26 =

7 + 15 ÷ 26 ≈

7.576923076923 ≈

7.58


As a percentage:

7.576923076923 =

7.576923076923 × 100/100 =

757.692307692308/100 =

757.692307692308% ≈

757.69%


In other words:

1) Calculate fraction's value.

2) Multiply that number by 100.

3) Add the percent sign % to it.



Final answer
continued below...

Final answer:
:: written in four ways ::

As an improper fraction
(numerator larger than denominator):
394/52 = 197/26

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
394/52 = 7 15/26

As a decimal number:
394/52 ≈ 7.576923076923 ≈ 7.58

As a percentage:
394/52 ≈ 757.69%

More operations of this kind:

reduce 394/199 = ? ... 454/52 = ?

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Tutoring: simplifying ordinary math fractions (reducing to the lowest terms)

Steps to simplify an ordinary fraction, to reduce it to its lowest terms:

  • 1) Factor both the numerator and the denominator of the fraction into prime factors.
  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.
  • 3) Divide both the numerator and the denominator of the fraction by the greatest common factor, GCF (GCD).
  • In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction.

Read the full article >> Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples

Why reducing (simplifying) fractions to lower terms?

  • When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.
  • Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.
  • By simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values. Well, these values are much easier to work with, reducing the overall effort of working with fractions.

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples