How to reduce (simplify) to lowest terms ordinary (common) math fraction 30/42? Result written as: a proper fraction, a decimal number and a percentage

What is the fraction 30/42 written as an equivalent reduced fraction, as a decimal number and as a percent value?

reduce 30/1,554 = ? ... 34/42 = ?

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 30/42

The number above the bar is the numerator: 30

The number below the bar is the denominator: 42

The fraction bar means that the two numbers are dividing themselves:
30/42 = 30 ÷ 42

Divide the numerator by the denominator to get fraction's value:
Value = 30 ÷ 42


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.

30 = 2 × 3 × 5;
30 is not a prime, is a composite number;

42 = 2 × 3 × 7;
42 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 (30; 42) = 2 × 3 = 6


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


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

30/42 =

(2 × 3 × 5)/(2 × 3 × 7) =

((2 × 3 × 5) ÷ (2 × 3)) / ((2 × 3 × 7) ÷ (2 × 3)) =

5/7


The fraction is now reduced to the lowest terms.

5/7 is a proper fraction.

A proper fraction: numerator smaller than denominator.


Rewrite the end result, continued below...

Rewrite the end result:

As a decimal number:

5/7 =

5 ÷ 7 ≈

0.714285714286 ≈

0.71


As a percentage:

0.714285714286 =

0.714285714286 × 100/100 =

71.428571428571/100 =

71.428571428571% ≈

71.43%


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 three ways ::

As a proper fraction
(numerator smaller than denominator):
30/42 = 5/7

As a decimal number:
30/42 ≈ 0.714285714286 ≈ 0.71

As a percentage:
30/42 ≈ 71.43%

More operations of this kind:

reduce 30/1,554 = ? ... 34/42 = ?

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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