How to reduce (simplify) into the lower terms the ordinary fraction 30/48? Fraction can be reduced (simplified): 30/48 = 5/8 = 0.625; Result written as a proper fraction (ordinary, common) and a decimal number.

Reduce (simplify) ordinary fraction to lowest terms: 30/48

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

Step 1. Calculate the greatest (highest) common factor (divisor).

Integer numbers prime factorization:
30 = 2 * 3 * 5;
48 = 24 * 3;
Take all the common prime factors, by the lowest powers.
Greatest (highest) common factor (divisor), gcf, gcd:
gcf, gcd (30; 48) = 2 * 3 = 6;

Step 2: Divide fraction's both numerator and denominator by their greatest common factor (divisor), gcf (gcd).

30/48 =
(2 * 3 * 5)/(24 * 3) =
((2 * 3 * 5) : (2 * 3)) / ((24 * 3) : (2 * 3)) =
5/23 =
5/8

Step 3: Rewrite the end result:

5 : 8 = 0.625 as a decimal number.

Final answer
:: written in two ways ::
As a proper fraction (ordinary, common):
30/48 = 5/8
As a decimal number:
30/48 = 0.625

Writing numbers: a comma ',' is used as thousands separator (whenever the case);

Reduce (simplify) fractions to lowest terms

Latest ordinary fractions reduced to lowest terms (simplified)

30/48 = (30 : 6)/(48 : 6) = 5/8 Feb 22 21:53 UTC (GMT)
66/57 = (66 : 3)/(57 : 3) = 22/19;
22 > 19 => improper fraction

Rewrite:
22 : 19 = 1 and remainder = 3 =>
22/19 = (1 * 19 + 3)/19 = 1 + 3/19 =
= 1 3/19, mixed number (mixed fraction)
Feb 22 21:53 UTC (GMT)
92/24 = (92 : 4)/(24 : 4) = 23/6;
23 > 6 => improper fraction

Rewrite:
23 : 6 = 3 and remainder = 5 =>
23/6 = (3 * 6 + 5)/6 = 3 + 5/6 =
= 3 5/6, mixed number (mixed fraction)
Feb 22 21:53 UTC (GMT)
14/21 = (14 : 7)/(21 : 7) = 2/3 Feb 22 21:53 UTC (GMT)
7,332/100 = (7,332 : 4)/(100 : 4) = 1,833/25;
1,833 > 25 => improper fraction

Rewrite:
1,833 : 25 = 73 and remainder = 8 =>
1,833/25 = (73 * 25 + 8)/25 = 73 + 8/25 =
= 73 8/25, mixed number (mixed fraction)
Feb 22 21:53 UTC (GMT)
723/144 = (723 : 3)/(144 : 3) = 241/48;
241 > 48 => improper fraction

Rewrite:
241 : 48 = 5 and remainder = 1 =>
241/48 = (5 * 48 + 1)/48 = 5 + 1/48 =
= 5 1/48, mixed number (mixed fraction)
Feb 22 21:53 UTC (GMT)
1,800/25 = (1,800 : 25)/(25 : 25) = 72 Feb 22 21:53 UTC (GMT)
2/14 = (2 : 2)/(14 : 2) = 1/7 Feb 22 21:53 UTC (GMT)
516/156 = (516 : 12)/(156 : 12) = 43/13;
43 > 13 => improper fraction

Rewrite:
43 : 13 = 3 and remainder = 4 =>
43/13 = (3 * 13 + 4)/13 = 3 + 4/13 =
= 3 4/13, mixed number (mixed fraction)
Feb 22 21:53 UTC (GMT)
148/324 = (148 : 4)/(324 : 4) = 37/81 Feb 22 21:53 UTC (GMT)
225/180 = (225 : 45)/(180 : 45) = 5/4;
5 > 4 => improper fraction

Rewrite:
5 : 4 = 1 and remainder = 1 =>
5/4 = (1 * 4 + 1)/4 = 1 + 1/4 =
= 1 1/4, mixed number (mixed fraction)
Feb 22 21:53 UTC (GMT)
480/16 = (480 : 16)/(16 : 16) = 30 Feb 22 21:53 UTC (GMT)
6/10 = (6 : 2)/(10 : 2) = 3/5 Feb 22 21:53 UTC (GMT)

Tutoring: simplifying ordinary math fractions (reducing to lower terms)

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

  • Factor the fraction's numerator and denominator into prime factors. If you don't know how, you can do numbers prime factorization at this page on www.numere-prime.ro: numbers prime factorization.
  • Calculate fraction's numerator and denominator greatest common factor, GCF (greatest common denominator, GCD). If you don't know how, you can calculate two numbers greatest common factor GCF (denominator, GCD) at this address on www.numere-prime.ro: greatest common factor GCF (or denominator GCD).
  • Divide both the fraction's numerator and denominator by the greatest common factor GCF (denominator GCD). Fraction thus obtained is called a reduced fraction (simplified) to its lowest terms.

Example: reduce fraction 24/32 to its lower terms.

  • Fraction's numerator, 24, prime factorization is: 23 * 3.
    Fraction's denominator, 16, prime factorization is: 25.
  • The greatest common factor, GCF (24, 32), is calculated by multiplying all the common factors of numerator and denominator, at their lowest powers, such as:
    GCF (24, 32) = (23 * 3, 25) = 23.
  • Both fraction's numerator and denominator are divided by the greatest common factor GCF (or denominator GCD):
    24/32 = (24 : 8) / (32 : 8) = 3/4.
    Fraction thus obtained is called a reduced fraction (simplified) to its lowest terms.

Why reducing fractions to lower terms (simplifying)?

Operations with fractions often involve fractions being brought to the same denominator and sometimes both numerators and denominators are large numbers. Doing calculations with such large numbers could be more difficult. By simplifying (reducing) a fraction, both the numerator and denominator of the fraction are reduced to smaller values, much easier to work with, reducing the computational effort of working with fractions.