How to reduce (simplify) the common fraction 45/120 to its simplest equivalent form, irreducible? Result written as a proper fraction, as a decimal number and as a percentage %

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

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

in the notation with exponents:


45 = 32 × 5


120 = 23 × 3 × 5

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 (32 × 5; 23 × 3 × 5) = 3 × 5

Calculate the greatest common factor, GCF, online calculator


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

45/120 =


(32 × 5)/(23 × 3 × 5) =


((32 × 5) ÷ (3 × 5)) / ((23 × 3 × 5) ÷ (3 × 5)) =


3/23 =


3/8

Rewrite the end result:

As a decimal number:

3/8 =


3 ÷ 8 =


0.375 ≈


0.38

As a percentage:

0.375 =


0.375 × 100/100 =


37.5/100 =


37.5%

Convert fractions to percentages, online calculator


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

As a positive proper fraction
(numerator < denominator):
45/120 = 3/8

As a decimal number:
45/1200.38

As a percentage:
45/120 = 37.5%

How to reduce (simplify) the common fraction: 55/127?


Writing numbers: point '.' used as a decimal mark;

Symbols: / fraction bar; ÷ divide; × multiply; ≈ approximation; = equal;

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

45/120 = (45 ÷ 15)/(120 ÷ 15) = 3/8 Jul 02 18:42 UTC (GMT)
3,526/15 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
3,526 ÷ 15 = 235 and remainder = 1 =>
3,526/15 = (235 × 15 + 1)/15 = 235 + 1/15 = 235 1/15
Jul 02 18:42 UTC (GMT)
45/12 = (45 ÷ 3)/(12 ÷ 3) = 15/4
Improper fraction, rewrite it as a mixed number:
15 ÷ 4 = 3 and remainder = 3 =>
15/4 = (3 × 4 + 3)/4 = 3 + 3/4 = 3 3/4
Jul 02 18:42 UTC (GMT)
1,361/48 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,361 ÷ 48 = 28 and remainder = 17 =>
1,361/48 = (28 × 48 + 17)/48 = 28 + 17/48 = 28 17/48
Jul 02 18:42 UTC (GMT)
1,361/48 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,361 ÷ 48 = 28 and remainder = 17 =>
1,361/48 = (28 × 48 + 17)/48 = 28 + 17/48 = 28 17/48
Jul 02 18:42 UTC (GMT)
1,361/48 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,361 ÷ 48 = 28 and remainder = 17 =>
1,361/48 = (28 × 48 + 17)/48 = 28 + 17/48 = 28 17/48
Jul 02 18:42 UTC (GMT)
280/2 = (280 ÷ 2)/(2 ÷ 2) = 140/1 = 140 Jul 02 18:42 UTC (GMT)
33/821 already reduced (simplified) Jul 02 18:42 UTC (GMT)
33/821 already reduced (simplified) Jul 02 18:42 UTC (GMT)
226/299 already reduced (simplified) Jul 02 18:42 UTC (GMT)
39/89 already reduced (simplified) Jul 02 18:42 UTC (GMT)
138/444 = (138 ÷ 6)/(444 ÷ 6) = 23/74 Jul 02 18:42 UTC (GMT)
- 80/ - 10 = (80 ÷ 10)/(10 ÷ 10) = 8/1 = 8 Jul 02 18:42 UTC (GMT)
see more... reduced fractions

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: