How to reduce (simplify) the common fraction 35/150 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:


35 = 5 × 7


150 = 2 × 3 × 52

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 (5 × 7; 2 × 3 × 52) = 5

Calculate the greatest common factor, GCF, online calculator


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

35/150 =


(5 × 7)/(2 × 3 × 52) =


((5 × 7) ÷ 5) / ((2 × 3 × 52) ÷ 5) =


7/(2 × 3 × 5) =


7/30

Rewrite the end result:

As a decimal number:

7/30 =


7 ÷ 30 =


0.233333333333 ≈


0.23

As a percentage:

0.233333333333 =


0.233333333333 × 100/100 =


23.333333333333/100 =


23.333333333333% ≈


23.33%

Convert fractions to percentages, online calculator


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

As a positive proper fraction
(numerator < denominator):
35/150 = 7/30

As a decimal number:
35/1500.23

As a percentage:
35/15023.33%

How to reduce (simplify) the common fraction: 42/157?


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

35/150 = (35 ÷ 5)/(150 ÷ 5) = 7/30 Jun 03 21:51 UTC (GMT)
330/360 = (330 ÷ 30)/(360 ÷ 30) = 11/12 Jun 03 21:51 UTC (GMT)
535/4 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
535 ÷ 4 = 133 and remainder = 3 =>
535/4 = (133 × 4 + 3)/4 = 133 + 3/4 = 133 3/4
Jun 03 21:51 UTC (GMT)
189/8 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
189 ÷ 8 = 23 and remainder = 5 =>
189/8 = (23 × 8 + 5)/8 = 23 + 5/8 = 23 5/8
Jun 03 21:51 UTC (GMT)
214/7 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
214 ÷ 7 = 30 and remainder = 4 =>
214/7 = (30 × 7 + 4)/7 = 30 + 4/7 = 30 4/7
Jun 03 21:51 UTC (GMT)
- 20/6 = - (20 ÷ 2)/(6 ÷ 2) = - 10/3
Improper fraction, rewrite it as a mixed number:
- 10 ÷ 3 = - 3 and remainder = - 1 =>
- 10/3 = ( - 3 × 3 - 1)/3 = - 3 - 1/3 = - 3 1/3
Jun 03 21:50 UTC (GMT)
102/80 = (102 ÷ 2)/(80 ÷ 2) = 51/40
Improper fraction, rewrite it as a mixed number:
51 ÷ 40 = 1 and remainder = 11 =>
51/40 = (1 × 40 + 11)/40 = 1 + 11/40 = 1 11/40
Jun 03 21:50 UTC (GMT)
36/591 = (36 ÷ 3)/(591 ÷ 3) = 12/197 Jun 03 21:50 UTC (GMT)
102/80 = (102 ÷ 2)/(80 ÷ 2) = 51/40
Improper fraction, rewrite it as a mixed number:
51 ÷ 40 = 1 and remainder = 11 =>
51/40 = (1 × 40 + 11)/40 = 1 + 11/40 = 1 11/40
Jun 03 21:50 UTC (GMT)
4,446/213 = (4,446 ÷ 3)/(213 ÷ 3) = 1,482/71
Improper fraction, rewrite it as a mixed number:
1,482 ÷ 71 = 20 and remainder = 62 =>
1,482/71 = (20 × 71 + 62)/71 = 20 + 62/71 = 20 62/71
Jun 03 21:50 UTC (GMT)
14/8 = (14 ÷ 2)/(8 ÷ 2) = 7/4
Improper fraction, rewrite it as a mixed number:
7 ÷ 4 = 1 and remainder = 3 =>
7/4 = (1 × 4 + 3)/4 = 1 + 3/4 = 1 3/4
Jun 03 21:50 UTC (GMT)
6/6 = (6 ÷ 6)/(6 ÷ 6) = 1 Jun 03 21:50 UTC (GMT)
23/19 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
23 ÷ 19 = 1 and remainder = 4 =>
23/19 = (1 × 19 + 4)/19 = 1 + 4/19 = 1 4/19
Jun 03 21:49 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?

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