How to reduce (simplify) the common fraction 30/7 to its simplest equivalent form, irreducible? Result written as an improper fraction, as a mixed number, 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:

30 = 2 × 3 × 5


7 is a prime number, it cannot be factored into other prime factors

Calculate the prime factors of numbers, online calculator


Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.


But, the numerator and the denominator have no common factors.


gcf (2 × 3 × 5; 7) = 1

Calculate the greatest common factor, GCF, online calculator


The numerator and the denominator of the fraction are coprime numbers (no common prime factors, GCF = 1), the fraction cannot be reduced (simplified): irreducible fraction.

Positive improper fraction (numerator > denominator)
Rewrite the fraction:

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.


Proper fraction = numerator smaller than denominator.


30 ÷ 7 = 4 and remainder = 2 =>


30 = 4 × 7 + 2 =>


30/7 =


(4 × 7 + 2) / 7 =


4 + 2/7 =


2/7

As a decimal number:

2/7 =


4 + 2/7 =


4 + 2 ÷ 7 =


4.285714285714 ≈


4.29

As a percentage:

4.285714285714 =


4.285714285714 × 100/100 =


428.571428571429/100 =


428.571428571429% ≈


428.57%

Convert fractions to percentages, online calculator


The final answer:
:: written in four ways ::

As a positive improper fraction (numerator > denominator):
30/7 = 30/7

As a mixed number
(a whole number and a proper fraction, of the same sign):
30/7 = 2/7

As a decimal number:
30/74.29

As a percentage:
30/7428.57%

How to reduce (simplify) the common fraction: 38/11?


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

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

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

30/7 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
30 ÷ 7 = 4 and remainder = 2 =>
30/7 = (4 × 7 + 2)/7 = 4 + 2/7 = 4 2/7
Jul 04 08:38 UTC (GMT)
80/50 = (80 ÷ 10)/(50 ÷ 10) = 8/5
Improper fraction, rewrite it as a mixed number:
8 ÷ 5 = 1 and remainder = 3 =>
8/5 = (1 × 5 + 3)/5 = 1 + 3/5 = 1 3/5
Jul 04 08:38 UTC (GMT)
348/1,000,000 = (348 ÷ 4)/(1,000,000 ÷ 4) = 87/250,000 Jul 04 08:38 UTC (GMT)
248/21 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
248 ÷ 21 = 11 and remainder = 17 =>
248/21 = (11 × 21 + 17)/21 = 11 + 17/21 = 11 17/21
Jul 04 08:37 UTC (GMT)
122/3 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
122 ÷ 3 = 40 and remainder = 2 =>
122/3 = (40 × 3 + 2)/3 = 40 + 2/3 = 40 2/3
Jul 04 08:37 UTC (GMT)
1,989/30 = (1,989 ÷ 3)/(30 ÷ 3) = 663/10
Improper fraction, rewrite it as a mixed number:
663 ÷ 10 = 66 and remainder = 3 =>
663/10 = (66 × 10 + 3)/10 = 66 + 3/10 = 66 3/10
Jul 04 08:37 UTC (GMT)
4/25 already reduced (simplified) Jul 04 08:37 UTC (GMT)
55/24 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
55 ÷ 24 = 2 and remainder = 7 =>
55/24 = (2 × 24 + 7)/24 = 2 + 7/24 = 2 7/24
Jul 04 08:37 UTC (GMT)
2,008/81 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
2,008 ÷ 81 = 24 and remainder = 64 =>
2,008/81 = (24 × 81 + 64)/81 = 24 + 64/81 = 24 64/81
Jul 04 08:37 UTC (GMT)
375/100 = (375 ÷ 25)/(100 ÷ 25) = 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 04 08:37 UTC (GMT)
85/15 = (85 ÷ 5)/(15 ÷ 5) = 17/3
Improper fraction, rewrite it as a mixed number:
17 ÷ 3 = 5 and remainder = 2 =>
17/3 = (5 × 3 + 2)/3 = 5 + 2/3 = 5 2/3
Jul 04 08:37 UTC (GMT)
625/6 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
625 ÷ 6 = 104 and remainder = 1 =>
625/6 = (104 × 6 + 1)/6 = 104 + 1/6 = 104 1/6
Jul 04 08:37 UTC (GMT)
84/16 = (84 ÷ 4)/(16 ÷ 4) = 21/4
Improper fraction, rewrite it as a mixed number:
21 ÷ 4 = 5 and remainder = 1 =>
21/4 = (5 × 4 + 1)/4 = 5 + 1/4 = 5 1/4
Jul 04 08:37 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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