How to reduce (simplify) the common fraction 72/45 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:

in the notation with exponents:


72 = 23 × 32


45 = 32 × 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 (23 × 32; 32 × 5) = 32

Calculate the greatest common factor, GCF, online calculator


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

72/45 =


(23 × 32)/(32 × 5) =


((23 × 32) ÷ 32) / ((32 × 5) ÷ 32) =


23/5 =


8/5

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.


8 ÷ 5 = 1 and remainder = 3 =>


8 = 1 × 5 + 3 =>


8/5 =


(1 × 5 + 3) / 5 =


1 + 3/5 =


3/5

As a decimal number:

3/5 =


1 + 3/5 =


1 + 3 ÷ 5 =


1.6

As a percentage:

1.6 =


1.6 × 100/100 =


160/100 =


160%

Convert fractions to percentages, online calculator


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

As a positive improper fraction (numerator > denominator):
72/45 = 8/5

As a mixed number
(a whole number and a proper fraction, of the same sign):
72/45 = 3/5

As a decimal number:
72/45 = 1.6

As a percentage:
72/45 = 160%

How to reduce (simplify) the common fraction: 81/53?


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

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

Reduce (simplify) ordinary fractions, online calculator

The latest fractions reduced to the lowest terms

72/45 = (72 ÷ 9)/(45 ÷ 9) = 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 06 22:58 UTC (GMT)
739/93 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
739 ÷ 93 = 7 and remainder = 88 =>
739/93 = (7 × 93 + 88)/93 = 7 + 88/93 = 7 88/93
Jul 06 22:58 UTC (GMT)
69/120 = (69 ÷ 3)/(120 ÷ 3) = 23/40 Jul 06 22:58 UTC (GMT)
584/365 = (584 ÷ 73)/(365 ÷ 73) = 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 06 22:58 UTC (GMT)
- 64/12 = - (64 ÷ 4)/(12 ÷ 4) = - 16/3
Improper fraction, rewrite it as a mixed number:
- 16 ÷ 3 = - 5 and remainder = - 1 =>
- 16/3 = ( - 5 × 3 - 1)/3 = - 5 - 1/3 = - 5 1/3
Jul 06 22:58 UTC (GMT)
9,302/25 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
9,302 ÷ 25 = 372 and remainder = 2 =>
9,302/25 = (372 × 25 + 2)/25 = 372 + 2/25 = 372 2/25
Jul 06 22:58 UTC (GMT)
36/70 = (36 ÷ 2)/(70 ÷ 2) = 18/35 Jul 06 22:58 UTC (GMT)
64/50 = (64 ÷ 2)/(50 ÷ 2) = 32/25
Improper fraction, rewrite it as a mixed number:
32 ÷ 25 = 1 and remainder = 7 =>
32/25 = (1 × 25 + 7)/25 = 1 + 7/25 = 1 7/25
Jul 06 22:58 UTC (GMT)
69/120 = (69 ÷ 3)/(120 ÷ 3) = 23/40 Jul 06 22:58 UTC (GMT)
73/40 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
73 ÷ 40 = 1 and remainder = 33 =>
73/40 = (1 × 40 + 33)/40 = 1 + 33/40 = 1 33/40
Jul 06 22:58 UTC (GMT)
1,001/100 already reduced (simplified)
Improper fraction, rewrite it as a mixed number:
1,001 ÷ 100 = 10 and remainder = 1 =>
1,001/100 = (10 × 100 + 1)/100 = 10 + 1/100 = 10 1/100
Jul 06 22:58 UTC (GMT)
- 24/386 = - (24 ÷ 2)/(386 ÷ 2) = - 12/193 Jul 06 22:57 UTC (GMT)
4,855/40 = (4,855 ÷ 5)/(40 ÷ 5) = 971/8
Improper fraction, rewrite it as a mixed number:
971 ÷ 8 = 121 and remainder = 3 =>
971/8 = (121 × 8 + 3)/8 = 121 + 3/8 = 121 3/8
Jul 06 22:57 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: