How to reduce (simplify) fraction 78/9 to lowest terms? Write it as an improper fraction, a mixed number, a decimal number, a percentage

Reduce: 78/9

Detailed calculations below:

Introduction. Fractions

A fraction consists of two numbers and a fraction bar: 78/9


The number above the bar is the numerator: 78


The number below the bar is the denominator: 9


The fraction bar means that the two numbers are dividing themselves:
78/9 = 78 ÷ 9


Divide the numerator by the denominator to get fraction's value:
Value = 78 ÷ 9


Introduction. Percent

'Percent (%)' means 'out of one hundred':


p% = p 'out of one hundred',


p% = p/100 = p ÷ 100


Note:

The fraction 100/100 = 100 ÷ 100 = 100% = 1


Multiply a number by the fraction 100/100,
... and its value doesn't change.



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

Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


78 = 2 × 3 × 13;
78 is not a prime, is a composite number;


9 = 32;
9 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.


Calculate the greatest (highest) common factor (divisor), gcf, hcf, gcd:

Multiply all the common prime factors, by the lowest exponents (if any).


gcf, hcf, gcd (78; 9) = 3



Divide both the numerator and the denominator by their greatest common factor.

78/9 =


(2 × 3 × 13)/32 =


((2 × 3 × 13) ÷ 3) / (32 ÷ 3) =


(2 × 13)/3 =


26/3


The fraction is now reduced to the lowest terms.

26/3 is an improper fraction.

An improper fraction: numerator larger than denominator.


Rewrite the end result, continued below...

Rewrite the fraction:

As a mixed number (mixed fraction):

A mixed number (mixed fraction): a whole number and a proper fraction, of the same sign.


A proper fraction: numerator smaller than denominator.


26 ÷ 3 = 8 and remainder = 2 =>


26 = 8 × 3 + 2 =>


26/3 =


(8 × 3 + 2) / 3 =


(8 × 3) / 3 + 2 / 3 =


8 + 2/3 =


2/3


As a decimal number:

2/3 =


8 + 2/3 =


8 + 2 ÷ 3 ≈


8.666666666667


8.67


As a percentage:

8.666666666667 =


8.666666666667 × 100/100 =


866.666666666667/100 =


866.666666666667% ≈


866.67%


In other words:

1) Calculate fraction's value.


2) Multiply that number by 100.


3) Add the percent sign % to it.



Final answer
continued below...

Final answer:
:: written in four ways ::

As an improper fraction
(numerator larger than denominator):
78/9 = 26/3

As a mixed number (mixed fraction)
(a whole number and a proper fraction, of the same sign):
78/9 = 2/3

As a decimal number:
78/98.6666666666678.67

As a percentage:
78/9866.67%

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Tutoring: simplifying ordinary math fractions (reducing to the lowest terms)

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

  • 1) Factor both the numerator and the denominator of the fraction into prime factors.
  • 2) Calculate the greatest common factor, GCF (or the greatest common divisor, GCD) of the fraction's numerator and denominator.
  • 3) Divide both the numerator and the denominator of the fraction by the greatest common factor, GCF (GCD).
  • In conclusion: the fraction thus obtained is called a reduced fraction or a fraction simplified to its lowest terms.
  • A fraction reduced to its lowest terms cannot be further reduced and it is called an irreducible fraction.

Read the full article >> Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples


Why reducing (simplifying) fractions to lower terms?

  • When running operations with fractions we are often required to bring them to the same denominator, for example when adding, subtracting or comparing.
  • Sometimes both the numerators and the denominators of those fractions are large numbers and doing calculations with such numbers could be difficult.
  • By simplifying (reducing) a fraction, both the numerator and denominator of a fraction are reduced to smaller values. Well, these values are much easier to work with, reducing the overall effort of working with fractions.

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples