## Reduce: ^{4,925}/_{3,105}

## Detailed calculations below:

### Introduction. Fractions

#### A fraction consists of two numbers and a fraction bar: ^{4,925}/_{3,105}

#### The number above the bar is the numerator: 4,925

#### The number below the bar is the denominator: 3,105

#### The fraction bar means that the two numbers are dividing themselves:

^{4,925}/_{3,105} = 4,925 ÷ 3,105

#### Divide the numerator by the denominator to get fraction's value:

Value = 4,925 ÷ 3,105

### 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.

#### To calculate the greatest common factor, we build the prime factorization of the two numbers.

### Integer numbers prime factorization:

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

#### 4,925 = 5^{2} × 197;

4,925 is not a prime, is a composite number;

#### 3,105 = 3^{3} × 5 × 23;

3,105 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 (4,925; 3,105) = 5

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

^{4,925}/_{3,105} =

^{(52 × 197)}/_{(33 × 5 × 23)} =

^{((52 × 197) ÷ 5)} / _{((33 × 5 × 23) ÷ 5)} =

^{(5 × 197)}/_{(33 × 23)} =

^{985}/_{621}

## The fraction is now reduced to the lowest terms.

^{985}/_{621} 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.

#### 985 ÷ 621 = 1 and remainder = 364 =>

#### 985 = 1 × 621 + 364 =>

^{985}/_{621} =

^{(1 × 621 + 364)} / _{621} =

^{(1 × 621)} / _{621} + ^{364} / _{621} =

#### 1 + ^{364}/_{621} =

#### 1 ^{364}/_{621}

### As a decimal number:

#### 1 ^{364}/_{621} =

#### 1 + ^{364}/_{621} =

#### 1 + 364 ÷ 621 ≈

#### 1.58615136876 ≈

#### 1.59

### As a percentage:

#### 1.58615136876 =

#### 1.58615136876 × ^{100}/_{100} =

#### ^{158.615136876006}/_{100} =

#### 158.615136876006% ≈

#### 158.62%

#### 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):

^{4,925}/_{3,105} = ^{985}/_{621}

## As a mixed number (mixed fraction)

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

^{4,925}/_{3,105} = 1 ^{364}/_{621}

## As a decimal number:

^{4,925}/_{3,105} ≈ 1.58615136876 ≈ 1.59

## As a percentage:

^{4,925}/_{3,105} ≈ 158.62%

## More operations of this kind:

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