# Multiplying the common ordinary fractions: ^{50}/_{80} × - ^{153}/_{57} = ? The multiplication process explained. The result written: As a negative improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage

^{50}/_{80} × - ^{153}/_{57} = ?

## Simplify the operation

### Rewrite the equivalent simplified operation:

#### Combine the signs of the fractions into a single one, placed in front of the expression. If the sign is + then it is usually not written.

#### The sign of a multiplication operation:

#### + 1 × + 1 = + 1

#### + 1 × - 1 = - 1

#### - 1 × - 1 = + 1

^{50}/_{80} × - ^{153}/_{57} =

#### - ^{50}/_{80} × ^{153}/_{57}

## Simplify the operation

### Reduce (simplify) the fractions to their lowest terms equivalents:

#### To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.

#### * By reducing the values of the numerators and the denominators of the fractions the calculations are easier to make.

#### A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

#### * In order to easily reduce a fraction, factor its numerator and denominator. This way all the common prime factors are easily identified and crossed out, without calculating the GCF.

^{50}/_{80} =

^{(2 × 52)}/_{(24 × 5)} =

^{((2 × 52) ÷ (2 × 5))}/_{((24 × 5) ÷ (2 × 5))} =

^{(2 ÷ 2 × 52 ÷ 5)}/_{(24 ÷ 2 × 5 ÷ 5)} =

^{(1 × 5(2 - 1))}/_{(2(4 - 1) × 1)} =

^{(1 × 51)}/_{(23 × 1)} =

^{(1 × 5)}/_{(23 × 1)} =

^{5}/_{8}

^{153}/_{57} =

^{(32 × 17)}/_{(3 × 19)} =

^{((32 × 17) ÷ 3)}/_{((3 × 19) ÷ 3)} =

^{(32 ÷ 3 × 17)}/_{(3 ÷ 3 × 19)} =

^{(3(2 - 1) × 17)}/_{(1 × 19)} =

^{(31 × 17)}/_{(1 × 19)} =

^{(3 × 17)}/_{(1 × 19)} =

^{51}/_{19}

### Rewrite the equivalent simplified operation:

#### - ^{50}/_{80} × ^{153}/_{57} =

#### - ^{5}/_{8} × ^{51}/_{19}

## Perform the operation of calculating the fractions

### Multiply the fractions:

#### 1) Multiply the numerators, that is, all the numbers above the fractions bars, separately.

#### 2) Multiply the denominators, that is, all the numbers below the fractions bars, separately.

#### * Factor all the numerators and all the denominators in order to easily reduce (simplify) the end fraction.

#### - ^{5}/_{8} × ^{51}/_{19} =

#### - ^{(5 × 51)} / _{(8 × 19)} =

#### - ^{(5 × 3 × 17)} / _{(23 × 19)} =

#### - ^{(3 × 5 × 17)} / _{(23 × 19)}

## Fully reduce (simplify) the end fraction to its lowest terms equivalent:

### Calculate the greatest common factor, GCF,

of the numerator and denominator of the fraction:

#### A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.

#### To fully reduce a fraction, to the lowest terms equivalent: divide the numerator and denominator by their greatest common factor, GCF.

#### * To calculate the GCF, we need to factor the numerator and the denominator of the fraction into prime factors.

#### Then multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).

#### But the numerator and the denominator have no common prime factors:

#### GCF (3 × 5 × 17; 2^{3} × 19) = 1

### Divide the numerator and the denominator by their GCF:

#### The numerator and the denominator of the fraction are coprime numbers (there are no common prime factors, the GCF = 1). The end fraction can no longer be shortened, it already has the smallest possible numerator and denominator, it is an irreducible fraction.

#### - ^{(3 × 5 × 17)} / _{(23 × 19)} =

#### - ^{255}/_{152}

## Rewrite the fraction

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

#### A mixed number: a whole number and a proper fraction, both having the same sign.

#### A proper fraction: the value of the numerator is smaller than the value of the denominator.

#### Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:

#### - 255 ÷ 152 = - 1 and the remainder = - 103 ⇒

#### - 255 = - 1 × 152 - 103 ⇒

#### - ^{255}/_{152} =

^{( - 1 × 152 - 103)}/_{152} =

^{( - 1 × 152)}/_{152} - ^{103}/_{152} =

#### - 1 - ^{103}/_{152} =

#### - 1 ^{103}/_{152}

### As a decimal number:

#### Simply divide the numerator by the denominator, without a remainder, as shown below:

#### - 1 - ^{103}/_{152} =

#### - 1 - 103 ÷ 152 ≈

#### - 1.677631578947 ≈

#### - 1.68

### As a percentage:

#### A percentage value p% is equal to the fraction: ^{p}/_{100}, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.

#### To do that, multiply the number by the fraction ^{100}/_{100}.

#### The value of the fraction ^{100}/_{100} = 1, so by multiplying the number by this fraction the result is not changing, only the form.

#### - 1.677631578947 =

#### - 1.677631578947 × ^{100}/_{100} =

^{( - 1.677631578947 × 100)}/_{100} =

^{ - 167.763157894737}/_{100} ≈

#### - 167.763157894737% ≈

#### - 167.76%

## The final answer:

written in four ways

## As a negative improper fraction:

(the numerator >= the denominator)

^{50}/_{80} × - ^{153}/_{57} = - ^{255}/_{152}

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

^{50}/_{80} × - ^{153}/_{57} = - 1 ^{103}/_{152}

## As a decimal number:

^{50}/_{80} × - ^{153}/_{57} ≈ - 1.68

## As a percentage:

^{50}/_{80} × - ^{153}/_{57} ≈ - 167.76%

#### How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.

## Other similar operations

## Multiply common ordinary fractions, online calculator: