# Multiplying the common ordinary fractions: - ^{34}/_{68} × - ^{57}/_{32} = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage

## - ^{34}/_{68} × - ^{57}/_{32} = ?

## 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

#### - ^{34}/_{68} × - ^{57}/_{32} =

^{34}/_{68} × ^{57}/_{32}

## 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.

^{34}/_{68} =

^{(2 × 17)}/_{(22 × 17)} =

^{((2 × 17) ÷ (2 × 17))}/_{((22 × 17) ÷ (2 × 17))} =

^{(2 ÷ 2 × 17 ÷ 17)}/_{(22 ÷ 2 × 17 ÷ 17)} =

^{(1 × 1)}/_{(2(2 - 1) × 1)} =

^{(1 × 1)}/_{(2 × 1)} =

^{1}/_{2}

^{57}/_{32} is already reduced to the lowest terms.

#### The numerator and denominator have no common prime factors.

#### Their prime factorization:

57 = 3 × 19

32 = 2^{5}

### Rewrite the equivalent simplified operation:

^{34}/_{68} × ^{57}/_{32} =

^{1}/_{2} × ^{57}/_{32}

## 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.

^{1}/_{2} × ^{57}/_{32} =

^{57} / _{(2 × 32)} =

^{(3 × 19)} / _{(2 × 25)} =

^{(3 × 19)} / _{26}

## 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 × 19; 2^{6}) = 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 × 19)} / _{26} =

^{57}/_{64}

## Rewrite the fraction

### As a decimal number:

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

^{57}/_{64} =

#### 57 ÷ 64 =

#### 0.890625 ≈

#### 0.89

### 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.

#### 0.890625 =

#### 0.890625 × ^{100}/_{100} =

^{(0.890625 × 100)}/_{100} =

^{89.0625}/_{100} =

#### 89.0625% ≈

#### 89.06%

## The final answer:

written in three ways

## As a positive proper fraction:

(the numerator < the denominator)

- ^{34}/_{68} × - ^{57}/_{32} = ^{57}/_{64}

## As a decimal number:

- ^{34}/_{68} × - ^{57}/_{32} ≈ 0.89

## As a percentage:

- ^{34}/_{68} × - ^{57}/_{32} ≈ 89.06%

#### 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: