# Multiplying the common ordinary fractions: ^{140}/_{37} × ^{79}/_{40} = ? The multiplication process explained. The result written: As a positive improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage

^{140}/_{37} × ^{79}/_{40} = ?

## 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.

^{140}/_{37} is already reduced to the lowest terms.

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

#### Their prime factorization:

140 = 2^{2} × 5 × 7

37 is a prime number (it cannot be factored into other prime factors)

^{79}/_{40} is already reduced to the lowest terms.

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

#### Their prime factorization:

79 is a prime number (it cannot be factored into other prime factors)

40 = 2^{3} × 5

## 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.

^{140}/_{37} × ^{79}/_{40} =

^{(140 × 79)} / _{(37 × 40)} =

^{(22 × 5 × 7 × 79)} / _{(37 × 23 × 5)} =

^{(22 × 5 × 7 × 79)} / _{(23 × 5 × 37)}

## 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).

#### GCF (2^{2} × 5 × 7 × 79; 2^{3} × 5 × 37) = 2^{2} × 5

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

^{(22 × 5 × 7 × 79)} / _{(23 × 5 × 37)} =

^{((22 × 5 × 7 × 79) ÷ (22 × 5))} / _{((23 × 5 × 37) ÷ (22 × 5))} =

^{(22 ÷ 22 × 5 ÷ 5 × 7 × 79)}/_{(23 ÷ 22 × 5 ÷ 5 × 37)} =

^{(2(2 - 2) × 1 × 7 × 79)}/_{(2(3 - 2) × 1 × 37)} =

^{(20 × 1 × 7 × 79)}/_{(2 × 1 × 37)} =

^{(1 × 1 × 7 × 79)}/_{(2 × 1 × 37)} =

^{(7 × 79)}/_{(2 × 37)} =

^{553}/_{74}

## 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:

#### 553 ÷ 74 = 7 and the remainder = 35 ⇒

#### 553 = 7 × 74 + 35 ⇒

^{553}/_{74} =

^{(7 × 74 + 35)}/_{74} =

^{(7 × 74)}/_{74} + ^{35}/_{74} =

#### 7 + ^{35}/_{74} =

#### 7 ^{35}/_{74}

### As a decimal number:

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

#### 7 + ^{35}/_{74} =

#### 7 + 35 ÷ 74 ≈

#### 7.472972972973 ≈

#### 7.47

### 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.

#### 7.472972972973 =

#### 7.472972972973 × ^{100}/_{100} =

^{(7.472972972973 × 100)}/_{100} =

^{747.297297297297}/_{100} ≈

#### 747.297297297297% ≈

#### 747.3%

## The final answer:

written in four ways

## As a positive improper fraction:

(the numerator >= the denominator)

^{140}/_{37} × ^{79}/_{40} = ^{553}/_{74}

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

^{140}/_{37} × ^{79}/_{40} = 7 ^{35}/_{74}

## As a decimal number:

^{140}/_{37} × ^{79}/_{40} ≈ 7.47

## As a percentage:

^{140}/_{37} × ^{79}/_{40} ≈ 747.3%

#### 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: