- 27/15 × 905/18 × 18/31 = ? Multiply the Common (Ordinary) Fractions, Online Calculator. Multiplication Operation Explained Step by Step
The numerators and the denominators of the fractions are multiplied separately
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 905/18 × 18/31 = 905/31
Rewrite the equivalent simplified operation:
- 27/15 × 905/18 × 18/31 =
- 27/15 × 905/31
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- 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.
- * By reducing the values of the numerators and denominators of fractions, subsequent calculations become easier to perform.
To reduce a fraction to the lowest terms equivalent divide its numerator and denominator by their greatest common factor, GCF.
- To calculate the GCF, factor the numerator and 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 exponents (the lowest powers).
The fraction: 27/15
The prime factorizations of the numerator and denominator:
27 = 33
15 = 3 × 5
GCF (27; 15) = 3
27/15 =
(27 ÷ 3)/(15 ÷ 3) =
9/5
Yet another method to reduce a fraction:
* To reduce a fraction without calculating the GCF: factor its numerator and denominator, then all the common prime factors are easily identified and crossed out.
27/15 =
33/(3 × 5) =
(33 ÷ 3)/((3 × 5) ÷ 3) =
(33 ÷ 3)/(3 ÷ 3 × 5) =
3(3 - 1)/(1 × 5) =
32/(1 × 5) =
9/5
The fraction: 905/31
905/31 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
905 = 5 × 181
31 is a prime number (it cannot be factored into other prime factors)
GCF (905; 31) = 1
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
- 27/15 × 905/31 =
- 9/5 × 905/31
Perform the operation of calculating the fractions
Multiply the fractions:
Multiply the numerators, that is, all the numbers above fractions bars, separately.
Multiply the denominators, that is, all the numbers below fractions bars, separately.
* Factor all the numerators and all the denominators in order to easily reduce (simplify) the end fraction.
External link » Factor (decompose) composite numbers into prime factors, online calculator
- 9/5 × 905/31 =
- (9 × 905) / (5 × 31) =
- (32 × 5 × 181) / (5 × 31)
Reduce (simplify) the end fraction to its lowest terms equivalent:
Calculate the greatest common factor, GCF,
of the numerator and denominator of the fraction:
To reduce a fraction to the lowest terms equivalent divide its numerator and denominator by their greatest common factor, GCF.
- To calculate the GCF, factor the numerator and 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 exponents (the lowest powers).
GCF (32 × 5 × 181; 5 × 31) = 5
External link » Calculate the greatest common factor, GCF, of two numbers, online calculator
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Divide the numerator and the denominator by their GCF:
- (32 × 5 × 181) / (5 × 31) =
- ((32 × 5 × 181) ÷ 5) / ((5 × 31) ÷ 5) =
- (32 × 5 ÷ 5 × 181)/(5 ÷ 5 × 31) =
- (32 × 1 × 181)/(1 × 31) =
- (32 × 181)/31 =
- (9 × 181)/31 =
- 1,629/31
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:
- 1,629 ÷ 31 = - 52 and the remainder = - 17 ⇒
- 1,629 = - 52 × 31 - 17 ⇒
- 1,629/31 =
( - 52 × 31 - 17)/31 =
( - 52 × 31)/31 - 17/31 =
- 52 - 17/31 =
- 52 17/31
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 52 - 17/31 =
- 52 - 17 ÷ 31 ≈
- 52.548387096774 ≈
- 52.55
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.
- 52.548387096774 =
- 52.548387096774 × 100/100 =
( - 52.548387096774 × 100)/100 =
- 5,254.838709677419/100 ≈
- 5,254.838709677419% ≈
- 5,254.84%
External link » Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator
The final answer:
written in four ways
As a negative improper fraction:
(the numerator >= the denominator)
- 27/15 × 905/18 × 18/31 = - 1,629/31
As a mixed number (also called a mixed fraction):
- 27/15 × 905/18 × 18/31 = - 52 17/31
As a decimal number:
- 27/15 × 905/18 × 18/31 ≈ - 52.55
As a percentage:
- 27/15 × 905/18 × 18/31 ≈ - 5,254.84%
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.