17/12 × 1/3 × 6/17 × 15/17 = ? 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: 17/12 × 6/17 = 6/12
Rewrite the equivalent simplified operation:
17/12 × 1/3 × 6/17 × 15/17 =
6/12 × 1/3 × 15/17
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: 6/12
The prime factorizations of the numerator and denominator:
6 = 2 × 3
12 = 22 × 3
GCF (6; 12) = 2 × 3 = 6
6/12 =
(6 ÷ 6)/(12 ÷ 6) =
1/2
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.
6/12 =
(2 × 3)/(22 × 3) =
((2 × 3) ÷ (2 × 3))/((22 × 3) ÷ (2 × 3)) =
(2 ÷ 2 × 3 ÷ 3)/(22 ÷ 2 × 3 ÷ 3) =
(1 × 1)/(2(2 - 1) × 1) =
(1 × 1)/(2 × 1) =
1/2
The fraction: 15/17
15/17 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
15 = 3 × 5
17 is a prime number (it cannot be factored into other prime factors)
GCF (15; 17) = 1
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
6/12 × 1/3 × 15/17 =
1/2 × 1/3 × 15/17
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
1/2 × 1/3 × 15/17 =
15 / (2 × 3 × 17) =
(3 × 5) / (2 × 3 × 17)
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 (3 × 5; 2 × 3 × 17) = 3
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:
(3 × 5) / (2 × 3 × 17) =
((3 × 5) ÷ 3) / ((2 × 3 × 17) ÷ 3) =
(3 ÷ 3 × 5)/(2 × 3 ÷ 3 × 17) =
(1 × 5)/(2 × 1 × 17) =
5/(2 × 17) =
5/34
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
5/34 =
5 ÷ 34 ≈
0.147058823529 ≈
0.15
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.
0.147058823529 =
0.147058823529 × 100/100 =
(0.147058823529 × 100)/100 =
14.705882352941/100 ≈
14.705882352941% ≈
14.71%
External link » Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
17/12 × 1/3 × 6/17 × 15/17 = 5/34
As a decimal number:
17/12 × 1/3 × 6/17 × 15/17 ≈ 0.15
As a percentage:
17/12 × 1/3 × 6/17 × 15/17 ≈ 14.71%
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.