105/137 × 137/95 × 89/135 × 105/152 × 99/120 = ? 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: 105/137 × 137/95 = 105/95
Rewrite the equivalent simplified operation:
105/137 × 137/95 × 89/135 × 105/152 × 99/120 =
105/95 × 89/135 × 105/152 × 99/120
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: 105/95
The prime factorizations of the numerator and denominator:
105 = 3 × 5 × 7
95 = 5 × 19
GCF (105; 95) = 5
105/95 =
(105 ÷ 5)/(95 ÷ 5) =
21/19
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.
105/95 =
(3 × 5 × 7)/(5 × 19) =
((3 × 5 × 7) ÷ 5)/((5 × 19) ÷ 5) =
(3 × 5 ÷ 5 × 7)/(5 ÷ 5 × 19) =
(3 × 1 × 7)/(1 × 19) =
21/19
The fraction: 89/135
89/135 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
89 is a prime number (it cannot be factored into other prime factors)
135 = 33 × 5
GCF (89; 135) = 1
The fraction: 105/152
105/152 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
105 = 3 × 5 × 7
152 = 23 × 19
GCF (105; 152) = 1
The fraction: 99/120
The prime factorizations of the numerator and denominator:
99 = 32 × 11
120 = 23 × 3 × 5
GCF (99; 120) = 3
99/120 =
(99 ÷ 3)/(120 ÷ 3) =
33/40
Yet another method to reduce a fraction:
99/120 =
(32 × 11)/(23 × 3 × 5) =
((32 × 11) ÷ 3)/((23 × 3 × 5) ÷ 3) =
(32 ÷ 3 × 11)/(23 × 3 ÷ 3 × 5) =
(3(2 - 1) × 11)/(23 × 1 × 5) =
(31 × 11)/(23 × 1 × 5) =
(3 × 11)/(23 × 1 × 5) =
33/40
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
105/95 × 89/135 × 105/152 × 99/120 =
21/19 × 89/135 × 105/152 × 33/40
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
21/19 × 89/135 × 105/152 × 33/40 =
(21 × 89 × 105 × 33) / (19 × 135 × 152 × 40) =
(3 × 7 × 89 × 3 × 5 × 7 × 3 × 11) / (19 × 33 × 5 × 23 × 19 × 23 × 5) =
(33 × 5 × 72 × 11 × 89) / (26 × 33 × 52 × 192)
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 (33 × 5 × 72 × 11 × 89; 26 × 33 × 52 × 192) = 33 × 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:
(33 × 5 × 72 × 11 × 89) / (26 × 33 × 52 × 192) =
((33 × 5 × 72 × 11 × 89) ÷ (33 × 5)) / ((26 × 33 × 52 × 192) ÷ (33 × 5)) =
(33 ÷ 33 × 5 ÷ 5 × 72 × 11 × 89)/(26 × 33 ÷ 33 × 52 ÷ 5 × 192) =
(3(3 - 3) × 1 × 72 × 11 × 89)/(26 × 3(3 - 3) × 5(2 - 1) × 192) =
(30 × 1 × 72 × 11 × 89)/(26 × 30 × 51 × 192) =
(1 × 1 × 72 × 11 × 89)/(26 × 1 × 5 × 192) =
(72 × 11 × 89)/(26 × 5 × 192) =
(49 × 11 × 89)/(64 × 5 × 361) =
47,971/115,520
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
47,971/115,520 =
47,971 ÷ 115,520 ≈
0.415261426593 ≈
0.42
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.
0.415261426593 =
0.415261426593 × 100/100 =
(0.415261426593 × 100)/100 =
41.52614265928/100 ≈
41.52614265928% ≈
41.53%
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)
105/137 × 137/95 × 89/135 × 105/152 × 99/120 = 47,971/115,520
As a decimal number:
105/137 × 137/95 × 89/135 × 105/152 × 99/120 ≈ 0.42
As a percentage:
105/137 × 137/95 × 89/135 × 105/152 × 99/120 ≈ 41.53%
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.