- 130/229 × 221/133 × 133/265 × 106/224 = ? 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: 221/133 × 133/265 = 221/265
Rewrite the equivalent simplified operation:
- 130/229 × 221/133 × 133/265 × 106/224 =
- 130/229 × 221/265 × 106/224
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: 130/229
130/229 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
130 = 2 × 5 × 13
229 is a prime number (it cannot be factored into other prime factors)
GCF (130; 229) = 1
The fraction: 221/265
221/265 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
221 = 13 × 17
265 = 5 × 53
GCF (221; 265) = 1
The fraction: 106/224
The prime factorizations of the numerator and denominator:
106 = 2 × 53
224 = 25 × 7
GCF (106; 224) = 2
106/224 =
(106 ÷ 2)/(224 ÷ 2) =
53/112
Yet another method to reduce a fraction:
106/224 =
(2 × 53)/(25 × 7) =
((2 × 53) ÷ 2)/((25 × 7) ÷ 2) =
(2 ÷ 2 × 53)/(25 ÷ 2 × 7) =
(1 × 53)/(2(5 - 1) × 7) =
(1 × 53)/(24 × 7) =
53/112
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
- 130/229 × 221/265 × 106/224 =
- 130/229 × 221/265 × 53/112
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
- 130/229 × 221/265 × 53/112 =
- (130 × 221 × 53) / (229 × 265 × 112) =
- (2 × 5 × 13 × 13 × 17 × 53) / (229 × 5 × 53 × 24 × 7) =
- (2 × 5 × 132 × 17 × 53) / (24 × 5 × 7 × 53 × 229)
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 (2 × 5 × 132 × 17 × 53; 24 × 5 × 7 × 53 × 229) = 2 × 5 × 53
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:
- (2 × 5 × 132 × 17 × 53) / (24 × 5 × 7 × 53 × 229) =
- ((2 × 5 × 132 × 17 × 53) ÷ (2 × 5 × 53)) / ((24 × 5 × 7 × 53 × 229) ÷ (2 × 5 × 53)) =
- (2 ÷ 2 × 5 ÷ 5 × 132 × 17 × 53 ÷ 53)/(24 ÷ 2 × 5 ÷ 5 × 7 × 53 ÷ 53 × 229) =
- (1 × 1 × 132 × 17 × 1)/(2(4 - 1) × 1 × 7 × 1 × 229) =
- (1 × 1 × 132 × 17 × 1)/(23 × 1 × 7 × 1 × 229) =
- (132 × 17)/(23 × 7 × 229) =
- (169 × 17)/(8 × 7 × 229) =
- 2,873/12,824
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 2,873/12,824 =
- 2,873 ÷ 12,824 ≈
- 0.224033063007 ≈
- 0.22
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.
- 0.224033063007 =
- 0.224033063007 × 100/100 =
( - 0.224033063007 × 100)/100 =
- 22.403306300686/100 ≈
- 22.403306300686% ≈
- 22.4%
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 negative proper fraction:
(the numerator < the denominator)
- 130/229 × 221/133 × 133/265 × 106/224 = - 2,873/12,824
As a decimal number:
- 130/229 × 221/133 × 133/265 × 106/224 ≈ - 0.22
As a percentage:
- 130/229 × 221/133 × 133/265 × 106/224 ≈ - 22.4%
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.