Multiplying the common ordinary fractions: - 105/5 × 43/10 × 30/7 = ? The multiplication process explained. The result written: As a negative integer number. As a negative improper fraction (the denominator = 1). As a percentage
- 105/5 × 43/10 × 30/7 = ?
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.
105/5 =
(3 × 5 × 7)/5 =
((3 × 5 × 7) ÷ 5)/(5 ÷ 5) =
(3 × 5 ÷ 5 × 7)/(5 ÷ 5) =
(3 × 1 × 7)/1 =
21/1 =
21
43/10 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
43 is a prime number (it cannot be factored into other prime factors)
10 = 2 × 5
30/7 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
30 = 2 × 3 × 5
7 is a prime number (it cannot be factored into other prime factors)
Rewrite the equivalent simplified operation:
- 105/5 × 43/10 × 30/7 =
- 21 × 43/10 × 30/7
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.
- 21 × 43/10 × 30/7 =
- (21 × 43 × 30) / (10 × 7) =
- (3 × 7 × 43 × 2 × 3 × 5) / (2 × 5 × 7) =
- (2 × 32 × 5 × 7 × 43) / (2 × 5 × 7)
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 × 32 × 5 × 7 × 43; 2 × 5 × 7) = 2 × 5 × 7
Divide the numerator and the denominator by their GCF:
- (2 × 32 × 5 × 7 × 43) / (2 × 5 × 7) =
- ((2 × 32 × 5 × 7 × 43) ÷ (2 × 5 × 7)) / ((2 × 5 × 7) ÷ (2 × 5 × 7)) =
- (2 ÷ 2 × 32 × 5 ÷ 5 × 7 ÷ 7 × 43)/(2 ÷ 2 × 5 ÷ 5 × 7 ÷ 7) =
- (1 × 32 × 1 × 1 × 43)/(1 × 1 × 1) =
- (32 × 43)/1 =
- 9 × 43 =
- 387
Rewrite the intermediate result
As a negative improper fraction:
(the denominator = 1)
An improper fraction: the value of the numerator is larger than or equal to the value of the denominator.
- 387 = - 387/1
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.
- 387 =
- 387 × 100/100 =
( - 387 × 100)/100 =
- 38,700/100 =
- 38,700%
The final answer:
written in three ways
As a negative integer number:
- 105/5 × 43/10 × 30/7 = - 387
As a negative improper fraction:
(the denominator = 1)
- 105/5 × 43/10 × 30/7 = - 387/1
As a percentage:
- 105/5 × 43/10 × 30/7 = - 38,700%
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
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