Multiplying the common ordinary fractions: - 24/34 × 25/22 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 24/34 × 25/22 = ?
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.
24/34 =
(23 × 3)/(2 × 17) =
((23 × 3) ÷ 2)/((2 × 17) ÷ 2) =
(23 ÷ 2 × 3)/(2 ÷ 2 × 17) =
(2(3 - 1) × 3)/(1 × 17) =
(22 × 3)/(1 × 17) =
12/17
25/22 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
25 = 52
22 = 2 × 11
Rewrite the equivalent simplified operation:
- 24/34 × 25/22 =
- 12/17 × 25/22
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.
- 12/17 × 25/22 =
- (12 × 25) / (17 × 22) =
- (22 × 3 × 52) / (17 × 2 × 11) =
- (22 × 3 × 52) / (2 × 11 × 17)
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 (22 × 3 × 52; 2 × 11 × 17) = 2
Divide the numerator and the denominator by their GCF:
- (22 × 3 × 52) / (2 × 11 × 17) =
- ((22 × 3 × 52) ÷ 2) / ((2 × 11 × 17) ÷ 2) =
- (22 ÷ 2 × 3 × 52)/(2 ÷ 2 × 11 × 17) =
- (2(2 - 1) × 3 × 52)/(1 × 11 × 17) =
- (21 × 3 × 52)/(1 × 11 × 17) =
- (2 × 3 × 52)/(1 × 11 × 17) =
- (2 × 3 × 52)/(11 × 17) =
- (2 × 3 × 25)/(11 × 17) =
- 150/187
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 150/187 =
- 150 ÷ 187 ≈
- 0.802139037433 ≈
- 0.8
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.
- 0.802139037433 =
- 0.802139037433 × 100/100 =
( - 0.802139037433 × 100)/100 =
- 80.213903743316/100 ≈
- 80.213903743316% ≈
- 80.21%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 24/34 × 25/22 = - 150/187
As a decimal number:
- 24/34 × 25/22 ≈ - 0.8
As a percentage:
- 24/34 × 25/22 ≈ - 80.21%
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.
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