Multiplying the common ordinary fractions: 48/72 × 105/138 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
48/72 × 105/138 = ?
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.
48/72 =
(24 × 3)/(23 × 32) =
((24 × 3) ÷ (23 × 3))/((23 × 32) ÷ (23 × 3)) =
(24 ÷ 23 × 3 ÷ 3)/(23 ÷ 23 × 32 ÷ 3) =
(2(4 - 3) × 1)/(2(3 - 3) × 3(2 - 1)) =
(2 × 1)/(20 × 31) =
(2 × 1)/(1 × 3) =
2/3
105/138 =
(3 × 5 × 7)/(2 × 3 × 23) =
((3 × 5 × 7) ÷ 3)/((2 × 3 × 23) ÷ 3) =
(3 ÷ 3 × 5 × 7)/(2 × 3 ÷ 3 × 23) =
(1 × 5 × 7)/(2 × 1 × 23) =
35/46
Rewrite the equivalent simplified operation:
48/72 × 105/138 =
2/3 × 35/46
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.
2/3 × 35/46 =
(2 × 35) / (3 × 46) =
(2 × 5 × 7) / (3 × 2 × 23) =
(2 × 5 × 7) / (2 × 3 × 23)
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 × 5 × 7; 2 × 3 × 23) = 2
Divide the numerator and the denominator by their GCF:
(2 × 5 × 7) / (2 × 3 × 23) =
((2 × 5 × 7) ÷ 2) / ((2 × 3 × 23) ÷ 2) =
(2 ÷ 2 × 5 × 7)/(2 ÷ 2 × 3 × 23) =
(1 × 5 × 7)/(1 × 3 × 23) =
(5 × 7)/(3 × 23) =
35/69
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
35/69 =
35 ÷ 69 ≈
0.507246376812 ≈
0.51
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.
0.507246376812 =
0.507246376812 × 100/100 =
(0.507246376812 × 100)/100 =
50.724637681159/100 ≈
50.724637681159% ≈
50.72%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
48/72 × 105/138 = 35/69
As a decimal number:
48/72 × 105/138 ≈ 0.51
As a percentage:
48/72 × 105/138 ≈ 50.72%
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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