Multiplying the common ordinary fractions: 49/78 × - 48/81 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
49/78 × - 48/81 = ?
Simplify the operation
Rewrite the equivalent simplified operation:
Combine the signs of the fractions into a single one, placed in front of the expression. If the sign is + then it is usually not written.
The sign of a multiplication operation:
+ 1 × + 1 = + 1
+ 1 × - 1 = - 1
- 1 × - 1 = + 1
49/78 × - 48/81 =
- 49/78 × 48/81
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.
49/78 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
49 = 72
78 = 2 × 3 × 13
48/81 =
(24 × 3)/34 =
((24 × 3) ÷ 3)/(34 ÷ 3) =
(24 × 3 ÷ 3)/(34 ÷ 3) =
(24 × 1)/3(4 - 1) =
(24 × 1)/33 =
16/27
Rewrite the equivalent simplified operation:
- 49/78 × 48/81 =
- 49/78 × 16/27
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.
- 49/78 × 16/27 =
- (49 × 16) / (78 × 27) =
- (72 × 24) / (2 × 3 × 13 × 33) =
- (24 × 72) / (2 × 34 × 13)
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 (24 × 72; 2 × 34 × 13) = 2
Divide the numerator and the denominator by their GCF:
- (24 × 72) / (2 × 34 × 13) =
- ((24 × 72) ÷ 2) / ((2 × 34 × 13) ÷ 2) =
- (24 ÷ 2 × 72)/(2 ÷ 2 × 34 × 13) =
- (2(4 - 1) × 72)/(1 × 34 × 13) =
- (23 × 72)/(1 × 34 × 13) =
- (23 × 72)/(34 × 13) =
- (8 × 49)/(81 × 13) =
- 392/1,053
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 392/1,053 =
- 392 ÷ 1,053 ≈
- 0.372269705603 ≈
- 0.37
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.
- 0.372269705603 =
- 0.372269705603 × 100/100 =
( - 0.372269705603 × 100)/100 =
- 37.226970560304/100 ≈
- 37.226970560304% ≈
- 37.23%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
49/78 × - 48/81 = - 392/1,053
As a decimal number:
49/78 × - 48/81 ≈ - 0.37
As a percentage:
49/78 × - 48/81 ≈ - 37.23%
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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