Multiplying the common ordinary fractions: 65/102 × - 63/112 = ? The multiplication process explained. The result written: As a negative proper fraction (the numerator < the denominator). As a decimal number. As a percentage
65/102 × - 63/112 = ?
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
65/102 × - 63/112 =
- 65/102 × 63/112
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.
65/102 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
65 = 5 × 13
102 = 2 × 3 × 17
63/112 =
(32 × 7)/(24 × 7) =
((32 × 7) ÷ 7)/((24 × 7) ÷ 7) =
(32 × 7 ÷ 7)/(24 × 7 ÷ 7) =
(32 × 1)/(24 × 1) =
9/16
Rewrite the equivalent simplified operation:
- 65/102 × 63/112 =
- 65/102 × 9/16
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.
- 65/102 × 9/16 =
- (65 × 9) / (102 × 16) =
- (5 × 13 × 32) / (2 × 3 × 17 × 24) =
- (32 × 5 × 13) / (25 × 3 × 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 (32 × 5 × 13; 25 × 3 × 17) = 3
Divide the numerator and the denominator by their GCF:
- (32 × 5 × 13) / (25 × 3 × 17) =
- ((32 × 5 × 13) ÷ 3) / ((25 × 3 × 17) ÷ 3) =
- (32 ÷ 3 × 5 × 13)/(25 × 3 ÷ 3 × 17) =
- (3(2 - 1) × 5 × 13)/(25 × 1 × 17) =
- (31 × 5 × 13)/(25 × 1 × 17) =
- (3 × 5 × 13)/(25 × 1 × 17) =
- (3 × 5 × 13)/(25 × 17) =
- (3 × 5 × 13)/(32 × 17) =
- 195/544
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 195/544 =
- 195 ÷ 544 ≈
- 0.358455882353 ≈
- 0.36
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.
- 0.358455882353 =
- 0.358455882353 × 100/100 =
( - 0.358455882353 × 100)/100 =
- 35.845588235294/100 ≈
- 35.845588235294% ≈
- 35.85%
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
65/102 × - 63/112 = - 195/544
As a decimal number:
65/102 × - 63/112 ≈ - 0.36
As a percentage:
65/102 × - 63/112 ≈ - 35.85%
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
Multiply common ordinary fractions, online calculator: