Multiplying the common ordinary fractions: - 37/70 × - 42/80 = ? The multiplication process explained. The result written: As a positive proper fraction (the numerator < the denominator). As a decimal number. As a percentage
- 37/70 × - 42/80 = ?
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
- 37/70 × - 42/80 =
37/70 × 42/80
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.
37/70 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
37 is a prime number (it cannot be factored into other prime factors)
70 = 2 × 5 × 7
42/80 =
(2 × 3 × 7)/(24 × 5) =
((2 × 3 × 7) ÷ 2)/((24 × 5) ÷ 2) =
(2 ÷ 2 × 3 × 7)/(24 ÷ 2 × 5) =
(1 × 3 × 7)/(2(4 - 1) × 5) =
(1 × 3 × 7)/(23 × 5) =
21/40
Rewrite the equivalent simplified operation:
37/70 × 42/80 =
37/70 × 21/40
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.
37/70 × 21/40 =
(37 × 21) / (70 × 40) =
(37 × 3 × 7) / (2 × 5 × 7 × 23 × 5) =
(3 × 7 × 37) / (24 × 52 × 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 (3 × 7 × 37; 24 × 52 × 7) = 7
Divide the numerator and the denominator by their GCF:
(3 × 7 × 37) / (24 × 52 × 7) =
((3 × 7 × 37) ÷ 7) / ((24 × 52 × 7) ÷ 7) =
(3 × 7 ÷ 7 × 37)/(24 × 52 × 7 ÷ 7) =
(3 × 1 × 37)/(24 × 52 × 1) =
(3 × 37)/(24 × 52) =
(3 × 37)/(16 × 25) =
111/400
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
111/400 =
111 ÷ 400 =
0.2775 ≈
0.28
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.
0.2775 =
0.2775 × 100/100 =
(0.2775 × 100)/100 =
27.75/100 =
27.75%
The final answer:
written in three ways
As a positive proper fraction:
(the numerator < the denominator)
- 37/70 × - 42/80 = 111/400
As a decimal number:
- 37/70 × - 42/80 ≈ 0.28
As a percentage:
- 37/70 × - 42/80 = 27.75%
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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