Multiply fractions: 61/14 × - 37/12 = ? Multiplication result of the ordinary (simple, common) fractions explained

61/14 × - 37/12 = ?

Rewrite the equivalent simplified operation:

Combine the signs of the fractions into a single one, placed in front of the expression.

The sign of the multiplication: + 1 × + 1 = + 1; + 1 × - 1 = - 1; - 1 × - 1 = + 1.

61/14 × - 37/12 =

- 61/14 × 37/12

Reduce (simplify) fractions to their lowest terms equivalents:

Factor all the numbers in order to easily reduce (simplify) the end fraction.

Fraction: 61/14 already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
Their prime factorization:
61 is a prime number, it cannot be factored into other prime factors;
14 = 2 × 7;


Fraction: 37/12 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;
12 = 22 × 3;


Multiply the numerators and denominators of the fractions separately:

Factor all the numbers in order to easily reduce (simplify) the end fraction.

- 61/14 × 37/12 =

- (61 × 37) / (14 × 12) =

- (61 × 37) / (2 × 7 × 22 × 3) =

- (37 × 61) / (23 × 3 × 7)

>> Calculate the prime factors of numbers, online calculator


Reduce (simplify) the fraction to its lowest terms equivalent:

Calculate the greatest common factor, GCF:

Multiply all the common prime factors, by the lowest exponents.

But, the numerator and denominator have no common factors.

gcf(37 × 61; 23 × 3 × 7) = 1

>> Calculate the greatest common factor, GCF, online calculator


Divide the numerator and denominator by GCF.

The numerator and denominator of the fraction are coprime numbers (no common prime factors, GCF = 1). The fraction cannot be reduced (simplified): irreducible fraction.

- (37 × 61) / (23 × 3 × 7) =

- 2,257/168

>> Reduce (simplify) fractions to their simplest form, online calculator


Rewrite the fraction

As a mixed number (also called a mixed fraction):

Mixed number = a whole number and a proper fraction, of the same sign.

Proper fraction = numerator smaller than denominator.


- 2,257 ÷ 168 = - 13 and remainder = - 73 =>

- 2,257 = - 13 × 168 - 73 =>

- 2,257/168 =

( - 13 × 168 - 73)/168 =

( - 13 × 168)/168 - 73/168 =

- 13 - 73/168 =

- 13 73/168

As a decimal number:

- 13 - 73/168 =

- 13 - 73 ÷ 168 ≈

- 13.434523809524 ≈

- 13.43

As a percentage:

- 13.434523809524 =

- 13.434523809524 × 100/100 =

( - 13.434523809524 × 100)/100 =

- 1,343.452380952381/100 ≈

- 1,343.452380952381% ≈

- 1,343.45%

>> Convert fractions to percentages, online calculator


The final answer:
:: written in four ways ::

As a negative improper fraction (numerator >= denominator):
61/14 × - 37/12 = - 2,257/168

As a mixed number (also called a mixed fraction):
61/14 × - 37/12 = - 13 73/168

As a decimal number:
61/14 × - 37/12 ≈ - 13.43

As a percentage:
61/14 × - 37/12 ≈ - 1,343.45%

More operations of this kind:

How to multiply the ordinary fractions:
- 73/19 × - 48/19

Writing numbers: comma ',' used as a thousands separator; point '.' used as a decimal mark; numbers rounded to max. 12 decimals (whenever the case);

Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; ≈ approximation;

Multiply ordinary fractions, online calculator

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Multiplying fractions. How to multiply ordinary math fractions? Steps. Example.

How to multiply two fractions?

When we multiply ordinary fractions, the end fraction will have:

  • as a numerator, the result of multiplying all the numerators of the fractions,
  • as a denominator, the result of multiplying all the denominators of the fractions.
  • a/b × c/d = (a × c) / (b × d)
  • a, b, c, d are integer numbers;
  • if the pairs (a × c) and (b × d) are not coprime (they have common prime factors) the end fraction should be reduced (simplified) to lower terms.

How to multiply ordinary fractions? Steps.

  • Start by reducing fractions to lower terms (simplifying).
  • Reduce math fractions to lower terms, online, with explanations.
  • Factor the numerators and the denominators of the reduced fractions: break them down to their prime factors.
  • Calculate the prime factors of numbers, online calculator
  • Above the fraction bar we write the product of all the prime factors of the fractions' numerators, without doing any calculations.
  • Below the fraction bar we write the product of all the prime factors of the fractions' denominators, without doing any calculations.
  • Cross out all the common prime factors that appear both above and below the fraction bar.
  • Multiply the remaining prime factors above the fraction bar - this will be the numerator of the resulted fraction.
  • Multiply the remaining prime factors below the fraction bar - this will be the denominator of the resulted fraction.
  • There is no need to reduce (simplify) the resulting fraction, since we have already crossed out all the common prime factors.
  • If the resulted fraction is an improper one (without considering the sign, the numerator is larger than the denominator), it could be written as a mixed number, consisting of an integer and a proper fraction of the same sign.
  • Write improper fractions as mixed numbers, online.
  • Multiply ordinary fractions, online, with explanations.

... Read the rest of this article, here: How to multiply ordinary (common) fractions?

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?

(2) Fractions changing form, expand and reduce (simplify) fractions

(3) Reducing fractions. The greatest common factor, GCF

(4) How to, comparing two fractions with unlike (different) numerators and denominators

(5) Sorting fractions in ascending order

(6) Adding ordinary (common, simple) fractions

(7) Subtracting ordinary (common, simple) fractions

(8) Multiplying ordinary (common, simple) fractions

(9) Fractions, theory: rational numbers