Multiplying the common ordinary fractions: ³⁷/₆₃ × - ⁶⁶/₃₅ = ? The multiplication process explained. The result written: As a negative improper fraction (the numerator >= the denominator). As a mixed number. As a decimal number. As a percentage

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

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.

³⁷/₆₃ 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)
63 = 3² × 7

⁶⁶/₃₅ is already reduced to the lowest terms.

The numerator and denominator have no common prime factors.

Their prime factorization:
66 = 2 × 3 × 11
35 = 5 × 7

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.

External link » Factor (decompose) composite numbers into prime factors, online calculator

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 × 3 × 11 × 37; 3² × 5 × 7²) = 3

External link » Calculate the greatest common factor, GCF, of two numbers, online calculator

Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator

A mixed number: a whole number and a proper fraction, both having the same sign.

A proper fraction: the value of the numerator is smaller than the value of the denominator.

Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:

Simply divide the numerator by the denominator, without a remainder, as shown below:

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.

External link » Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator

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.