Reduce the Common Fraction ⁶⁸/₄₂, Simplify It to the Lowest Terms, the Simplest Equivalent Form, Irreducible. Online Calculator

• The integer number above the bar is called numerator: 68
• The integer number below the bar is called denominator: 42
• The fraction bar means that the numerator is divided by the denominator.
• To get the fraction's value divide the numerator by the denominator:
  The value = 68 ÷ 42

• 1. Factor the numerator and the denominator (into prime factors), build their prime factorizations.
• 2. Multiply all their common prime factors, taken by the lowest exponents.

To factor a number (into prime factors) - or, in other words, to break it down to prime factors - or, in other words, to build its prime factorization: find the prime numbers that multiply together to get that number.

• Exponential notation. 2³ is the writing in exponential notation of the repeating multiplication: 2 × 2 × 2. Also: 2³ is called the power. 2 is the base. 3 is the exponent. 8 is the value of the power: 2³ = 8.
• Prime number: a positive integer that is dividing evenly (without a remainder) only by itself and 1. A prime number has only two factors. Composite number: a positive integer that has at least one factor (divisor) other than 1 and itself.

• External link » Check whether numbers are prime or not. Factor (decompose) composite numbers into prime factors, online calculator

• 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).

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

To reduce a fraction without calculating the GCF: factor its numerator and denominator, then all the common prime factors are easily identified and crossed out.

• The fraction is now reduced to the lowest terms equivalent.
• The fraction is called irreducible and it has the smallest possible numerator and denominator.
• By reducing the values of the numerator and of the denominator of a fraction the calculations with that fraction are becoming easier to do.

• A mixed number: a whole number and a proper fraction, both having the same sign.
• A proper fraction is a fraction in which the value of the numerator is less 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.

• In other words:
• (1) Calculate the fraction's value, (2) multiply that number by 100, and (3) add the percent sign % to it.

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

How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). Used symbols: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.