Fractions

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Math fractions are numbers expressed as the ratio of two numbers. They are mainly used as a comparison between parts and the whole. A fraction could be a part of an object or a group of objects, for example; one half of pastry is found by cutting the whole pastry into two equal parts. Likewise, one half of a packet of jelly beans by dividing the jelly beans into two equal groups. Each group or share is better known as one half, which is the same for other fractions. In essence, fractions that are equivalent are nothing but fractions that are equal.

An example of this is that 3 out of 7 is equivalent to 6 out of 14.

In learning fractions, you may learn about fractions as follows:

  • Addition
  • Subtraction
  • Multiplication
  • Division
  • Comparing fractions
  • Converting fractions.

Fractions are expressed in two different forms: display notation a/b and in-line notation \frac{a}{b}, where a is the numerator, and b is the denominator.

The numerator shows how many of parts belong to the fraction and the denominator shows into what parts the unit is divided.

Below are some basic formulas with fractions:

Addition: \frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{(ad + bc)}{bd}

Subtraction: \frac{a}{b} - \frac{c}{d} = \frac{ad}{bd} - \frac{bc}{bd} = \frac{(ad - bc)}{bd}

Multiplication: \frac{a}{b} \ast \frac{c}{d} = \frac{ac}{bd}

Division: \frac{a}{b} \div \frac{c}{d} = \frac{ad}{bс}

Fraction Calculator

When there are difficult Math problems with fractions you can use online fraction calculators to compute any Math question concerning fractions.

How to Simplify Fractions

There are basic principles to simplifying fractions:

  • Find the common factor of both the numerator and denominator (A common factor is any number that divides both the numerator and denominator).  Like 3 divides 6 and 21.
  • Continue dividing the fraction with the common factor till there are no more common factors in the numerator and denominator.
  • The fraction is regarded as a simplified fraction as there are no common factors remaining that can divide both the numerator and denominator.