What are Fractions?
Fractions are defined as numeric values that express a part of a whole or group of items. A fraction represents a part of the whole in which the numerator (top number) and the denominator (bottom number) are differentiated by a horizontal bar called a fractional bar. The numerator expresses the number of parts of the whole, while the denominator represents the number of equal parts the whole is divided into. For example, \(\frac{1}{4}\), is a fraction, in which ‘1’ represents part of the whole, which is 4.
What are the Types of Fractions?
The following are the different types of fractions:
- Unit Fractions – These fractions have 1 as their numerator.
- Proper Fractions – These are the fractions in which the numerator is less than the denominator.
- Improper Fractions – These are the fractions in which the numerator is more than or equal to the denominator.
- Mixed Fractions – These fractions have a fraction and a whole number together. Mixed fractions are always greater than 1 and are also called mixed numbers.
- Like Fractions – Two or more fractions having the same denominators.
- Unlike Fractions – Two or more fractions that have different denominators.
- Equivalent Fractions – These fractions when simplified, result in the same value of the numerator and denominator.
Solved Examples
Example 1: Amy and her friends participated in a writing contest. 3 of her 10 friends are left-handed, while the remaining are right-handed. What fraction of Amy’s friends are right-handed?
Solution:
Let us find out the number of right-handed writers.
There are 10 – 3 = 7 children who are right-handed.
7 out of 10 children are right-handed.
Hence, we can write the fraction as \(\frac{7}{10}\), or ‘seven-tenths’ of Amy’s friends are right-handed.
Example 2: Which type of fraction are the following fractions?
\(\frac{1}{4}, \frac{2}{8}, \frac{3}{12}, \frac{4}{16}.\)
Solution:
Let’s simplify each fraction,
\(\frac{1}{4}\) is already in its simplified form.
\(\frac{2}{8} = \frac{2\div 2}{8 \div 2} = \frac{1}{4}\)
\(\frac{3}{12} = \frac{3\div 3}{12 \div 3} = \frac{1}{4}\)
\(\frac{4}{16} = \frac{4\div 4}{16 \div 4} = \frac{1}{4}\)
So, \(\frac{1}{4} = \frac{2}{8} = \frac{3}{12} = \frac{4}{16}.\)
Hence, the given fractions form a set of equivalent fractions.
Example 3: Is \(\frac{5}{8} \) an improper fraction?
Solution:
The given fraction, \(\frac{5}{8} \) has a numerator of 5 and a denominator of 8.
Now, 5 < 8, that is, the numerator is less than the denominator, so \(\frac{5}{8} \) is a proper fraction, and not an improper fraction.
Hence, \(\frac{5}{8} \) is not an improper fraction.
Unit fractions always have a numerator equal to 1 and a denominator equal to any natural number. So, all unit fractions are proper fractions.
Knowledge of fractions comes in handy when splitting bills, cooking, percentage scores, discount calculations and in many other situations.
Fractions are generally simplified to their lowest forms to ease and simplify mathematical calculations.
Divide the numerator of an improper fraction by its denominator to express improper fractions as mixed numbers. Write the quotient as the whole number part and the fractional part will have the remainder as the numerator and the original denominator of the improper fraction is retained.