What are Fractions?
Fractions are parts of a whole or a collection of objects. A fraction is usually represented with two parts. The number on the top shows how many equal parts of the whole are considered. It’s known as the numerator. The number below the numerator expresses the total number of equal parts the whole has been divided into, and it’s known as the denominator.
For example, there are four equal parts as a whole out of which three parts have been shaded. Hence, the fraction will be \(\frac{3}{4}\).
What is the Denominator?
As we have already learned, denominators are an integral part of fractions.
Denominators are written as the bottom numbers in a fraction. This number gives us information about the number of equal parts that the whole has been divided into, as mentioned earlier.
From the example about the fraction \(\frac{3}{4}\), we can show the denominator as:
Give a Real Life Example of a Denominator
One of the classic examples of a denominator is shown with a pizza. Suppose there are 8 slices of pizza in total, and you take one slice from it. So your share from the total number of pizza pieces is \(\frac{1}{8}\).
Solved Examples on Denominator
Example 1: Annete bought an orange and divided it into 8 pieces to distribute it among her siblings. She gave 3 pieces out of the total to her brother. Now write it in fraction form to show what Annete’s brother got from the orange.
Answer:
Total number of orange pieces = 8
The number of pieces Annete gave to her brother = 3
Hence, we can write it in fraction form as \(\frac{3}{8}\), where the numerator is the number of pieces of orange given to him, while the denominator is the total number of pieces of the orange.
Example 2: Find the total of \(\frac{2}{3}+\frac{4}{5}\).
Answer:
Since we have fractions having different denominators, we will convert the unlike fractions(with different denominators) to like fractions(with the same denominator) by changing them to equivalent fractions.
The L.C.M of denominators 3 and 5 will be 15.
Now, \(\frac{2}{3\ }=\frac{2\times5}{3\times5}=\frac{10}{15}\) [Multiply numerator and denominator with 5]
and, \(\frac{4}{5\ }=\frac{4\times3}{5\times3}=\frac{12}{15}\) [Multiply numerator and denominator with 3]
So, \(\frac{2}{3\ }+ \frac{4}{5}=\frac{10}{15\ }+\frac{12}{15}\)
= \(\frac{22}{15}\)
When the denominators are the same, the numerators are added as normal addition.
Hence, the required total is \(\frac{22}{15}.\)
Example 3: Find the total of \( \frac{2}{3}+\frac{7}{3}.\)
Answer:
Since the denominators are the same, we are going to add the like fractions(same denominator) in a simple addition method and maintain the same denominator.
So, \( \frac{2}{3}+ \frac{7}{3}=\frac{9}{3}=3\)
Hence, the required total is 3.
Example 4: In the Sahara Deserts, it rains \(\frac{2}{10}\) inches in September, \(\frac{3}{10}\) inches in October, \(\frac{4}{10}\) inches in November. Find the total quantity of rain across these three months?
Answer:
To find the total rain in three months, we have to add all the values.
Since the denominators are the same, we are going to add the like fractions(same denominator) in a simple addition method and retain the same denominator.
So, \( \frac{2}{10}+ \frac{3}{10}+\frac{4}{10}=\frac{2~+~3~+~4}{10}\)
= \(\frac{9}{10}\) inch
Hence, the total rain in the three months is \(\frac{9}{10}\) inches.
Yes, a denominator can be negative.
Fractions having the same denominator are known as common denominators. Common denominators are ideal for various mathematical operations and comparisons.
Unlike denominators are two or more fractions with different denominators.