CBSE Notes Class 6 Maths Chapter 7 Fractions

Fractions are an essential concept in mathematics that appear in many areas of life, from measuring ingredients to dividing a pizza! In Class 6, students are introduced to fractions in a deeper way, exploring various types and operations involving fractions. In this blog, we’ll take a closer look at key topics related to fractions, including fractional units, unit fractions, mixed fractions, equivalent fractions, and more. Let’s dive into the world of fractions!

1.0What is a Fraction?

A fraction represents a part of a whole or a part of a group. It is written as a numerator (the top number) and a denominator (the bottom number), separated by a slash or a horizontal line (Eg:$\frac{1}{2},\frac{3}{4},\frac{5}{6}$). Understanding fractions involves recognizing how a whole can be divided into equal parts.

2.0Fractional Units as Parts of a Whole

In the world of fractions, the fractional unit refers to one of the equal parts into which a whole is divided. For example, if you divide a pizza into 8 equal slices, each slice is a fractional unit. In this case, each slice represents $\frac{1}{8}$ of the whole pizza. When you divide something into fractional units, you're essentially splitting it into parts that represent a fraction of the entire object.

Unit Fractions

A unit fraction is a fraction where the numerator is always 1, and the denominator represents the number of equal parts the whole is divided into. For example:

• $\frac{1}{2}$ is a unit fraction representing one half of a whole.
• $\frac{1}{3}$ represents one third of a whole.

Unit fractions are the building blocks of all other fractions. They help us understand how a whole can be divided into smaller parts.

3.0Measuring Using Fractional Units

Measuring with fractional units allows us to quantify portions of objects or quantities. For instance, when you measure $\frac{3}{4}$ of a meter, it means that the meter has been divided into four equal parts, and three of those parts are being used. This is especially helpful in real-world applications like cooking, construction, or tailoring, where portions of a whole are often required.

4.0Marking Fraction Lengths on the Number Line

A number line is a powerful tool for visualizing fractions. To mark fractional lengths on a number line, first, divide the segment between two whole numbers into equal parts. These parts represent the fractional units. For example, if you're working with $\frac{3}{4}$, divide the segment between 0 and 1 into four equal parts, and mark the point that represents $\frac{3}{4}$.

5.0Mixed Fractions

A mixed fraction is a combination of a whole number and a fraction. 

For example, $2\frac{1}{2}$ is a mixed fraction, where 2 is the whole number and $\frac{1}{2}$ is the fractional part. Mixed fractions are often used in everyday situations, such as when measuring distances or quantities that aren't whole numbers. 

Converting Between Mixed Fractions and Improper Fractions

Sometimes it’s useful to convert a mixed fraction into an improper fraction (where the numerator is larger than the denominator), or vice versa. For example:

• $2\frac{1}{2}$ can be written as the improper fraction $\frac{5}{2}(since2\times 2+1=5)$.
• $\frac{5}{2}$ can be rewritten as the mixed fraction $2\frac{1}{2}.$

6.0Equivalent Fractions

Two fractions are equivalent if they represent the same portion of a whole, even though they may have different numerators and denominators. For example:

• $\frac{1}{2}$ is equivalent to $\frac{2}{4},\frac{4}{8},\frac{8}{16}$, and so on.

To find equivalent fractions, you can multiply or divide both the numerator and the denominator by the same number. For instance, if you multiply both the numerator and denominator of $\frac{1}{2}$ by 2, you get $\frac{2}{4}$, which is an equivalent fraction.

7.0Comparing Fractions

To compare fractions, it’s helpful to:

1. Find a common denominator: This makes the fractions easier to compare. For example, to compare $\frac{1}{3}$ and $\frac{2}{5}$, you could find the least common denominator (LCD) and rewrite both fractions with that denominator.
2. Use the number line: Marking fractions on a number line allows for a clear visual comparison. The fraction closer to 0 is the smaller fraction.

Which Fraction is Bigger?

To compare fractions with the same denominator, simply look at the numerators. The fraction with the larger numerator is the larger fraction. For example, $\frac{3}{8}$ is greater than $\frac{2}{8}$ because 3 is greater than 2.

8.0Addition and Subtraction of Fractions

Adding and subtracting fractions can be tricky, but once you understand the process, it becomes much easier.

1. Addition of Fractions

If the denominators are the same, just add the numerators. For example:

$\frac{1}{4}+\frac{2}{4}=\frac{3}{4}$

If the denominators are different, first find the LCM (Least Common Multiple) of the denominators, rewrite the fractions with a common denominator, and then add the numerators. For example:

$\frac{1}{3}+\frac{1}{6}$: The LCM of 3 and 6 is 6, so rewrite as

$\frac{2}{6}+\frac{1}{6}=\frac{3}{6}=\frac{1}{2}.$

2. Subtraction of Fractions

Subtraction is similar to addition. Ensure the fractions have the same denominator, then subtract the numerators. For example:

$\frac{3}{5}-\frac{1}{5}=\frac{2}{5}$

If the denominators are different, find a common denominator, just like in addition, and then subtract the numerators.

9.0A Pinch of History: The Origins of Fractions

Fractions have a long history that dates back thousands of years. The ancient Egyptians were among the first to use fractions, especially in their mathematical texts. They primarily used unit fractions, as they believed fractions could only be represented as a sum of unit fractions.

The concept of fractions evolved over time, especially during the Islamic Golden Age, when mathematicians like Al-Khwarizmi contributed to understanding fractions as parts of a whole. Today, fractions are a foundational concept in mathematics, essential for everything from algebra to calculus.