How do you find equivalent fractions?

Multiply or divide both the numerator and denominator by the same non-zero number. For example, 1/3 = 2/6 = 3/9 = 4/12. All of these are equivalent because you are multiplying top and bottom by the same number (2, 3, 4, etc.).

How do you add fractions with different denominators?

First, find the LCM of the denominators. Then convert each fraction to an equivalent fraction with that LCM as the denominator. Finally, add the numerators and keep the common denominator. Simplify if possible. For example, 1/3 + 1/4: LCM of 3 and 4 is 12. So 4/12 + 3/12 = 7/12.

What is the simplest form of a fraction?

A fraction is in its simplest form when the numerator and denominator have no common factor other than 1. To simplify, divide both by their HCF. For example, 8/12: HCF of 8 and 12 is 4. So 8/12 = 2/3, which is in simplest form.

Why can the denominator of a fraction not be zero?

The denominator tells you how many equal parts the whole is divided into. Dividing something into 0 parts does not make sense. Mathematically, division by zero is undefined, so a fraction with denominator 0 has no meaning.

Study Guide

Fractions Class 6: Types, Comparison, Addition & Subtraction

Q: What is the difference between a proper and an improper fraction?

In a proper fraction, the numerator is smaller than the denominator (e.g., 3/4), so the value is less than 1. In an improper fraction, the numerator is greater than or equal to the denominator (e.g., 7/4), so the value is 1 or more. Every improper fraction can be written as a mixed fraction.

A clear, visual guide to fractions for Class 6 CBSE. From understanding what a fraction means to adding and subtracting unlike fractions, this covers it all.

CBSEClass 6

SparkEd Team · Reviewed by Vivek Verma15 March 202610 min read

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What Is a Fraction?

Looking for a class 6 math worksheet or maths worksheet for class 6 with answers? This comprehensive resource covers everything you need. A fraction represents a part of a whole. When you cut a pizza into 4 equal slices and eat 1 slice, you have eaten $\frac{1}{4}$ of the pizza.

A fraction is written as:

\frac{\text{Numerator}}{\text{Denominator}}

- The numerator (top number) tells you how many parts you have.
- The denominator (bottom number) tells you how many equal parts the whole is divided into.

For example, in $\frac{3}{5}$ : the numerator is $3$ (you have 3 parts) and the denominator is $5$ (the whole is divided into 5 equal parts).

Important: The denominator can never be zero. $\frac{3}{0}$ is undefined.

Beyond this worksheet, SparkEd offers interactive online practice for Fractions with step-by-step solutions and progress tracking — perfect for daily revision.

Fractions on the Number Line

Just like whole numbers, fractions can be placed on a number line.

To plot $\frac{3}{4}$ on a number line:
1. The fraction is between $0$ and $1$ (since $\frac{3}{4} < 1$ ).
2. Divide the segment from $0$ to $1$ into $4$ equal parts.
3. Count $3$ parts from $0$ . That point is $\frac{3}{4}$ .

To plot $\frac{7}{4}$ on a number line:
1. $\frac{7}{4} = 1\frac{3}{4}$ , so it is between $1$ and $2$ .
2. Divide the segment from $1$ to $2$ into $4$ equal parts.
3. Count $3$ parts from $1$ . That point is $\frac{7}{4}$ .

The number line helps you see that fractions are not just "parts of things" but actual numbers with precise positions.

Types of Fractions

There are several ways to classify fractions.

Proper, Improper, and Mixed Fractions

Proper fraction: The numerator is less than the denominator. The fraction is less than $1$ .

\frac{2}{5},\ \frac{3}{7},\ \frac{11}{12} \quad (\text{all less than } 1)

Improper fraction: The numerator is greater than or equal to the denominator. The fraction is greater than or equal to $1$ .

\frac{7}{4},\ \frac{5}{3},\ \frac{9}{9} \quad (\text{all } \ge 1)

Mixed fraction: A combination of a whole number and a proper fraction.

1\frac{3}{4},\ 2\frac{1}{3},\ 5\frac{2}{7}

Converting improper fraction to mixed fraction:
Divide the numerator by the denominator.

\frac{7}{4} = 1 \text{ remainder } 3 = 1\frac{3}{4}

Converting mixed fraction to improper fraction:

a\frac{b}{c} = \frac{a \times c + b}{c}

2\frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{13}{5}

Like and Unlike Fractions

Like fractions: Fractions with the same denominator.

\frac{2}{7},\ \frac{5}{7},\ \frac{1}{7} \quad (\text{all have denominator } 7)

Unlike fractions: Fractions with different denominators.

\frac{2}{3},\ \frac{4}{5},\ \frac{1}{6} \quad (\text{different denominators})

Like fractions are easy to compare and add. Unlike fractions need to be converted to like fractions first (by finding a common denominator).

Unit Fractions

A unit fraction has $1$ as its numerator.

\frac{1}{2},\ \frac{1}{3},\ \frac{1}{4},\ \frac{1}{5},\ \frac{1}{10}

Unit fractions are important because any fraction can be thought of as a multiple of a unit fraction:

\frac{3}{5} = 3 \times \frac{1}{5}

Comparing unit fractions: Among unit fractions, the one with the smaller denominator is larger.

\frac{1}{3} > \frac{1}{5} > \frac{1}{8} > \frac{1}{100}

This makes sense: if you divide a pizza into 3 pieces, each piece is bigger than if you divided it into 5 pieces.

Equivalent Fractions

Equivalent fractions are different fractions that represent the same value.

\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10}

To get an equivalent fraction, multiply (or divide) both the numerator and denominator by the same non-zero number.

\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}

\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}

How to check if two fractions are equivalent: Cross multiply. If the cross products are equal, the fractions are equivalent.

\frac{a}{b} = \frac{c}{d} \quad \text{if and only if} \quad a \times d = b \times c

Example: Are $\frac{3}{4}$ and $\frac{9}{12}$ equivalent?
$3 \times 12 = 36$ and $4 \times 9 = 36$ . Yes, they are equivalent.

Simplest Form (Lowest Terms)

A fraction is in its simplest form (or lowest terms) when the numerator and denominator have no common factor other than $1$ .

To reduce a fraction to its simplest form, divide both the numerator and the denominator by their HCF (Highest Common Factor).

Example: Simplify $\frac{12}{18}$ .
- HCF of $12$ and $18$ is $6$ .
- $\frac{12}{18} = \frac{12 \div 6}{18 \div 6} = \frac{2}{3}$

Example: Simplify $\frac{35}{49}$ .
- HCF of $35$ and $49$ is $7$ .
- $\frac{35}{49} = \frac{35 \div 7}{49 \div 7} = \frac{5}{7}$

Quick check: If the numerator and denominator are both even, you can definitely simplify by dividing by $2$ . If both end in $0$ or $5$ , divide by $5$ . Keep dividing until no common factor remains.

Comparing Fractions

There are several methods to compare fractions.

Comparing Like Fractions

When the denominators are the same, compare the numerators. The fraction with the larger numerator is greater.

\frac{5}{9} > \frac{3}{9} > \frac{1}{9}

This is intuitive: out of 9 equal pieces, having 5 pieces is more than having 3 pieces.

Comparing Unlike Fractions

When the denominators are different, convert to like fractions by finding the LCM of the denominators.

Example: Compare $\frac{3}{4}$ and $\frac{5}{6}$ .

LCM of $4$ and $6 = 12$ .

\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}

\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}

Now compare: $\frac{10}{12} > \frac{9}{12}$ , so $\frac{5}{6} > \frac{3}{4}$ .

Cross multiplication shortcut: To compare $\frac{a}{b}$ and $\frac{c}{d}$ :
- If $a \times d > b \times c$ , then $\frac{a}{b} > \frac{c}{d}$
- If $a \times d < b \times c$ , then $\frac{a}{b} < \frac{c}{d}$
- If $a \times d = b \times c$ , then $\frac{a}{b} = \frac{c}{d}$

For $\frac{3}{4}$ and $\frac{5}{6}$ : $3 \times 6 = 18$ and $4 \times 5 = 20$ . Since $18 < 20$ , $\frac{3}{4} < \frac{5}{6}$ .

Addition and Subtraction of Fractions

Adding and subtracting fractions is one of the most important skills in Class 6 Maths.

Like Fractions (Same Denominator)

When the denominators are the same, simply add (or subtract) the numerators. The denominator stays the same.

\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

Examples:

\frac{2}{7} + \frac{3}{7} = \frac{2 + 3}{7} = \frac{5}{7}

\frac{5}{9} - \frac{2}{9} = \frac{5 - 2}{9} = \frac{3}{9} = \frac{1}{3}

Always simplify the result to its lowest terms.

Unlike Fractions (Different Denominators)

When the denominators are different, you must first convert them to like fractions.

Step 1: Find the LCM of the denominators.
Step 2: Convert each fraction to an equivalent fraction with the LCM as the denominator.
Step 3: Add or subtract the numerators.
Step 4: Simplify if possible.

Example: $\frac{2}{3} + \frac{1}{4}$

LCM of $3$ and $4 = 12$ .

\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}

\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}

\frac{8}{12} + \frac{3}{12} = \frac{11}{12}

Example: $\frac{5}{6} - \frac{1}{4}$

LCM of $6$ and $4 = 12$ .

\frac{5}{6} = \frac{10}{12}, \quad \frac{1}{4} = \frac{3}{12}

\frac{10}{12} - \frac{3}{12} = \frac{7}{12}

Adding and Subtracting Mixed Fractions

Method 1: Convert to improper fractions first.

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

= \frac{7}{3} + \frac{5}{4}

LCM of $3$ and $4 = 12$ .

= \frac{28}{12} + \frac{15}{12} = \frac{43}{12} = 3\frac{7}{12}

Method 2: Add whole parts and fraction parts separately.

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

Whole parts: $2 + 1 = 3$
Fraction parts: $\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$
Result: $3\frac{7}{12}$

Both methods give the same answer. Use whichever feels more comfortable.

Common Mistakes to Avoid

\frac{1}{2} + \frac{1}{3} \ne \frac{2}{5}

Practice on SparkEd

Fractions are one of those topics that come back again and again, in Class 7 (multiplication and division of fractions), Class 8 (rational numbers), and all the way through Class 10. Getting the basics right now will save you a lot of trouble later.

SparkEd has 60 practice questions on Fractions for Class 6 CBSE, covering every type discussed above. Each question has a detailed step-by-step solution.

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