Fractions — Class 6

Fractions are how we describe parts of a whole. When we cut a roti into 4 equal parts and eat 1 piece, we’ve eaten one-fourth or $\frac{1}{4}$ of it. That little stack of two numbers separated by a line is a fraction. Once we get comfortable with what fractions mean, addition, subtraction, and comparison all become natural.

This chapter is the foundation for everything that comes later — decimals, ratios, percentages, and even algebra. So let’s understand fractions properly, not just memorise rules.

What Exactly is a Fraction?

A fraction has two parts:

Numerator (top number): how many parts we have
Denominator (bottom number): how many equal parts the whole is divided into

So $\frac{3}{4}$ means: the whole was cut into 4 equal parts, and we have 3 of them.

The line between them means “out of” or “divided by”. $\frac{3}{4}$ literally reads “3 out of 4” or “3 divided by 4”.

Types of Fractions

Proper fraction — Numerator smaller than denominator. Value less than 1. Examples: $\frac{1}{2}, \frac{3}{4}, \frac{5}{8}$

Improper fraction — Numerator equal to or greater than denominator. Value 1 or more. Examples: $\frac{5}{3}, \frac{7}{2}, \frac{9}{9}$

Mixed fraction — A whole number plus a proper fraction. Examples: $1\frac{1}{2}$ (read “one and a half”), $2\frac{3}{4}$

Unit fraction — A proper fraction with numerator 1. Examples: $\frac{1}{2}, \frac{1}{3}, \frac{1}{10}$

Like fractions — Fractions with the same denominator. Examples: $\frac{2}{7}, \frac{3}{7}, \frac{5}{7}$

Unlike fractions — Fractions with different denominators. Examples: $\frac{1}{2}, \frac{1}{3}, \frac{1}{5}$

Equivalent Fractions

Two fractions are equivalent if they represent the same amount, even though they look different.

$\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{50}{100}$

All of these mean “half” — half a chapati, half a glass of water, half an hour.

If you multiply the numerator and denominator by the same non-zero number, you get an equivalent fraction:

$\frac{a}{b} = \frac{a \times k}{b \times k}$

If you divide both by the same non-zero number, you also get an equivalent fraction (provided the division gives whole numbers).

Example

$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$ . So $\frac{2}{3}$ and $\frac{10}{15}$ are equivalent.

Simplest Form (Lowest Terms)

A fraction is in simplest form when the numerator and denominator have no common factor other than 1.

To simplify a fraction:

Find the greatest common factor (GCF) of numerator and denominator
Divide both by it

Example: Simplify $\frac{12}{18}$ .

GCF of 12 and 18 is 6.

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

So $\frac{12}{18}$ in simplest form is $\frac{2}{3}$ .

Comparing Fractions

Like fractions (same denominator): the one with the bigger numerator is bigger. $\frac{3}{7} > \frac{2}{7}$ because we have 3 parts versus 2 parts of the same size.

Unlike fractions (different denominators): convert to like fractions first by finding a common denominator (LCM of denominators).

Example: Compare $\frac{2}{3}$ and $\frac{3}{5}$ .

LCM of 3 and 5 is 15.

$\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}$

$\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}$

Now compare like fractions: $\frac{10}{15} > \frac{9}{15}$ , so $\frac{2}{3} > \frac{3}{5}$ .

Adding and Subtracting Fractions

Like fractions: Add (or subtract) numerators; keep the same denominator.

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

$\frac{5}{9} - \frac{2}{9} = \frac{3}{9} = \frac{1}{3}$ (after simplification)

Unlike fractions: First convert to like fractions using LCM, then add/subtract.

Example: $\frac{1}{4} + \frac{2}{6}$

LCM of 4 and 6 is 12.

$\frac{1}{4} = \frac{3}{12}$ , $\frac{2}{6} = \frac{4}{12}$

$\frac{3}{12} + \frac{4}{12} = \frac{7}{12}$

Mixed and Improper Conversions

Mixed → Improper: Multiply whole part by denominator, add numerator, keep same denominator.

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

Improper → Mixed: Divide numerator by denominator. Quotient is the whole part; remainder over original denominator is the fraction part.

$\frac{17}{4}$ : $17 \div 4 = 4$ remainder $1$ . So $\frac{17}{4} = 4\frac{1}{4}$ .

Worked Examples

Example 1 — Easy

Add $\frac{1}{3}$ and $\frac{1}{6}$ .

LCM of 3 and 6 is 6. $\frac{1}{3} = \frac{2}{6}$ .

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

Example 2 — Medium

Ravi ate $\frac{2}{5}$ of a cake. His sister ate $\frac{1}{4}$ of the same cake. How much cake did they eat together?

LCM of 5 and 4 is 20.

$\frac{2}{5} = \frac{8}{20}$ , $\frac{1}{4} = \frac{5}{20}$ .

Total: $\frac{8}{20} + \frac{5}{20} = \frac{13}{20}$ .

They ate $\frac{13}{20}$ of the cake together.

Example 3 — Hard

Convert $3\frac{2}{7}$ to an improper fraction, then add it to $\frac{4}{7}$ .

$3\frac{2}{7} = \frac{3 \times 7 + 2}{7} = \frac{23}{7}$ .

$\frac{23}{7} + \frac{4}{7} = \frac{27}{7} = 3\frac{6}{7}$ .

Common Mistakes to Avoid

Mistake 1: Adding numerators AND denominators directly.

$\frac{1}{2} + \frac{1}{3} \neq \frac{2}{5}$ . Wrong! You can’t add denominators. Find a common denominator first.

Mistake 2: Forgetting to simplify the final answer.

$\frac{6}{12}$ should be written as $\frac{1}{2}$ . Always simplify at the end.

Mistake 3: Confusing “smaller denominator means smaller fraction”.

$\frac{1}{2}$ is bigger than $\frac{1}{4}$ even though 2 is smaller than 4. Smaller denominator = bigger pieces!

Mistake 4: Mishandling mixed fractions in addition.

For $1\frac{1}{2} + 2\frac{1}{3}$ , convert both to improper fractions first, then add. Don’t add whole parts and fraction parts separately without care.

Practice Questions

Identify the fraction: a green parrot pecks 3 mangoes out of a total of 8 mangoes on a tree. What fraction did it peck?
Find an equivalent fraction of $\frac{3}{5}$ with denominator 20.
Simplify $\frac{18}{24}$ to its lowest terms.
Compare $\frac{4}{9}$ and $\frac{1}{2}$ . Which is bigger?
Add $\frac{2}{5} + \frac{3}{10}$ .
Subtract: $\frac{7}{12} - \frac{1}{4}$ .
Convert $\frac{19}{6}$ to a mixed fraction.
Convert $4\frac{2}{3}$ to an improper fraction.

Q1: $\frac{3}{8}$

Q2: $\frac{3 \times 4}{5 \times 4} = \frac{12}{20}$

Q3: GCF of 18, 24 is 6. $\frac{18}{24} = \frac{3}{4}$

Q5: LCM of 5, 10 is 10. $\frac{2}{5} = \frac{4}{10}$ . Total: $\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$ .

FAQs

Q: Why do we need a common denominator to add fractions?

Because we can only add quantities of the same size. $\frac{1}{2}$ + $\frac{1}{3}$ is like adding “half a roti” and “third of a roti” — different sizes. Once we convert both to “sixths” ( $\frac{3}{6}$ and $\frac{2}{6}$ ), they’re the same size and we can add them.

Q: What’s the difference between a fraction and a ratio?

A fraction $\frac{3}{4}$ describes a part of a whole (3 out of 4 parts). A ratio 3:4 compares two separate quantities (3 of one thing, 4 of another). They look similar but are used differently.

Q: How do I quickly compare fractions in head?

Use cross-multiplication: to compare $\frac{a}{b}$ and $\frac{c}{d}$ , compare $a \times d$ with $b \times c$ . Whichever is bigger means that fraction is bigger.

Q: When should I leave the answer as an improper fraction vs a mixed fraction?

Both are correct. CBSE Class 6 typically expects mixed fractions in word problems (more readable) and either form in pure-arithmetic problems. Follow your textbook’s convention.

Q: Are decimals just fractions in disguise?

Yes! $0.5 = \frac{1}{2}$ , $0.25 = \frac{1}{4}$ . Decimals are fractions with denominators that are powers of 10 (10, 100, 1000, etc.). Class 6 introduces decimals in a separate chapter, but the concept is the same.