Chapter 7 — Fractions

Chapter 7 teaches fractions as equal shares of a whole. It covers fractional units, numerator and denominator, fractions on the number line, mixed fractions, equivalent fractions, simplest form, comparing fractions, and adding or subtracting fractions using Brahmagupta's method.

A fractional unit is each equal part when one whole unit is divided into equal parts. For example, when 1 is divided into 4 equal parts, each part is 1/4, which is a fractional unit. These are also called unit fractions.

Think of them as shares: 1/5 means one unit shared among 5 people, and 1/9 means shared among 9 people. More people means a smaller share, so 1/5 > 1/9. In general, for unit fractions, the larger the denominator, the smaller the fraction.

In a proper fraction, the numerator is smaller than the denominator (e.g., 3/5), so the fraction is less than 1. In an improper fraction, the numerator is larger than the denominator (e.g., 7/3), so the fraction is greater than 1. Improper fractions can be written as mixed fractions.

Divide the numerator by the denominator. The quotient is the whole number part and the remainder becomes the new numerator. For example, 8/3: 8 ÷ 3 = 2 remainder 2, so 8/3 = 2 and 2/3.

Equivalent fractions represent the same value, like 1/2 = 2/4 = 3/6. To find an equivalent fraction, multiply (or divide) both the numerator and denominator by the same non-zero number.

Find the highest common factor (HCF) of the numerator and denominator, then divide both by it. For example, 36/60: HCF is 12, so 36÷12 = 3 and 60÷12 = 5, giving 3/5 in lowest terms.

Use Brahmagupta's method: (1) Find a common multiple of the denominators. (2) Convert each fraction to an equivalent fraction with that common denominator. (3) Add the numerators. (4) Simplify to lowest terms if needed. Example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12.

Same as Brahmagupta's method for addition: convert to a common denominator, then subtract numerators. Example: 3/4 - 2/3 = 9/12 - 8/12 = 1/12.

Brahmagupta was a 7th-century Indian mathematician (628 CE) who first formally codified the rules for adding, subtracting, and working with fractions in general. His method — converting fractions to a common denominator and then operating on numerators — is exactly what students learn and use today worldwide.

The modern way of writing fractions originated in India. The Bakshali manuscript (around 300 CE) shows fractions written very similarly to how we write them today. The line (vinculum) between numerator and denominator was added by the Moroccan mathematician Al-Hassar in the 12th century. The notation spread to Europe via Arabic scholars and became globally standard by the 17th century.

Yes. The official NCERT PDF for Ganita Prakash Class 6 Chapter 7 (Fractions) is available free of charge on the NCERT website (ncert.nic.in) with no sign-up required. Our app also provides it free — no account needed.