Notes Maths Class 7 Chapter 8 Ganita Prakash

Notes For All Chapters – Ganita Prakash Class 7th

Working with Fractions

1 Multiplication of Fractions

Fraction × Whole Number

Multiply the whole number with the numerator of the fraction.

Example:

\(\frac{2}{5}\)×3 = \(\frac{6}{5}\)

​Whole Number × Fraction

Same rule as above, order doesn’t matter.

3×\(\frac{2}{5}\) = \(\frac{6}{5}\)

Mixed Fraction × Whole Number

Convert the mixed number to improper fraction first.

Example:

1\(\frac{1}{4}\) ​= \(\frac{5}{4}\)

​\(\frac{5}{4}\)×8 = \(\frac{40}{4}\) = 10

2. Multiplication of Two Fractions

Multiply Numerators and Denominators:

​​\(\frac{a}{b}\) × ​​\(\frac{c}{d}\) = ​\(\frac{a\times c}{b\times d}\)  

Example:

​​​\(\frac{2}{3}\) × ​​​\(\frac{3}{4}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\)

Simplify before multiplying:

Cancel common factors to make calculations easier.

Example:

​​​\(\frac{5}{12}\) × ​​​\(\frac{6}{10}\) =​​​ \(\frac{1}{2}\)

3. Division of Fractions

Use Reciprocal

​​​\(\frac{a}{b}\) ​÷ ​​​\(\frac{c}{d}\) = ​​​\(\frac{a}{b}\) × \(\frac{d}{c}\)

Flip the second fraction and multiply.

​​​\(\frac{2}{3}\) ​÷ ​​​\(\frac{4}{5}\) = ​​​\(\frac{2}{3}\) × ​​​\(\frac{5}{4}\) = ​​​\(\frac{10}{12}\) = ​​​\(\frac{5}{6}\)

​4. Word Problems

• Rate Problems: Multiply time/distance with the rate.
• Sharing Equally: Use division of fractions.
• Area: Multiply length × breadth, even for fractional sides.

Example:

Q. If 1 litre of milk makes 5 cups of tea, how much milk in 1 cup?

A. ​​​\(\frac{1}{5}\) litre

5. Important Concepts and Observations

When is the product smaller or bigger?

Multiplication Comparison Cases

6. Geometry and Fractions

Area of Rectangle = Length × Breadth

Even with fractions:

​​​\(\frac{1}{2}\) × ​​​\(\frac{1}{4}\) = \(\frac{1}{8}\) sq. units

7. Historical Notes (Optional for Interest)

Indian mathematicians like Brahmagupta, Bhāskara II gave rules for multiplying and dividing fractions.

Example from Līlāvatī:

​​​\(\frac{1}{2}\) × ​​​\(\frac{2}{3}\) × ​​​\(\frac{3}{4}\) × ​​​\(\frac{1}{5}\) × ​​​\(\frac{1}{16}\) × ​​​\(\frac{1}{4}\)  = \(\frac{1}{1280}\)

​8. Keywords and Definitions