Working With | Class 7 Mathematics Notes

Multiplying a Fraction by a Fraction

In this section, the multiplication of one fraction by another fraction is introduced. This operation is a natural extension of multiplying a fraction by a whole number. The key idea is to find a part of a part, which means multiplying the numerators to get the new numerator and the denominators to get the new denominator. The section explains this with detailed examples and visual models such as area models and number lines. For example, multiplying (2/3) by (3/4) means taking (3/4) of (2/3), which is (2 × 3)/(3 × 4) = 6/12, which simplifies to 1/2. The section emphasizes the importance of simplifying the product to its lowest terms. Visual models like shaded rectangles divided into rows and columns help students see why the multiplication rule works. The area model shows a rectangle divided into 3 equal parts horizontally and 4 equal parts vertically, shading 2 parts horizontally and 3 parts vertically, and the overlapping shaded area represents the product fraction. The section also discusses how this method applies to real-life problems such as calculating discounts, probability, and parts of quantities. Step-by-step problem-solving strategies are provided to build confidence in multiplying fractions. The section concludes with practice problems to reinforce the concept.

📊 Diagram: The section includes an area model diagram where a rectangle is divided into 3 equal parts horizontally and 4 equal parts vertically. Two parts are shaded horizontally and three parts vertically. The overlapping shaded area (6 parts out of 12 total parts) represents the product (2/3) × (3/4) = 6/12 = 1/2.

🧪 Activity: Activity 3: Students use grid paper to shade fractions and find the product by counting overlapping shaded squares, reinforcing the area model concept.

🔗 Connection: This section prepares students for multiplying mixed numbers and understanding how to convert between mixed numbers and improper fractions for multiplication.