Working With | Class 7 Mathematics Notes

Multiplying a Fraction by a Whole Number

This section focuses on the multiplication of a fraction by a whole number, a concept that builds on the idea of repeated addition. When a fraction is multiplied by a whole number, it means adding that fraction as many times as the whole number indicates. The section explains this concept with step-by-step examples and visual illustrations. For example, multiplying 4 by (3/7) means adding (3/7) four times: (3/7) + (3/7) + (3/7) + (3/7) = (12/7). The section also introduces the shortcut method of multiplication where the whole number is converted into a fraction by placing it over 1, i.e., 4 becomes (4/1), and then the numerators and denominators are multiplied directly: (4/1) × (3/7) = (4 × 3)/(1 × 7) = 12/7. This method is more efficient and is used for multiplying any two fractions. The section emphasizes the importance of simplifying the product to its lowest terms or converting improper fractions to mixed numbers for better understanding. Visual aids such as number lines and shaded diagrams are used to illustrate the process clearly. The section also discusses real-life applications such as calculating quantities in recipes or measurements where fractions are multiplied by whole numbers. By the end of this section, students should be confident in multiplying fractions by whole numbers using both repeated addition and the multiplication rule.

📊 Diagram: Diagrams include a rectangle divided into 3 equal parts with 2 parts shaded to represent 2/3, repeated 5 times side by side to illustrate 5 × (2/3). Number line diagrams show jumps of (2/3) repeated 5 times to reach 10/3.

🧪 Activity: Activity 2: Students use colored paper strips divided into equal parts to visually multiply fractions by whole numbers by combining shaded parts and counting total parts.

🔗 Connection: This section leads to the multiplication of two fractions, where both numbers are fractions, extending the concept beyond whole numbers.