Skip to main content

Class 7 Maths Chapter 8 Working with Fractions NCERT Solutions (Step-by-Step Answers, Concepts & Examples | Ganita Prakash)

Class 7 Maths Chapter 8 Working with Fractions NCERT Solutions (Step-by-Step Answers, Concepts & Examples | Ganita Prakash)

Class 7 Ganita Prakash Navigation

📘 Class 7 Ganita Prakash Chapters

..................................................................................................................

Introduction: 

Hey there, young mathematicians! Imagine you're Aaron from your NCERT Class 7 Math textbook, zooming through 3 km in an hour—or maybe you're his slow-but-steady pet tortoise, covering just 1/4 km. Either way, what if you need to figure out distances for fractional hours or split land equally among friends? That's where multiplication of fractions comes in—it's not just boring numbers; it's the key to real-life problems like sharing pizza, calculating costs, or even tracking the Moon's setting time!

In Chapter 8: Working with Fractions from Ganita Prakash (NCERT Class 7), we dive deep into multiplying whole numbers with fractions and fractions with fractions. This chapter builds on basics like addition but amps up the fun with visual tools like unit squares and rectangles. By the end, you'll not only solve problems effortlessly but also see how fractions connect to areas and everyday scenarios.

Why focus on retention? We've broken it down with step-by-step solutions, engaging examples, quick tips, and visuals from the book. Read on, practice along, and watch your confidence soar—perfect for exams or just conquering math anxiety!

This visual hook shows the 3 km in 5 hours vs. 1/4 km in 3 hours timeline.]

Key Terms and Definitions: Your Fraction Toolkit

Before we multiply like pros, let's nail the basics. Understanding these terms is like having a cheat sheet—quick recall means faster solving!

  • Fraction: A part of a whole, written as numerator/denominator (e.g., 3/4 means 3 parts out of 4 equal parts).
  • Numerator: The top number (tells "how many parts you have").
  • Denominator: The bottom number (tells "total parts in the whole").
  • Whole Number: Integers like 1, 2, 5 (can be rewritten as fractions, e.g., 3 = 3/1).
  • Mixed Fraction: A whole number plus a fraction (e.g., 1 1/4 = 5/4).
  • Multiplicand: The number being multiplied (first in the ×).
  • Multiplier: The number doing the multiplying (second in the ×).
  • Unit Square: A visual tool (1x1 square) representing the "whole" for shading fractions—great for beginners!
  • Simplifying to Lowest Form: Divide numerator and denominator by their greatest common factor (GCF) to get the simplest fraction (e.g., 6/20 = 3/10).

Section 8.1: Multiplying Whole Numbers with Fractions

This section kicks off with relatable stories: Aaron's walks and tortoise trots. The big idea? Multiplication works the same way with fractions—it's just repeated addition in disguise!

Key Concept: Whole × Fraction

To multiply a whole number by a fraction (or vice versa), divide the whole into the fraction's denominator parts, then multiply by the numerator.

Example 1 from Book: A farmer distributes 2/3 acre to each of 5 grandchildren. Total land?

  • Step 1: Recognize it's 5 × (2/3).
  • Step 2: Add repeatedly: 2/3 + 2/3 + 2/3 + 2/3 + 2/3 = (2/3 × 5) = 10/3 acres.
  • Solution: 10/3 acres (or 3 1/3 acres).

Example 2 from Book: 1 hour internet costs ₹8. Cost for 1 1/4 hours?

  • Step 1: Convert mixed: 1 1/4 = 5/4 hours.
  • Step 2: 5/4 × 8 = (5 × 8)/4 = 40/4 = 10.
  • Solution: ₹10

Figure it Out Questions: Step-by-Step Solutions

  1. Tenzin drinks 1/2 glass milk daily. Glasses in a week? In January?
    • Week: 7 days × 1/2 = 7/2 = 3 1/2 glasses.
    • January: 31 days × 1/2 = 31/2 = 15 1/2 glasses.
    • Tip: January has 31 days—quick fact recall!
  2. Team makes 1 km canal in 8 days. Per day? In a week (5 days)?
    • Per day: 1/8 km.
    • Week: 5 × 1/8 = 5/8 km.
  3. Manju's group buys 5 liters oil weekly, shares among 3 families. Per family per week? In 4 weeks?
    • Per week per family: 5/3 liters.
    • 4 weeks: 4 × 5/3 = 20/3 = 6 2/3 liters.
  4. Moon sets 5/6 hour later daily. From Monday 10 pm, when on Thursday?
    • Days: Tue (+5/6), Wed (+5/6), Thu (+5/6). Total: 3 × 5/6 = 15/6 = 2 3/6 = 2 1/2 hours after 10 pm.
    • Solution: 12:30 am Thursday.
  5. Multiply and convert to mixed fraction:
    • (a) 7 × 3/5 = 21/5 = 4 1/5
    • (b) 4 × 1/3 = 4/3 = 1 1/3
    • (c) 9/7 × 6 = 54/7 = 7 5/7
    • (d) 13/11 × 6 = 78/11 = 7 1/7

Multiplying Two Fractions: From Tortoise Trot to Unit Squares

Now, level up! When both are fractions (e.g., time as fraction × distance as fraction), use visuals like unit squares to "shade" the answer.

Key Concept: Fraction × Fraction

Divide the first fraction into the second's denominator parts, then multiply by its numerator. Or, shortcut: (Numerator1 × Numerator2) / (Denominator1 × Denominator2).

Book Example: Tortoise walks 1/4 km/hour. In 1/2 hour?

  • Visual: Divide 1/4 into 2 parts → 1/8 km.
  • Formula: (1×1)/(2×4) = 1/8 km.

Another Example: Faster tortoise: 2/5 km/hour in 3/4 hour?

  • Step 1: Divide 2/5 into 4 parts → 2/20 per part.
  • Step 2: ×3 = 6/20 = 3/10 km.
  • Formula: (3×2)/(4×5) = 6/20 = 3/10.

Visual Insight: 5/4 × 3/2

  • Represent 3/2 (1 whole + 1/2) in unit square.
  • Divide into 4 parts → 3/8 yellow shaded.
  • ×5 = 15/8.

Connection to Rectangle Area

The product of two fractions? It's the area of a rectangle with those sides! E.g., 1/2 × 1/4 = 1/8 (area of shaded rectangle in unit square).

Figure it Out: Visual Products

  1. Using unit square:
    • (a) 1/3 × 1/5 = 1/15 (15 parts, 1 shaded).
    • (b) 1/4 × 1/3 = 1/12.
    • (c) 1/5 × 1/2 = 1/10.
    • (d) 1/6 × 1/5 = 1/30.
    • Now, 1/12 × 1/18 = 1/216 (rows=18, columns=12).
  2. With operations:
    • (a) 2/3 × 4/5 = 8/15.
    • (b) 1/4 × 2/3 = 2/12 = 1/6.
    • (c) 3/5 × 1/2 = 3/10.
    • (d) 4/6 × 3/5 = 12/30 = 2/5.

Multiplying Numerators and Denominators: The Brahmagupta Shortcut

Credit to ancient mathematician Brahmagupta (628 CE)—just multiply tops and bottoms!

General Rule: a/b × c/d = (a×c)/(b×d). Works for wholes too (e.g., 3 = 3/1).

Example: 5/12 × 7/18 = (5×7)/(12×18) = 35/216.

Simplifying to Lowest Form

Don't multiply first—cancel common factors early!

Book Example: 12/7 × 5/24

  • Cancel 12 and 24 by 12: 12÷12=1, 24÷12=2.
  • Now: 1/7 × 5/2 = 5/14.
  • Solution: 5/14.

Retention Tip: Always "cross-cancel" before multiplying—saves time and errors. Practice: 3/8 × 4/9 = ? (Cancel 3 and 9 by 3: 1/8 × 4/3 = 4/24 = 1/6).

Wrapping Up: Practice for Mastery & Next Steps

You've just unlocked fraction multiplication—like turning tortoise speed into Aaron's sprint! Key takeaway: Visualize with squares, simplify early, and relate to real life.

Quick Retention Quiz:

  1. 2/3 × 3/4 = ? (A: 1/2)
  2. Cost for 3/2 hours at ₹10/hour? (A: ₹15)

For more, download full NCERT solutions or join Fuzy Math Academy's free webinars. What's your toughest fraction problem? Comment below—we reply fast!

Math Academy: Making Math Fun & Fearless | Follow for daily tips!









For more clear explanations and solved questions, keep visiting

Fuzymath Academy

✔ For more NCERT Maths solutions and online classes, visit

www.fuzymathacademy.com

📞 Call: 6264302661

Next Chapter More Chapters Coming Soon

15 FAQs – Ganita Prakash (Class 7, Chapter 8 Working with Fractions)

Q1. How do we multiply a fraction with a whole number?
Divide the whole number by the denominator, then multiply by the numerator. Example: \( \frac{2}{5} \times 3 = \frac{6}{5} \).
Q2. How do we multiply two fractions?
Multiply numerators together and denominators together. Example: \( \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \).
Q3. What is the area model for fraction multiplication?
Represent fractions as sides of a rectangle. The area equals the product of the fractions.
Q4. How do we simplify fractions during multiplication?
Cancel common factors between numerator and denominator before multiplying. Example: \( \frac{12}{7} \times \frac{5}{24} = \frac{5}{14} \).
Q5. What is the reciprocal of a fraction?
Reciprocal means flipping numerator and denominator. Example: Reciprocal of \( \frac{3}{5} \) is \( \frac{5}{3} \).
Q6. How do we divide fractions?
Multiply the dividend by the reciprocal of the divisor. Example: \( \frac{2}{3} \div \frac{5}{6} = \frac{2}{3} \times \frac{6}{5} = \frac{12}{15} = \frac{4}{5} \).
Q7. When is the quotient greater than the dividend?
When dividing by a fraction less than 1, the quotient is greater than the dividend. Example: \( 6 \div \frac{1}{4} = 24 \).
Q8. What is the angle sum property of fractions in multiplication?
Not applicable to fractions. Instead, remember: product = numerator × numerator ÷ denominator × denominator.
Q9. How do we convert improper fractions to mixed fractions?
Divide numerator by denominator. Example: \( \frac{7}{3} = 2 \frac{1}{3} \).
Q10. What happens when both fractions are between 0 and 1?
The product is smaller than both fractions. Example: \( \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} \).
Q11. What happens when both fractions are greater than 1?
The product is greater than both numbers. Example: \( \frac{3}{2} \times \frac{5}{3} = \frac{15}{6} = \frac{5}{2} \).
Q12. What happens when one fraction is less than 1 and the other greater than 1?
The product lies between the two numbers. Example: \( \frac{1}{2} \times 4 = 2 \).
Q13. Does the order of multiplication of fractions matter?
No. Multiplication is commutative. Example: \( \frac{2}{3} \times \frac{4}{5} = \frac{4}{5} \times \frac{2}{3} \).
Q14. How do we find the area of a rectangle with fractional sides?
Multiply the fractional lengths of sides. Example: \( \frac{3}{2} \times \frac{9}{2} = \frac{27}{4} \).
Q15. What is Brahmagupta’s rule for fractions?
Multiplication: product of numerators ÷ product of denominators. Division: multiply by reciprocal of divisor.
💬