Fractions and Decimals Class 7 Most Important Questions Note

Fractions and Decimals Class 7 Notes | Complete Study Guide with Examples

Introduction

Fractions and Decimals are among the most important topics in Class 7 Mathematics. They form the foundation for higher-level concepts such as Percentage, Ratio & Proportion, Profit & Loss, Algebra, and Data Handling. Previous topic : Algebraic Expressions

Fractions represent a part of a whole, while Decimals provide another way to express fractions using place values. Understanding these concepts helps students solve real-life problems involving money, measurements, and calculations.

हिंदी में:
Fractions (भिन्न) और Decimals (दशमलव) Class 7 Mathematics का एक महत्वपूर्ण अध्याय है। यह अध्याय Percentage, Ratio-Proportion, Algebra आदि जैसे अध्यायों की नींव तैयार करता है। Fractions किसी पूर्ण वस्तु के भाग को दर्शाती हैं जबकि Decimals उसी भिन्न को दशमलव रूप में व्यक्त करती हैं।

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Table of Contents

1. What are Fractions?
2. Types of Fractions
3. Addition and Subtraction of Fractions
4. Multiplication of Fractions
5. Division of Fractions
6. What are Decimals?
7. Place Value Chart
8. Conversion of Fractions into Decimals
9. Operations on Decimals
10. Key Points
11. Important Formulas
12. Practice Questions
13. Conclusion
14. Viewer Challenge

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Abbreviations

Abbreviation	Full Form
Num.	Numerator
Den.	Denominator
Dec.	Decimal
LCM	Least Common Multiple
HCF	Highest Common Factor
PV	Place Value

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1. What are Fractions?

A fraction represents a part of a whole.

Example:

3/5

Here,

• 3 = Numerator (अंश)
• 5 = Denominator (हर)

हिंदी में:
भिन्न किसी पूर्ण वस्तु के हिस्से को दर्शाती है।

उदाहरण: 3/5

जहाँ,

• 3 = अंश
• 5 = हर

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2. Types of Fractions

Proper Fraction

Numerator < Denominator

Example: 3/7

Improper Fraction

Numerator ≥ Denominator

Example: 9/5

Mixed Fraction

Combination of whole number and fraction.

Example: 2⅓

Equivalent Fractions

1/2 = 2/4 = 4/8

हिंदी में:
समान मान वाली भिन्नों को समतुल्य भिन्न कहते हैं।

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3. Addition and Subtraction of Fractions

Same Denominator

2/7 + 3/7 = 5/7

Different Denominator

1/2 + 1/3

LCM of 2 and 3 = 6

= 3/6 + 2/6

= 5/6

हिंदी में:
अलग-अलग हर होने पर पहले LCM निकालकर हर समान बनाया जाता है।

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4. Multiplication of Fractions

Formula:

(a/b) × (c/d) = ac/bd

Example:

2/3 × 5/4

= 10/12

= 5/6

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5. Division of Fractions

Formula:

(a/b) ÷ (c/d)

= (a/b) × (d/c)

Example:

3/5 ÷ 2/7

= 3/5 × 7/2

= 21/10

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6. What are Decimals?

Decimals represent fractions with denominator 10, 100, 1000 etc.

Examples:

• 0.5
• 2.75
• 10.125

हिंदी में:
दशमलव ऐसी संख्याएँ होती हैं जिनमें पूर्णांक और भिन्न भाग को दशमलव बिंदु (.) द्वारा अलग किया जाता है।

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7. Decimal Place Value Chart

Place	Value
Ones	1
Tenths	1/10
Hundredths	1/100
Thousandths	1/1000

Example:

12.345

• 1 = Tens
• 2 = Ones
• 3 = Tenths
• 4 = Hundredths
• 5 = Thousandths

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8. Conversion of Fractions into Decimals

Example 1

1/2 = 0.5

Example 2

3/4 = 0.75

Example 3

7/10 = 0.7

हिंदी में:
भिन्न को दशमलव में बदलने के लिए अंश को हर से भाग देते हैं।

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9. Operations on Decimals

Addition

2.35 + 1.20

= 3.55

Subtraction

5.40 − 2.15

= 3.25

Multiplication

1.5 × 2

= 3.0

Division

4.8 ÷ 2

= 2.4

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Important Formulas

1. Fraction × Fraction = Product of Numerators / Product of Denominators
2. Fraction ÷ Fraction = Multiply by Reciprocal
3. Decimal to Fraction:
   0.25 = 25/100 = 1/4
4. Fraction to Decimal:
   Numerator ÷ Denominator

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Key Points for Exam

Numerator is written above the denominator.

Proper Fraction has numerator smaller than denominator.

Decimal point separates whole and fractional parts.

While adding decimals, place decimal points in one line.

Reciprocal of a fraction is obtained by interchanging numerator and denominator.

LCM method is used when denominators are different.

Fractions and decimals are frequently asked in school exams and competitive exams.

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Practice Questions

Very Short Answer

1. Write the reciprocal of 5/7.
2. Convert 1/4 into decimal.
3. Is 7/5 a proper fraction?

Short Answer

4. Add 3/8 and 1/4.
5. Subtract 4.25 from 10.50.
6. Multiply 2/3 by 9/4.

Long Answer

7. Divide 7/9 by 14/27.
8. Convert 0.875 into fraction.
9. A rope is 5.5 m long. If 2.25 m is cut, how much rope remains?

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Conclusion

Fractions and Decimals are fundamental mathematical concepts that help students understand parts of a whole, measurements, and real-life calculations. A strong command over these topics improves problem-solving skills and prepares students for advanced mathematics.

निष्कर्ष:
Fractions और Decimals गणित के सबसे महत्वपूर्ण अध्यायों में से एक हैं। यदि विद्यार्थी इनकी मूल अवधारणाओं को अच्छी तरह समझ लेते हैं, तो आगे के कई अध्याय उनके लिए आसान हो जाते हैं।

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🎯 Viewer Challenge (Solve & Send)

Neeche diye gaye 5 questions ko solve karke comment ya message mein bhejiye:

1. 3/4 + 5/8 = ?
2. 7/9 × 3/7 = ?
3. 15.75 − 8.25 = ?
4. Convert 5/8 into decimal.
5. 2⅓ ÷ 7/3 = ?

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