Class 7th Ch 2 - Fractions and Decimals By PREM SIR

📘 Chapter 2: Fractions and Decimals | पूर्ण अध्‍याय सारांश

🔹 1. Definition (परिभाषा)

🔸 Fraction (भिन्न):

English: A number that represents a part of a whole.
Hindi: ऐसा संख्या जो किसी पूर्ण वस्तु का एक भाग दर्शाती है।

📌 Example:

🔸 Decimal (दशमलव):

English: A number expressed using a decimal point (.) to represent part of a whole.
Hindi: दशमलव वह संख्या होती है जिसमें पूर्णांक और भिन्न भाग दशमलव बिंदु से जुड़े होते हैं।

📌 Example:
0.5, 2.75, 3.2

🔹 2. Types of Fractions (भिन्नों के प्रकार)

English Type	Hindi Meaning	Example
Proper Fraction	सही भिन्न (Numerator < Denominator)	2/5, 3/8
Improper Fraction	अशुद्ध भिन्न (Numerator ≥ Denominator)	7/4, 5/5
Mixed Fraction	मिश्रित भिन्न	1½, 2¾
Like Fractions	समान हर वाले भिन्न	2/7, 5/7
Unlike Fractions	भिन्न हर वाले भिन्न	2/3, 5/4
Unit Fraction	इकाई भिन्न (Numerator = 1)	1/2, 1/7
Equivalent Fraction	समतुल्य भिन्न	1/2 = 2/4 = 3/6

🔹 3. Decimal Number Types (दशमलव संख्याओं के प्रकार)

Type	Hindi Meaning	Example
Terminating Decimal	समाप्त होने वाली दशमलव	0.25, 1.5
Non-Terminating	समाप्त न होने वाली	1.333..., 0.666...

🔹 4. Basic Formulas & Rules (मूल सूत्र और नियम)

🔸 Fractions:

Addition/Subtraction of Like Fractions:
Addition/Subtraction of Unlike Fractions:
Make LCM of denominators and convert into like fractions.
Multiplication of Fractions:
Division of Fractions:
(Reciprocal method)

🔸 Decimals:

Addition/Subtraction:
Align decimal points and then add/subtract.
Multiplication:
Multiply ignoring decimal → count decimal places in total → place decimal.
Division:
Move decimal of divisor to right to make it whole number → do same to dividend → divide normally.

🔹 5. Conversion Tips (परिवर्तन के टिप्स)

Convert from	To	Trick
Fraction → Decimal	Divide numerator by denominator	½ = 0.5
Decimal → Fraction	Remove decimal → divide by 10/100/1000	0.25 = 25/100
Mixed Fraction → Improper	a b/c = (a×c + b)/c	1¾ = 7/4
Improper → Mixed	Divide numerator ÷ denominator	7/4 = 1¾

🔹 6. Shortcuts, Tips & Tricks (जल्द याद करने के लिए टिप्स)

📌 Tip 1: Multiply faster

➡ Cancel before multiplying.

📌 Tip 2: Division trick

📌 Tip 3: Decimal Multiplication

0.4 × 0.2 → 4 × 2 = 8 → count 2 decimal places → 0.08

📌 Tip 4: Equivalent Fraction Shortcut

Multiply or divide numerator and denominator by same number.
1/2 = 2/4 = 3/6 = 4/8

🔹 7. Important Word Problems Concept (महत्वपूर्ण अवधारणाएं)

🧮 Example 1:

Q: A rope is 2¾ meters long. If cut into 5 equal parts, what is the length of one part?

A:
2¾ = 11/4
So, 1 part = meters

🧮 Example 2:

Q: Multiply: 0.5 × 1.2

Ignore decimal → 5 × 12 = 60
Decimal places = 1 (in 0.5) + 1 (in 1.2) = 2
Answer = 0.60 or 0.6 ✅

🔹 8. Golden Rules to Remember (याद रखने के लिए नियम)

✅ Always simplify fractions
✅ Always write final answer in simplest form
✅ Use reciprocal while dividing fractions
✅ Always align decimals before addition/subtraction
✅ Use estimation for checking

✅ Want More?

✅ 30+ MCQ
✅ Practice Worksheets
✅ Word Problems
✅ PDF Notes (Printable)

👉

🔹 1. Fraction (भिन्न) क्या होता है?

📗 Big Kid Definition:

A number that shows a part of a whole.
Hindi: ऐसा संख्या जो किसी पूरे का हिस्सा बताता है।

🧒 Bacchon wali Bhasha:

Jab hum kisi cheez ko tukdon mein baant dete hain, jaise pizza ke 4 tukde, aur ek tukda khayein — toh woh ek tukda "fraction" hai.

🍕 Example:
Pizza ke 4 tukde hain, maine 1 tukda khaya = 1/4 (one out of four)

🔹 2. Decimal (दशमलव) kya hota hai?

📗 Big Kid Definition:

A number that has a dot (.) to show small parts.
Hindi: जिस संख्या में “.” (दशमलव बिंदु) होता है और वो छोटे हिस्से को दिखाता है।

🧒 Bacchon wali Bhasha:

Jab hum toffee ya chocolate ko aadha ya chhota tukda bolte hain, tab hum point waali sankhya ka use karte hain.

🍫 Example:
1 toffee ka aadha part = 0.5 toffee

🔹 3. Types of Fractions – Bhinnon ke Prakar

Type	Bacchon wali samajh	Example
Proper (सही)	Chhoti cheez badi se	2/5 – 2 tukde 5 me se
Improper (अशुद्ध)	Badi cheez chhoti se	7/4 – 7 tukde 4 me baantna
Mixed (मिश्रित)	1 chocolate + aadhi	1¾
Like (समान हर)	Sab tukde same size ke	2/5, 3/5
Unlike (भिन्न हर)	Tukde alag size ke	1/2, 1/3
Unit (इकाई)	Sirf 1 tukda	1/4
Equivalent (बराबर)	Alag likhne par bhi same	1/2 = 2/4

🔹 4. Decimal Types – Bacchon ke liye

Type	Bacchon wali baat	Example
Terminating	Point waali sankhya jaldi khatam ho jaye	0.25
Non-Terminating	Point ke baad number rukta hi nahi	0.6666...

🔹 5. Formulas (सूत्र) – Bacchon ke liye asaan

✏️ Fractions:

✅ Addition (जोड़): Agar dono ke tukde same ho toh sirf upar waale jod do
Example: 2/5 + 1/5 = (2 + 1)/5 = 3/5
✅ Multiplication (गुणा): Upar se upar ×, neeche se neeche ×
Example: 2/3 × 3/4 = 6/12 = 1/2
✅ Division (भाग): Pehle waali bhinn × doosre ki ulta (उल्टा)
Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8

✏️ Decimals:

✅ Addition: Dot (.) waale point ko line mein likho
2.3 + 1.25 = 3.55
✅ Multiplication: Pehle point hata ke guna karo, baad mein point lagao
0.2 × 0.4 = 2×4 = 8 → 0.08
✅ Division: Point hatao aur dono ko bada banao, fir divide karo
1.2 ÷ 0.3 = 12 ÷ 3 = 4

🔹 6. Conversion Trick (Badalne ka Easy Tarika)

From	To	Easy Way (Bachon wali)
Fraction → Decimal	Divide karo	1/2 = 0.5
Decimal → Fraction	Point hatao, 10 ya 100 se divide	0.25 = 25/100
Mixed → Improper	Multiply + add karo	1¾ = (1×4 + 3)/4 = 7/4

🔹 7. Magic Tricks & Tips (Bacchon ke liye masti bhare shortcuts)

🎩 Trick 1:
Divide = multiply by ulta
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8

🎩 Trick 2:
Decimal multiplication = zero hatao, baad mein point lagao
0.3 × 0.2 → 3 × 2 = 6 → 0.06

🎩 Trick 3:
1/2 = 2/4 = 3/6 — Sab same taste waale chocolate 🍫

🔹 8. Examples for 5 saal ke bacche

🧒 Example 1:

Ravi ke paas 1 chocolate hai. Usne uska aadha khaya.
Q: Kitna chocolate bacha?
👉 A: 1 – 1/2 = 1/2

🧒 Example 2:

Mina ne 0.5 toffee aur 0.25 toffee khayi.
Q: Usne total kitni toffee khayi?
👉 A: 0.5 + 0.25 = 0.75 toffee

✅ Final Recap for Kids

🌟 Fraction = Tukde wali sankhya
🌟 Decimal = Point wali sankhya
🌟 Multiply = Seedha multiply
🌟 Divide = Pehle bhinn ko ulta karke multiply
🌟 Decimal addition = Line mein likho point ke neeche