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ADDITION of unlike fractions:
Step 1: Find LCM of denominators
Step 2: Convert to equivalent fractions
Step 3: Add numerators
1/3 + 1/4:
LCM of 3 and 4 = 12
1/3 = 4/12 (multiply top and bottom by 4)
1/4 = 3/12 (multiply top and bottom by 3)
4/12 + 3/12 = 7/12 ✓
SUBTRACTION of unlike fractions:
3/4 − 1/3:
LCM = 12
3/4 = 9/12, 1/3 = 4/12
9/12 − 4/12 = 5/12 ✓
MULTIPLICATION:
2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5
(multiply numerators, multiply denominators, simplify)
DIVISION: multiply by reciprocal
2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6
PLACE VALUE for decimals:
3 . 4 7 8
│ │ │ └── thousandths (÷1000)
│ │ └───── hundredths (÷100)
│ └──────── tenths (÷10)
└────────────── units
Converting:
Fraction → Decimal: 3/4 = 3÷4 = 0.75
Decimal → %: 0.75 × 100 = 75%
% → Fraction: 75% = 75/100 = 3/4
PERCENTAGE:
"Per cent" = per hundred
Finding % of a number:
25% of 80 = (25/100) × 80 = 20
Finding what % one number is of another:
What % is 15 of 60?
= (15/60) × 100 = 25%
Common percentages to remember:
50% = 1/2 25% = 1/4 75% = 3/4
10% = 1/10 20% = 1/5 33.3% ≈ 1/3
AVERAGE = Total sum ÷ Number of items
Marks of Priya in 5 subjects: 80, 85, 70, 90, 75
Average = (80+85+70+90+75) ÷ 5
= 400 ÷ 5
= 80
USES of average:
Average temperature, average speed, average score
Average speed = Total distance ÷ Total time
Travel 120 km in 3 hours: avg speed = 120÷3 = 40 km/h
VOLUME = space occupied by 3D object
Unit: cubic centimetre (cm³) or cubic metre (m³)
Volume of cuboid = length × breadth × height
Volume of cube = side³
CAPACITY = amount a container holds
Unit: millilitres (mL) and litres (L)
1 litre = 1000 millilitres
1 litre of water occupies 1000 cm³
Example:
Box: l=10cm, b=5cm, h=4cm
Volume = 10×5×4 = 200 cm³
Everyday capacity:
Teaspoon ≈ 5 mL
Glass ≈ 200 mL
Bottle ≈ 500 mL or 1 L
INTRODUCTION (1 paragraph):
Hook → Background → Thesis statement (main argument)
"Trees are the lifeline of our planet. Without them..."
BODY (2-3 paragraphs):
Each para: Topic sentence → Supporting details → Example
Para 1: Why forests are important
Para 2: Threats to forests
Para 3: What we should do
CONCLUSION (1 paragraph):
Restate thesis → Summary of points → Final thought/call to action
GOOD WRITING uses:
✓ Varied sentence length (short + long mixed)
✓ Transition words: firstly, furthermore, however, finally
✓ Specific examples
✓ Correct punctuation
DIRECT SPEECH: Exact words in quotes
Rahul said, "I am going to school."
INDIRECT SPEECH: Reported, no quotes
Rahul said that he was going to school.
CHANGES when converting:
Pronoun: "I" → "he/she"
Tense: am (present) → was (past)
"that" is added after "said"
Quotes removed
More examples:
Direct: She said, "I will come tomorrow."
Indirect: She said that she would come the next day.
(tomorrow → next day, will → would)
Direct: He asked, "Are you hungry?"
Indirect: He asked if I was hungry.
(question becomes indirect question with "if")
CLAUSE: group of words with subject + verb
Main clause (can stand alone):
She reads books.
Subordinate clause (cannot stand alone):
because she loves stories.
CONJUNCTIONS join clauses:
Coordinating: and, but, or, nor, for, yet, so
Subordinating: because, although, when, if, unless, since
Examples:
She reads books AND writes stories. (coordinating: and)
She reads books BECAUSE she loves stories. (subordinating: because)
He will come UNLESS it rains. (subordinating: unless)
ALTHOUGH it was cold, they played outside. (although)
INDIA AT A GLANCE:
Capital: New Delhi
Area: 3.29 million km² (7th largest in world)
States: 28 states + 8 Union Territories
Neighbours: Pakistan, China, Nepal, Bhutan, Bangladesh, Myanmar, Sri Lanka
INDIA REGIONS:
┌────────────────────────────────┐
│ North: Himalayas (J&K, HP, UK) │
│ Plains: Punjab, UP, Bihar │
│ East: WB, Odisha, Jharkhand │
│ South: TN, Kerala, Karnataka │
│ West: Rajasthan, Gujarat, MH │
│ Central: MP, Chhattisgarh │
│ NE: 7 sisters (Assam, etc.) │
└────────────────────────────────┘
RIVERS:
Himalayan (perennial, always flow):
Ganga, Yamuna, Brahmaputra, Indus
Peninsular (seasonal, monsoon-fed):
Godavari, Krishna, Kaveri, Narmada, Tapti
CROPS:
Kharif (summer): Rice, Cotton, Sugarcane, Maize
Rabi (winter): Wheat, Gram, Mustard, Barley
DIGESTIVE SYSTEM:
Mouth → Oesophagus → Stomach → Small intestine → Large intestine → Anus
Mouth: teeth chew, saliva starts digestion
Stomach: acid and enzymes break food further
Small intestine: absorbs nutrients into blood
Large intestine: absorbs water, forms solid waste
RESPIRATORY SYSTEM:
Nose/Mouth → Trachea → Bronchi → Lungs → Alveoli
Breathe in (inhale): O₂ enters
Breathe out (exhale): CO₂ exits
Lungs: spongy organs in chest
Diaphragm: muscle below lungs helps breathing
CIRCULATORY SYSTEM:
Heart → Arteries → Capillaries → Veins → Heart
Heart: pumps blood (beats ~72 times/min)
Arteries: carry oxygenated blood from heart
Veins: carry deoxygenated blood to heart
Blood: transports O₂, nutrients, waste
SKELETAL SYSTEM:
206 bones in adult human body
Functions: Support, protection, movement
Important bones: Skull (brain), Ribcage (heart/lungs), Spine (back)
Joints: Ball-and-socket (shoulder), Hinge (knee, elbow)
Cartilage: Flexible tissue at joints (ear, nose)
RENEWABLE RESOURCES (can be replenished):
Solar energy ☀ (inexhaustible)
Wind energy 🌬
Water 💧 (if managed well)
Forests 🌳 (if replanted)
NON-RENEWABLE RESOURCES (will run out):
Coal ⛏ (takes millions of years to form)
Petroleum 🛢 (estimated 50-60 years left)
Natural gas
Minerals (iron ore, copper, gold)
3 Rs — REDUCE, REUSE, RECYCLE:
Reduce: Use less (shorter showers, less plastic)
Reuse: Use again (cloth bags, glass bottles)
Recycle: Make new from old (paper, aluminium, glass)
Biodegradable vs Non-biodegradable:
Biodegradable: breaks down naturally (paper, food waste, cotton)
Non-biodegradable: does NOT break down (plastic, glass, metal)
वर्तमान काल (Present):
सामान्य: राम खाता है। (Ram eats.)
अपूर्ण: राम खा रहा है। (Ram is eating.)
पूर्ण: राम खा चुका है। (Ram has eaten.)
भूत काल (Past):
सामान्य: राम ने खाया। (Ram ate.)
अपूर्ण: राम खा रहा था। (Ram was eating.)
पूर्ण: राम खा चुका था। (Ram had eaten.)
भविष्य काल (Future):
राम खाएगा। (Ram will eat.)
राम खाता रहेगा। (Ram will keep eating.)
उपमा (Simile): दो चीजों की तुलना "जैसा/सा" से
चाँद-सा सुंदर मुख है। (Face is beautiful like the moon.)
शेर-सा बहादुर लड़का। (Boy as brave as a lion.)
रूपक (Metaphor): सीधी तुलना, "जैसा" नहीं:
जीवन एक सफर है। (Life is a journey.)
वह चाँद है। (She/He is the moon — beauty)
अनुप्रास (Alliteration): एक ही वर्ण की आवृत्ति:
कानन कुसुम कोमल काया (many 'k' sounds)
Maths:
English:
EVS:
Hindi:
Class 5 NCERT complete notes — fractions, decimals, percentage, geometry, English comprehension grammar, EVS: India's states, natural resources, human body systems, maps with diagrams.
34 pages · 1.2 MB · Updated 2026-03-11
Divide numerator by denominator. Example: 3/4 = 3÷4 = 0.75. Or convert denominator to 10/100/1000: 3/4 = 75/100 = 0.75. Common ones to remember: 1/2=0.5, 1/4=0.25, 3/4=0.75, 1/5=0.2, 1/10=0.1.
Digestive system: breaks food (mouth→stomach→intestines). Respiratory system: breathing (nose→lungs). Circulatory: blood circulation (heart→arteries→veins). Skeletal: bones (206 bones). Nervous: brain+spinal cord controls everything. Excretory: removes waste (kidneys→urine).
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