Fractions and Decimals — Lesson
1) Hook — A Fun Real-Life Story
Imagine you are at a cricket match at the iconic Eden Gardens in Kolkata. Your friend buys a large box of 12 samosas to share. But oh no! The samosas are not cut into equal parts yet. To share fairly among 4 friends, you need to divide the box into fractions. Each friend will get how much of the box? And if you want to pay your friend ₹50 for the samosas, how much will each pay? This is where fractions and decimals come to the rescue in everyday life!
2) Core Concepts — Understanding Fractions and Decimals
Fractions represent parts of a whole. A fraction has two parts:
- Numerator (top number): How many parts you have
- Denominator (bottom number): How many equal parts the whole is divided into
Example: If you cut a pizza into 8 equal slices and eat 3, the fraction of pizza eaten is 3/8.
| Fraction | Meaning | Example |
|---|---|---|
| 1/2 | One part out of two equal parts | Half a roti |
| 3/4 | Three parts out of four equal parts | 3/4 litre of mango juice |
Decimals are another way to represent fractions, especially parts of 10, 100, 1000, etc. They use a decimal point to separate the whole number from the fractional part.
Example: ₹12.75 means ₹12 and 75 paise (which is 75/100 of a rupee).
| Decimal | Fraction Equivalent | Example |
|---|---|---|
| 0.5 | 1/2 | Half a litre of milk |
| 0.25 | 1/4 | Quarter of a kilogram of sugar |
3) Key Formulas / Rules
Divide the numerator by the denominator.
Example: 3/4 = 3 ÷ 4 = 0.75
Write the decimal as a fraction with denominator 10, 100, 1000, etc., then simplify.
Example: 0.6 = 6/10 = 3/5
Make denominators same, then add/subtract numerators.
Example: 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
Multiply numerators and denominators.
Example: 2/5 × 3/4 = 6/20 = 3/10
4) Did You Know?
In cricket, the batting average is often expressed as a decimal. For example, if a player scores 450 runs in 10 innings and is out 9 times, the average is 450 ÷ 9 = 50.0 runs. This decimal helps compare players easily. So, decimals play a big role even in your favourite sport!
5) Exam Tips
- Always simplify fractions before answering — the board loves neat, simplest forms.
- When converting decimals to fractions, check place value carefully (tenths, hundredths, etc.).
- Practice division carefully when converting fractions to decimals — avoid calculation errors.
- Remember to align decimal points when adding or subtracting decimals.
- Board exam questions often ask for both fraction and decimal forms of the same number — practice both conversions.
- Use real-life examples in answers if asked to explain — like sharing sweets or money.
Fractions and Decimals — Mcq
Fractions and Decimals — Mnemonic
Mnemonic 1: “FRACTIONS” to Remember Fraction Basics 🥧
- F - Fraction means Part of a whole (जैसे एक पूरा पिज़्ज़ा का टुकड़ा)
- R - Remember numerator is on top (ऊपर वाला नंबर)
- A - Always denominator below (नीचे वाला नंबर)
- C - Compare fractions by Cross multiply (क्रॉस मल्टिप्लाई करो)
- T - To add/subtract, make denominators same (हर बार हर का ध्यान)
- I - Improper fractions > 1 (जैसे 7/4)
- O - Convert improper to mixed numbers (जैसे 7/4 = 1 3/4)
- N - Never forget to simplify fractions (सरल बनाना ज़रूरी)
- S - Same denominator? Add numerators straight! (सरल जोड़)
Mnemonic 2: Decimal Dance 💃🕺
"Point pe dhyaan do, place value samjho, zero se darr mat, number ko badhao!"
- Point pe dhyaan do - Always spot the decimal point first
- Place value samjho - Tenths, hundredths, thousandths... (जैसे ₹10.25 में 2 है दसवें हिस्से में)
- Zero se darr mat - Add zeros to equalize decimal places
- Number ko badhao - Multiply decimals by 10, 100, or 1000 to convert to whole numbers for easy calculation
Mnemonic 3: Cricket Fraction Fun 🏏
"If a batsman scored 3/4 of his runs in fours, remember: Numerator is runs made, denominator is total runs!"
- Runs scored in fours = Numerator (3)
- Total runs = Denominator (4)
- Fraction = 3/4, meaning 75% runs in boundaries
- Convert to decimal: 3 ÷ 4 = 0.75 (like a batting average!)
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