1. ๐ Important Keywords and Definitions
-
Fraction: A number that represents a part of a whole.
Example:32,85
-
Proper Fraction: Numerator < Denominator.
Example:53
-
Improper Fraction: Numerator โฅ Denominator.
Example:47
-
Mixed Fraction: A whole number with a proper fraction.
Example:231
-
Equivalent Fractions: Fractions that represent the same value.
Example:42=21
-
Like Fractions: Fractions with the same denominator.
-
Unlike Fractions: Fractions with different denominators.
-
Reciprocal: Inverse of a fraction.
Example: Reciprocal of43 is
34
2. ๐ง Key Concepts and Explanations
-
Fractions can be added, subtracted, multiplied, and divided.
-
For addition/subtraction:
-
Convert to like fractions (same denominator).
-
-
For multiplication:
-
Multiply numerators and denominators directly.
-
-
For division:
-
Multiply by the reciprocal of the second fraction.
-
3. ๐ Formulas and Rules
Operation | Rule |
---|---|
Addition (Like) | Add numerators; keep the denominator: ca+cb=ca+b |
Addition (Unlike) | Convert to like fractions โ then add |
Subtraction | Same as addition, but subtract numerators |
Multiplication |
baรdc=bรdaรc |
Division |
baรทdc=baรcd |
——————————————————-
4. ๐ Step-by-Step Methods
To Add/Subtract Fractions:
-
Find LCM of denominators.
-
Convert to like fractions.
-
Add or subtract numerators.
-
Simplify if needed.
To Multiply Fractions:
-
Multiply numerators and denominators.
-
Simplify the result.
To Divide Fractions:
-
Take reciprocal of the divisor.
-
Multiply with the dividend.
-
Simplify the answer.
5. โ Examples with Full Solutions
Example 1:
31+32=31+2=33=1
Example 2:
52+103
LCM of 5 and 10 = 10
Convert:
52=104
104+103=107
Example 3:
74ร52=358
Example 4:
43รท52=43ร25=815=187
6. โ ๏ธ Common Mistakes to Avoid
-
Adding unlike fractions without converting to same denominator.
-
Forgetting to take the reciprocal in division.
-
Not simplifying the final answer.
-
Mixing up rules of multiplication and addition.
7. โ๏ธ Practice Questions
-
Add:
53+102
-
Subtract:
87โ83
-
Multiply:
65ร32
-
Divide:
94รท32
-
Convert to like fractions:
32,65
-
Write the reciprocal of:
97
-
Express
143 as an improper fraction.
8. ๐ Conceptual Diagrams
-
Fraction strips or pie diagrams to show parts of a whole.
-
Number line showing comparison of fractions.
-
Flowchart for selecting the correct operation.
9. ๐ก Word Problems Section
Q: A recipe uses
43 cup of sugar. How much sugar is needed for 2 such recipes?
A:
43ร2=46=121 cups
Q: Raju walked
32 km in the morning and
61 km in the evening. How far did he walk in total?
A: LCM = 6 โ
32=64
64+61=65 km
10. ๐ Important Points / Quick Revision
-
Always simplify your final answer.
-
Convert mixed fractions to improper fractions before solving.
-
Use LCM to make denominators equal.
-
Multiplication and division are easier than addition and subtraction.
11. ๐ Connections to Other Chapters
-
Helps in Decimals and Ratios.
-
Required in Algebra and Mensuration.
-
Applied in real life: recipes, construction, time management.
12. ๐ฏ Extra Tips or Tricks
-
Always cross-check numerators and denominators.
-
For quick LCM, use factor method.
-
Practice with real-life situations to build fluency.