Understanding Fractions:
- A fraction represents how much each person gets when a whole number of items is shared equally.
- Example: If one roti is divided among two children, each gets half a roti, written as \(\frac{1}{2}\)
Fractional Units and Equal Shares:
- When a whole unit is divided into equal parts, each part is a fractional unit.
- Examples of fractional units: \(\frac{1}{2},\frac{1}{3},\frac{1}{4}\)
Comparing Fractions:
- Smaller denominators mean larger shares. For example, \(\frac{1}{5}\) is larger than \(\frac{1}{9}\)
- Equivalent fractions represent the same amount but with different numerators and denominators. Example: \(\frac{1}{2} =\frac{2}{4} \)
Fraction as Part of a Whole:
- A fraction can also represent parts of a whole object. Example: If a chikki is cut into 6 equal parts, each piece is \(\frac{1}{6}\)
Fractions on the Number Line:
- Fractions can be represented on a number line. For example, \(\frac{1}{2}\) marks the middle point between 0 and 1
Mixed Fractions:
- A mixed fraction has a whole number part and a fractional part. Example: \(\frac{7}{2}=3+\frac{1}{2}\)
Equivalent Fractions:
- Fractions like \(\frac{1}{2},\frac{2}{4},\frac{3}{6}\) are equivalent fractions.
Adding and Subtracting Fractions:
- When adding fractions with the same denominator, add the numerators. Example: \(\frac{2}{5}+\frac{1}{5},=\frac{3}{5}\)
- For fractions with different denominators, find equivalent fractions with a common denominator.
Expressing Fractions in Lowest Terms:
- A fraction is in its lowest terms when the numerator and denominator have no common factors. Example: \(\frac{16}{20} =\frac{4}{5} \)
Brahmagupta’s method for adding fractions
1. Find equivalent fractions so that the fractional unit is common for all fractions. This can be done by finding a common multiple of the denominators (e.g., the product of the denominators, or the smallest common multiple of the denominators).
2. Add these equivalent fractions with the same fractional units. This can be done by adding the numerators and keeping the same denominator.
3. Express the result in lowest terms if needed
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