Fractions Mixed Numbers D6Cf8F

1. Let's start by understanding what fractions and mixed numbers are. 2. A fraction is a number that represents a part of a whole and is written as $\frac{a}{b}$ where $a$ is the numerator and $b$ is the denominator. 3. A mixed number is a whole number combined with a fraction, for example, $2 \frac{1}{3}$. 4. To convert a mixed number to an improper fraction, use the formula: $$\text{Improper fraction} = \frac{(\text{whole number} \times \text{denominator}) + \text{numerator}}{\text{denominator}}$$ 5. For example, convert $2 \frac{1}{3}$ to an improper fraction: $$\frac{(2 \times 3) + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$$ 6. To convert an improper fraction back to a mixed number, divide the numerator by the denominator: $$7 \div 3 = 2 \text{ remainder } 1$$ So, the mixed number is $2 \frac{1}{3}$. 7. When adding or subtracting fractions, make sure the denominators are the same. If not, find the least common denominator (LCD). 8. For example, add $\frac{1}{4} + \frac{1}{6}$: - Find LCD of 4 and 6, which is 12. - Convert fractions: $\frac{1}{4} = \frac{3}{12}$ and $\frac{1}{6} = \frac{2}{12}$. - Add: $\frac{3}{12} + \frac{2}{12} = \frac{5}{12}$. 9. Simplify fractions by dividing numerator and denominator by their greatest common divisor (GCD). 10. For multiplication, multiply numerators and denominators directly: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 11. For division, multiply by the reciprocal: $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}$$ This covers the basics of fractions and mixed numbers.