Fraction Operations 369D11

1. **Problem:** Calculate $\frac{1}{2} + \frac{1}{3}$. **Step 1:** Find a common denominator. The least common denominator (LCD) of 2 and 3 is 6. **Step 2:** Convert fractions: $$\frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}$$ **Step 3:** Add numerators: $$\frac{3}{6} + \frac{2}{6} = \frac{3+2}{6} = \frac{5}{6}$$ **Answer:** $\frac{5}{6}$ 2. **Problem:** Calculate $\frac{3}{4} - \frac{1}{2}$. **Step 1:** LCD of 4 and 2 is 4. **Step 2:** Convert fractions: $$\frac{3}{4} = \frac{3}{4}, \quad \frac{1}{2} = \frac{2}{4}$$ **Step 3:** Subtract numerators: $$\frac{3}{4} - \frac{2}{4} = \frac{3-2}{4} = \frac{1}{4}$$ **Answer:** $\frac{1}{4}$ 3. **Problem:** Calculate $\frac{2}{3} \times \frac{3}{5}$. **Step 1:** Multiply numerators and denominators: $$\frac{2}{3} \times \frac{3}{5} = \frac{2 \times 3}{3 \times 5} = \frac{6}{15}$$ **Step 2:** Simplify fraction by dividing numerator and denominator by 3: $$\frac{\cancel{6}^{2}}{\cancel{15}^{5}} = \frac{2}{5}$$ **Answer:** $\frac{2}{5}$ 4. **Problem:** Calculate $\frac{4}{5} \div \frac{2}{5}$. **Step 1:** Division of fractions uses Keep-Change-Flip: $$\frac{4}{5} \div \frac{2}{5} = \frac{4}{5} \times \frac{5}{2}$$ **Step 2:** Multiply numerators and denominators: $$\frac{4 \times 5}{5 \times 2} = \frac{20}{10}$$ **Step 3:** Simplify fraction by dividing numerator and denominator by 10: $$\frac{\cancel{20}^{2}}{\cancel{10}^{1}} = 2$$ **Answer:** $2$ 5. **Problem:** Calculate $-8 + 11$. **Step 1:** Add integers: $$-8 + 11 = 3$$ **Answer:** $3$ 6. **Problem:** Calculate $-9 - (-6)$. **Step 1:** Subtracting a negative is adding positive: $$-9 - (-6) = -9 + 6$$ **Step 2:** Add integers: $$-9 + 6 = -3$$ **Answer:** $-3$ 7. **Problem:** Calculate $-3 \times \frac{1}{2}$. **Step 1:** Multiply numerator and denominator: $$-3 \times \frac{1}{2} = \frac{-3 \times 1}{2} = \frac{-3}{2}$$ **Answer:** $-\frac{3}{2}$ 8. **Problem:** Calculate $\frac{5}{6} + \frac{1}{6}$. **Step 1:** Same denominator, add numerators: $$\frac{5}{6} + \frac{1}{6} = \frac{5+1}{6} = \frac{6}{6} = 1$$ **Answer:** $1$ 9. **Problem:** Calculate $\frac{7}{8} \div \frac{7}{4}$. **Step 1:** Use Keep-Change-Flip: $$\frac{7}{8} \div \frac{7}{4} = \frac{7}{8} \times \frac{4}{7}$$ **Step 2:** Multiply numerators and denominators: $$\frac{7 \times 4}{8 \times 7} = \frac{28}{56}$$ **Step 3:** Simplify by dividing numerator and denominator by 28: $$\frac{\cancel{28}^{1}}{\cancel{56}^{2}} = \frac{1}{2}$$ **Answer:** $\frac{1}{2}$ 10. **Question:** Which operation uses Keep-Change-Flip? **Answer:** Division of fractions uses Keep-Change-Flip.