Question

$\frac{4}{5} + \frac{3}{10} =$
$\frac{6}{3} \times \frac{1}{5} =$
$\frac{1}{2} \times \frac{1}{2}$ (with cross - out)
$\frac{1}{3} \times \frac{81}{5} =$
$\frac{1}{2} + \frac{3}{8} =$
$\frac{2}{5} - \frac{1}{10} =$
$\frac{3}{4} - \frac{5}{12} =$
$\frac{3}{4} - \frac{1}{2}$
$\frac{1}{4} - \frac{1}{4}$
$\frac{1}{2} - \frac{3}{8}$
$\frac{1}{8} \times \frac{1}{3} =$
$\frac{1}{4} \times \frac{2}{3}$

Explanation:

Step1: Solve $\frac{4}{5}+\frac{3}{10}$

Find a common denominator, which is 10. Convert $\frac{4}{5}$ to $\frac{8}{10}$. Then add: $\frac{8}{10}+\frac{3}{10}=\frac{11}{10}$

Step2: Solve $\frac{5}{3}×\frac{1}{5}$

Multiply numerators and denominators: $\frac{5×1}{3×5}=\frac{1}{3}$ (simplify by canceling 5)

Step3: Solve $\frac{1}{2}×\frac{1}{2}$ (assuming the crossed - out part is a typo and we calculate this)

Multiply: $\frac{1×1}{2×2}=\frac{1}{4}$

Step4: Solve $\frac{1}{3}×\frac{81}{5}$

Multiply numerators: $1×81 = 81$, denominators: $3×5 = 15$. Simplify $\frac{81}{15}=\frac{27}{5}$

Step5: Solve $\frac{1}{2}+\frac{3}{8}$

Common denominator is 8. Convert $\frac{1}{2}$ to $\frac{4}{8}$. Add: $\frac{4}{8}+\frac{3}{8}=\frac{7}{8}$

Step6: Solve $\frac{2}{5}-\frac{1}{10}$

Common denominator is 10. Convert $\frac{2}{5}$ to $\frac{4}{10}$. Subtract: $\frac{4}{10}-\frac{1}{10}=\frac{3}{10}$

Step7: Solve $\frac{3}{4}-\frac{5}{12}$

Common denominator is 12. Convert $\frac{3}{4}$ to $\frac{9}{12}$. Subtract: $\frac{9}{12}-\frac{5}{12}=\frac{4}{12}=\frac{1}{3}$

Step8: Solve $\frac{3}{4}-\frac{1}{2}$

Common denominator is 4. Convert $\frac{1}{2}$ to $\frac{2}{4}$. Subtract: $\frac{3}{4}-\frac{2}{4}=\frac{1}{4}$

Step9: Solve $\frac{1}{4}-\frac{1}{6}$

Common denominator is 12. Convert $\frac{1}{4}$ to $\frac{3}{12}$ and $\frac{1}{6}$ to $\frac{2}{12}$. Subtract: $\frac{3}{12}-\frac{2}{12}=\frac{1}{12}$

Step10: Solve $\frac{1}{2}-\frac{3}{8}$

Common denominator is 8. Convert $\frac{1}{2}$ to $\frac{4}{8}$. Subtract: $\frac{4}{8}-\frac{3}{8}=\frac{1}{8}$

Step11: Solve $\frac{1}{3}×\frac{1}{3}$

Multiply: $\frac{1×1}{3×3}=\frac{1}{9}$

Step12: Solve $\frac{1}{4}×\frac{2}{3}$

Multiply numerators: $1×2 = 2$, denominators: $4×3 = 12$. Simplify $\frac{2}{12}=\frac{1}{6}$

Answer:

$\frac{4}{5}+\frac{3}{10}=\frac{11}{10}$; $\frac{5}{3}×\frac{1}{5}=\frac{1}{3}$; $\frac{1}{2}×\frac{1}{2}=\frac{1}{4}$; $\frac{1}{3}×\frac{81}{5}=\frac{27}{5}$; $\frac{1}{2}+\frac{3}{8}=\frac{7}{8}$; $\frac{2}{5}-\frac{1}{10}=\frac{3}{10}$; $\frac{3}{4}-\frac{5}{12}=\frac{1}{3}$; $\frac{3}{4}-\frac{1}{2}=\frac{1}{4}$; $\frac{1}{4}-\frac{1}{6}=\frac{1}{12}$; $\frac{1}{2}-\frac{3}{8}=\frac{1}{8}$; $\frac{1}{3}×\frac{1}{3}=\frac{1}{9}$; $\frac{1}{4}×\frac{2}{3}=\frac{1}{6}$