1. multiply.\n3 2/4×2 2/5 = \n2. write the rule for the table.\ninput output\n4 1\n8 2\n12 3\n16…

Answer:

1. First, convert mixed - numbers to improper fractions:
   • (3\frac{2}{4}=\frac{3\times4 + 2}{4}=\frac{14}{4}), (2\frac{2}{5}=\frac{2\times5+2}{5}=\frac{12}{5})
   • Then multiply: (\frac{14}{4}\times\frac{12}{5}=\frac{14\times12}{4\times5}=\frac{168}{20}=\frac{42}{5} = 8\frac{2}{5})
2. The rule for the table: Output=(\frac{Input}{4})
3. (5\div\frac{1}{10}=5\times10 = 50)
4. (2\div\frac{1}{3}=2\times3=6)
5. (4\div\frac{2}{9}=4\times\frac{9}{2}=18)
6. By sides: Equilateral triangle (all sides are 3 cm). By angles: Acute - angled triangle (since all angles of an equilateral triangle are (60^{\circ}))
7. By sides: Scalene triangle (no equal sides). By angles: Obtuse - angled triangle (one angle is (100^{\circ}))
8. By sides: Scalene triangle (sides are 3 in, 4 in, 5 in). By angles: Right - angled triangle (has a (90^{\circ}) angle)
9. Parallelogram (opposite sides are parallel and equal), Quadrilateral (4 - sided polygon)
10. Trapezoid (has one pair of parallel sides), Quadrilateral (4 - sided polygon)

Explanation:

Step1: Convert mixed - numbers

For (3\frac{2}{4}) and (2\frac{2}{5}), use (a\frac{b}{c}=\frac{ac + b}{c})

Step2: Multiply fractions

Use (\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd})

Step3: Find table rule

Notice (1=\frac{4}{4}), (2=\frac{8}{4}), (3=\frac{12}{4}), (4=\frac{16}{4})

Step4: Divide by a fraction

Use (a\div\frac{b}{c}=a\times\frac{c}{b})

Step5: Classify triangles by sides

Check for equal side lengths

Step6: Classify triangles by angles

Check for right ((90^{\circ})), acute ((<90^{\circ})), or obtuse ((>90^{\circ})) angles

Step7: Classify quadrilaterals

Check for parallel sides and general 4 - sided nature