Fraction multiplication involves multiplying the numerators and the denominators to get the numerator and the denominator of the product respectively

Please find the attached diagrams

1. $\dfrac{2}{15}$ , 2. $\dfrac{3}{8}$ , 3. $\dfrac{1}{12}$ , 4. $\dfrac{7}{21}$ , 5. $\dfrac{3}{10}$

6. 51, 7. 1, 8. 22, 9. $\dfrac{36}{55}$ , 10. $5\dfrac{1}{3}$

Reasons:

The process of multiplication of factors using a model includes;

Creating a table that have the number of rows and columns equal to the values in the denominator of the two fractions respectively

Shading the number of columns given by the numerator of the fraction that has a denominator equal to the number of columns in the table

Shading the number of rows given by the numerator of the fraction that has a denominator equal to the number of rows in the table

Ensuring that the common area are shaded to a different color

Simplifying the result

1. $\dfrac{2}{3} \times \dfrac{1}{5} = \dfrac{2}{15}$

2. $\dfrac{1}{2} \times \dfrac{3}{4} = \dfrac{3}{8}$

3. $\dfrac{1}{4} \times \dfrac{2}{6} = \dfrac{2}{24} = \dfrac{1}{12}$

4. $\dfrac{1}{7} \times \dfrac{2}{3} = \dfrac{7}{21}$

5. $\dfrac{4}{8} \times \dfrac{3}{5} = \dfrac{12}{40} = \dfrac{3}{10}$

Second part

6. When calculating fractions, 'of' means to 'multiply by', therefore, we have;

$\dfrac{17}{25} \times 75= \dfrac{17}{25} \times 25 \times 3 = 17 \times 3 = 51$

7. $\dfrac{7}{6} \times \dfrac{24}{28} = \dfrac{7}{6} \times \dfrac{6 \times 4}{7 \times 4} = \dfrac{7}{6} \times \dfrac{6}{7 } = 1$

8. $12 \times 1\dfrac{5}{6} =6 \times 2 \times \dfrac{11}{6} =2 \times {11} = 22$

9. $\dfrac{4}{5} \times \dfrac{9}{11} = \dfrac{4 \times 9}{5 \times 11} = \dfrac{36}{55}$

10. $6\dfrac{2}{3} \times \dfrac{12}{15} =\dfrac{20}{3} \times \dfrac{12}{15} = \dfrac{4 \times 5}{3} \times \dfrac{4 \times 3}{5 \times 3} = \dfrac{4}{3} \times {4} = \dfrac{16}{3} = 5\dfrac{1}{3}$