Question

Find the product using model or drawing

Answer 1

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

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