Solve 1 rac34 x ((4)/(9) + (1)/(3)) / (1 rac15 + 1 rac12) using the rule of BODMAS.

$$1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4}$$ $$1\frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{6}{5}$$ $$1\frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{3}{2}$$

The expression becomes:

$$\frac{7}{4} \times \left(\frac{4}{9} + \frac{1}{3}\right) \div \left(\frac{6}{5} + \frac{3}{2}\right)$$

$$\left(\frac{6}{5} + \frac{3}{2}\right)$$

The least common multiple of 5 and 2 is 10.

$$\left(\frac{6 \times 2}{5 \times 2} + \frac{3 \times 5}{2 \times 5}\right) = \left(\frac{12}{10} + \frac{15}{10}\right) = \frac{12+15}{10} = \frac{27}{10}$$

First, multiply.

$$\frac{7}{4} \times \frac{7}{9} = \frac{7 \times 7}{4 \times 9} = \frac{49}{36}$$

The expression becomes:

$$\frac{49}{36} \div \frac{27}{10}$$

$$\frac{49}{36} \times \frac{10}{27}$$

Simplify by canceling common factors (10 and 36 are divisible by 2):

$$\frac{49}{18 \times 2} \times \frac{5 \times 2}{27} = \frac{49 \times 5}{18 \times 27}$$ $$= \frac{245}{486}$$

The final answer is:

• $\boxed{\frac{245}{486}}$

.1.b: Using your knowledge on decimals, solve this: $\frac{4.2 \times 1.6 \times 3.4}{0.8 \times 3.2 \times 5.1}$

Since there are an equal number of decimal places in the numerator and denominator (one in each of the three numbers, totaling three decimal places for both), we can multiply the numerator and denominator by $10^3 = 1000$ to clear the decimals without changing the value of the fraction.

$$\frac{42 \times 16 \times 34}{8 \times 32 \times 51}$$

$$\frac{42 \times 16 \times 34}{8 \times 32 \times 51}$$

• Cancel 16 with 32: $\frac{16}{32} = \frac{1}{2}$. The expression becomes: $\frac{42 \times 1 \times 34}{8 \times 2 \times 51}$
• Cancel 34 with 51. Both are divisible by 17: $34 = 17 \times 2$ and $51 = 17 \times 3$. So, $\frac{34}{51} = \frac{2}{3}$. The expression becomes: $\frac{42 \times 1 \times 2}{8 \times 2 \times 3}$
• Cancel 2 from the numerator and denominator:

$$\frac{42 \times 1}{8 \times 3}$$

• Cancel 42 with 3: $\frac{42}{3} = 14$. The expression becomes: $\frac{14}{8}$
• Simplify $\frac{14}{8}$ by dividing both numerator and denominator by 2:

$$\frac{14 \div 2}{8 \div 2} = \frac{7}{4}$$

$$\frac{7}{4} = 1.75$$

The final answer is:

• $\boxed{\frac{7}{4} \text{ or } 1.75}$

.a: In a class of 70 pupils, $\frac{1}{2}$ of them speak English, $\frac{2}{5}$ speak... a. What is the percentage of pupils who speak both English...

This question is incomplete. The information about what the $\frac{2}{5}$ of pupils speak is cut off, and the full question for part 'a' is also cut off. Please provide the complete question for me to solve it.