Solve the math problems in the attached image.

Steps to Solve

1. Problem 6: Find a common denominator

To subtract fractions, we need a common denominator. The least common multiple of 3 and 12 is 12. Convert $\frac{2}{3}$ to a fraction with a denominator of 12: $$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $$

2. Problem 6: Subtract the fractions

Now that both fractions have the same denominator, we can subtract them: $$ \frac{8}{12} - \frac{1}{12} = \frac{8-1}{12} = \frac{7}{12} $$

3. Problem 6: Simplify the fraction

Check if the fraction $\frac{7}{12}$ can be simplified. Since 7 is a prime number and 7 does not divide 12, the fraction is already in its simplest form.

4. Problem 7: Calculate the bearing of $B$ from $A$

The bearing of $A$ from $B$ is $140^\circ$. This means that to go from $B$ to $A$, you move $140^\circ$ clockwise from North. The bearing of $B$ from $A$ will be $180^\circ$ different if the bearing of $A$ from $B$ is less than $180^\circ$, or $180^\circ$ less if the bearing from $A$ to $B$ is greater than $180^\circ$. In this case, the bearing of $A$ from $B$ is $140^\circ$, which is less than $180^\circ$, therefore we have $$ 140^\circ + 180^\circ = 320^\circ $$ Alternatively, visualize the two towns $A$ and $B$. The angle at $B$ is $140^\circ$ clockwise from the North line. The angle at $A$ is $180^\circ + 140^\circ = 320^\circ$ clockwise from the North line.

5. Problem 8(a): Identify the largest number

We are given the following numbers in standard form: $3.4 \times 10^{-1}$, $1.36 \times 10^{6}$, $7.9 \times 10^{0}$, $2.4 \times 10^{5}$, $5.21 \times 10^{-3}$, $4.3 \times 10^{-2}$

To find the largest number, we look for the number with the largest exponent of 10. The exponents are -1, 6, 0, 5, -3, -2. The largest exponent is 6. Therefore, the largest number is $1.36 \times 10^{6}$.

6. Problem 8(b): Identify the smallest number

To find the smallest number, we look for the number with the smallest exponent of 10. The exponents are -1, 6, 0, 5, -3, -2. The smallest exponent is -3. Therefore, the smallest number is $5.21 \times 10^{-3}$.