Let's address each question one by one:

Question 2:

Find the highest common factor of 24 and 96

To find the highest common factor (HCF), list the factors of each number:

• Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
• Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

The highest common factor is 24.

Question 3:

Find the nth term of 8, 19, 30, 41, ...

To find the nth term, we first identify the common difference between the terms:

• $19 - 8 = 11$
• $30 - 19 = 11$
• $41 - 30 = 11$

The common difference is 11, so this is an arithmetic sequence. The nth term formula for an arithmetic sequence is: $a_n = a_1 + (n - 1) \cdot d$ where $a_1 = 8$ and $d = 11$. Substituting these values, we get: $a_n = 8 + (n - 1) \cdot 11 = 11n - 3$

Question 6:

Work out $6 \times 7 - 2 \times 5$

Follow the order of operations (BIDMAS/BODMAS): $6 \times 7 = 42 \quad \text{and} \quad 2 \times 5 = 10$ $42 - 10 = 32$ So, the answer is 32.

Question 7:

Work out $33 \times 4.9$

$33 \times 4.9 = 161.7$

Question 10:

Work out $2520 \div 28$

$2520 \div 28 = 90$

Question 11:

$1\frac{1}{2} + \frac{2}{5}$

First, convert $1\frac{1}{2}$ to an improper fraction: $1\frac{1}{2} = \frac{3}{2}$ Now add $\frac{3}{2} + \frac{2}{5}$. To do this, find a common denominator, which is 10: $\frac{3}{2} = \frac{15}{10} \quad \text{and} \quad \frac{2}{5} = \frac{4}{10}$ $\frac{15}{10} + \frac{4}{10} = \frac{19}{10} = 1\frac{9}{10}$ So, the answer is $1\frac{9}{10}$.

Would you like further explanations on any of these solutions, or have additional questions?

Here are 5 related questions:

1. How do you find the highest common factor for more than two numbers?
2. What is the difference between arithmetic and geometric sequences?
3. How do you determine the nth term of a sequence with a different common difference?
4. Can you explain the order of operations for more complex calculations?
5. How do you add fractions with different denominators?

Tip: Always check for a common denominator when adding or subtracting fractions to make the process smoother.