Classify the following as odd or even numbers: 131, 108, 365, 329, 5124, 10687. 2. List all prime numbers between 1 and 20. 3. Classify the following as prime or composite numbers: 47, 89, 173, 353, 3

Here are the solutions to the questions.

1. Classify the following as odd or even numbers: $131, 108, 365, 329, 5124, 10687$

• Odd numbers: Numbers not divisible by 2.

• Even numbers: Numbers divisible by 2.

• Odd numbers: $131, 365, 329, 10687$

• Even numbers: $108, 5124$

2. List all prime numbers between 1 and 20.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

The prime numbers between 1 and 20 are:
$2, 3, 5, 7, 11, 13, 17, 19$

3. Classify the following as prime or composite numbers: $47, 89, 173, 353, 377, 421$

• A prime number has exactly two distinct positive divisors: 1 and itself.

• A composite number has more than two distinct positive divisors.

• 47: Prime (divisors: 1, 47)

• 89: Prime (divisors: 1, 89)

• 173: Prime (divisors: 1, 173)

• 353: Prime (divisors: 1, 353)

• 377: Composite ($13 \times 29 = 377$)

• 421: Prime (divisors: 1, 421)

4. Differentiate between rational and irrational numbers, giving an example in each case.

• Rational numbers are numbers that can be expressed as a fraction $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$. Their decimal representation either terminates or repeats.
  • Example: $\frac{1}{2} = 0.5$, $\frac{1}{3} = 0.333...$
• Irrational numbers are numbers that cannot be expressed as a simple fraction. Their decimal representation is non-terminating and non-repeating.
  • Example: $\sqrt{2} \approx 1.41421356...$, $\pi \approx 3.14159265...$

5. Determine the reciprocal of the following:
The reciprocal of a number $x$ is $\frac{1}{x}$.

• i) 4 $$\frac{1}{4} = \boxed{0.25}$$
• ii) 4/5 $$\frac{1}{\frac{4}{5}} = \frac{5}{4} = \boxed{1.25}$$
• iii) 3 1/2 First, convert the mixed number to an improper fraction: $3 \frac{1}{2} = \frac{3 \times 2 + 1}{2} = \frac{7}{2}$. $$\frac{1}{\frac{7}{2}} = \frac{2}{7} \approx \boxed{0.2857}$$

6. Use reciprocal tables to find the reciprocal of the following numbers:
(Assuming a calculator is used to find the values that would be found in a reciprocal table, rounded to 4 decimal places.)

• i) 3.4 $$\frac{1}{3.4} = \frac{10}{34} = \frac{5}{17} \approx \boxed{0.2941}$$
• ii) 2.43 $$\frac{1}{2.43} = \frac{100}{243} \approx \boxed{0.4115}$$
• iii) 2.437 $$\frac{1}{2.437} = \frac{1000}{2437} \approx \boxed{0.4103}$$

7. Determine the reciprocal of 227.4.
The reciprocal of 227.4 is $\frac{1}{227.4}$.

$$\frac{1}{227.4} = \frac{10}{2274} = \frac{5}{1137} \approx \boxed{0.0043975}$$

8. Evaluate: $\frac{2}{5} + \frac{3}{7}$