Explanation

To solve (+8) ÷ (-2):

(+8) ÷ (-2) = -4

When dividing a positive number by a negative number, the result is negative.

Explanation

Divide 4 ÷ 18 = 0.222..., which is a recurring decimal.

It can also be written as 0.overline{2} indicating the digit 2 repeats.

Explanation

The expression {x|x ∈ A ∨ x ∈ B} represents the set of elements that are in A or in B or in both.

This is the definition of the union of two sets, denoted as A ∪ B.

Explanation

Irrational numbers cannot be expressed as fractions and have infinite non-repeating decimals.

Examples include √2, π, which do not terminate or repeat in decimal form.

Explanation

The size of a class interval is calculated as:

Class Size = Upper Boundary - Lower Boundary

For (1 - 4): 4 - 1 = 3

Explanation

3/1000 is already a fraction.

To convert it to a decimal:

3/1000 = 0.003

Explanation

The first set {-7.2322, ..., √5, √15, 8.27541 ...} includes only irrational numbers because:

• √5 and √15 are irrational (not perfect squares).
• The decimals appear non-repeating and non-terminating.

Explanation

To compare the fractions 1/2, 2/3, and 7/8:

Step 1: Find a common denominator

The least common denominator for 2, 3, and 8 is 24.

Step 2: Convert fractions to have the common denominator

1/2 = 12/24

2/3 = 16/24

7/8 = 21/24

Step 3: Compare the fractions

Since 21 > 16 > 12, the order is 7/8 > 2/3 > 1/2.

Explanation

To find the LCM (Least Common Multiple) of 10, 16, and 25:

Prime factorization:

10 = 2 × 5

16 = 2⁴

25 = 5²

Now take the highest power of each prime:

2⁴ (from 16)

5² (from 25)

LCM = 2⁴ × 5² = 16 × 25 = 400

Explanation

To find the Highest Common Factor (HCF) of 12, 18, and 30, we follow these steps:

Find the prime factors:

12 = 2 × 2 × 3

18 = 2 × 3 × 3

30 = 2 × 3 × 5

Identify common factors:

Common prime factors: 2 and 3

Multiply them: 2 × 3 = 6