Question

Using the numbers 1, 2, 3, and 4, and the four operations, try and make all the numbers from 1 to 30.

a) 2 + 3 - 1 = 4
b) (2 + 3) * 4 = 20
c) 4 / (1 - 2/3) = 6
d) 4 * (3 - 2/1) = 8

Answer 1

The question involves creating all numbers from 1 to 30 using four basic mathematical operations and the numbers 1, 2, 3, and 4. It touches upon arithmetic rules such as sign rules for addition, subtraction, multiplication, and division, and requires an understanding of how to apply these rules in operations to reach various sums or products.

Step-by-step explanation:

The student's question involves using the four basic mathematical operations (addition, subtraction, multiplication, and division) with the numbers 1, 2, 3, and 4 to form all numbers from 1 to 30. Here is an example for the number 4:

• 2 + 3 - 1 = 4 (Using addition and subtraction)

Let’s look at some fundamental arithmetic rules:

• When two positive numbers add or multiply, the answer is positive (e.g., 2+3 = 5, 2x3 = 6).

• When two negative numbers add or multiply, the answer is negative when added (e.g., -4 + (-2) = -6), but positive when multiplied (e.g., (-4) x (-3) = 12).

• When numbers with opposite signs are involved, subtract the smaller number from the larger for addition, and the answer carries the sign of the larger (e.g., -5 +3 = -2), whereas for multiplication or division, the result is negative (e.g., (-3) x 2 = -6).

• Subtraction can be seen as adding the opposite (e.g., 5 - (+3) = 5 - 3 = 2, 2 - (-6) = 2 + 6 = 8).

Applying these rules helps in constructing equations to create the desired numbers using 1, 2, 3, and 4.