Question

how can you express (15 30) as a multiple of a sum of whole numbers with no common factor? a. 2 × (7.5 15) b. 3 × (5 10) c. 5 × (3 6) d. 15 × (1 2)

Answer 1

To express the pair (15, 30) in the requested format, the correct answer is option d (15 × (1, 2)), as 1 and 2 are whole numbers with no common factors.

Step-by-step explanation:

To express the pair (15, 30) as a multiple of a sum of whole numbers with no common factor, we need to find a common factor that can be factored out of both numbers in the pair. Looking at the options provided, we can see that:

• Option a (2 × (7.5, 15)) does not fit because it includes a non-whole number.
• Option b (3 × (5, 10)) contains the numbers 5 and 10 which have a common factor of 5, thus this is incorrect as well.
• Option c (5 × (3, 6)) also has numbers with a common factor of 3.
• Option d (15 × (1, 2)) is the correct answer because 1 and 2 are whole numbers with no common factor, and when multiplied by 15, they give us the original pair (15, 30).

Therefore, the correct way to express (15, 30) as a multiple of a sum of whole numbers with no common factor is 15 × (1, 2).

Answer 2

The correct expression for (15 + 30) as a multiple of a sum of whole numbers with no common factor is c. 5 × (3 + 6).

Step-by-step explanation:

Analyze the options:

a. 2 × (7.5 + 15): Both 7.5 and 15 have a common factor of 1.5, violating the condition of no common factor.

b. 3 × (5 + 10): Both 5 and 10 have a common factor of 5, violating the condition.

c. 5 × (3 + 6): Both 3 and 6 are prime numbers and therefore have no common factor. This satisfies the condition.

d. 15 × (1 + 2): 15 itself has a common factor of 3, violating the condition.

Therefore, c. 5 × (3 + 6) is the only option that expresses (15 + 30) as a multiple of a sum of whole numbers with no common factor.

The expression 5 × (3 + 6) translates to:

5 × 9: This clearly shows that 15 + 30 can be expressed as a multiple of a sum of whole numbers (3 + 6) with no common factor (both 3 and 6 are prime).