High School

Which of the following ratios form a proportion with [tex]\frac{2}{5}[/tex]?

A. [tex]\frac{16}{40}[/tex]
B. [tex]\frac{10}{30}[/tex]
C. [tex]\frac{12}{25}[/tex]
D. [tex]\frac{12}{35}[/tex]

Answer :

Answer: A) 16/40

Step-by-step explanation:

They are the same ratio, and when divided equal 0.4.

Final answer:

Only the ratio 16/40 simplifies to 2/5, making it the only option that forms a proportion with 2/5. The process involves simplifying each option to see if it matches 2/5 (option a).

Explanation:

To find which of the given ratios form a proportion with 2/5, we need to determine if each ratio can be simplified or scaled to match 2/5. A proportion exists when two ratios are equivalent, meaning one can be derived from the other through multiplication or division by the same number.

  • a) 16/40: This simplifies to 2/5 when both the numerator and denominator are divided by 8.
  • b) 10/30: This simplifies to 1/3 and does not form a proportion with 2/5.
  • c) 12/25: This ratio does not simplify to 2/5 and thus does not form a proportion with it.
  • d) 12/35: This ratio also does not simplify to 2/5, meaning it does not form a proportion with 2/5.

Therefore, the only ratio that forms a proportion with 2/5 is 16/40.