What happens to the largest share when $360 is divided in a ratio of 2:3:9?

• A. It doubles
• B. It triples
• C. It is larger by a factor of 6
• D. It is one third

Answer: (C)

To determine what happens to the largest share when $360 is divided in a ratio of 2:3:9, we first need to break down the ratio and calculate the individual shares.

The total parts in the given ratio (2 + 3 + 9) sum to 14. Each part of the ratio can be represented as follows:

• The first share (2 parts) = ( \frac{2}{14} \times 360 )

• The second share (3 parts) = ( \frac{3}{14} \times 360 )

• The largest share (9 parts) = ( \frac{9}{14} \times 360 )

Now, we calculate the largest share:

[

\text{Largest share} = \frac{9}{14} \times 360 = \frac{3240}{14} = 231.43

]

Now, let’s interpret what happens to the largest share given the factor in the answer choice. The contribution of each part in the total $360 is derived based on dividing it into smaller shares relative to the total number of parts.

The largest share is based on the interpretation of its ratio part (9) as it represents a