-2:5 1/3 -7/10 :1 1/15

To solve the ratio \(-2:5, \frac{1}{3}, -\frac{7}{10}:1 \frac{1}{15}\), we will first convert all mixed fractions into improper fractions.

1. Convert \(1 \frac{1}{15}\) to an improper fraction: \[ 1 \frac{1}{15} = \frac{1 \times 15 + 1}{15} = \frac{15 + 1}{15} = \frac{16}{15} \]

Now we have: \[ -2:5, \frac{1}{3}, -\frac{7}{10}:\frac{16}{15} \]

2. Now we can rewrite the whole expression in a simpler way: \[ \text{Let's denote the ratio as } a:b:c:d \] where: \[ a = -2, \quad b = 5, \quad c = \frac{1}{3}, \quad d = -\frac{7}{10}, \quad e = \frac{16}{15} \]

Now we will express all parts in terms of a common reference. Here we will address the two parts of the ratio separately:

Calculating the first part:

Considering \( -2:5\) and \(\frac{1}{3}\), we'll take the ratio of \(-2\) to \(5\) as one entity and \(\frac{1}{3}\) separately.

• The total value combines with one part through multiplication:

Let's scale to find common denominators; first, we'll scale them. However, since we're looking for ratios, we can keep relative values.

Calculating the second part:

Now, considering the other ratio, \(-\frac{7}{10}: \frac{16}{15}\):

• To simplify this, we can cross-multiply: \[ -\frac{7}{10} : \frac{16}{15} = -7 \times 15 : 10 \times 16 = -105 : 160 \]

Expressing all ratios together is quite complex, but we can write the entire expressions as:

If we combine all parts of the ratio, we can just express:

1. The first portion of the ratio: \[-2:5\]

2. And the additional fraction and ratios derived from combining: \[-105:160\]

Conclusively, the final representation would depend on how further you wish to express it, common context can deduce simple positive integer ratios, or retain negative signs based on value interpretation.

If a common value extraction is further required, please clarify, and I will assist in detail for relationships or comparative ratios following through mathematic reduction as you stated here.