**Calculation of 13/4 - 31/6:**

To calculate the subtraction of fractions, we need to have a common denominator.

First, let's find the common denominator for 4 and 6, which is 12.

Now, we need to convert the fractions to have a denominator of 12.

For 13/4, we multiply both the numerator and denominator by 3 to get 39/12.

For 31/6, we multiply both the numerator and denominator by 2 to get 62/12.

Now, we can subtract the two fractions.

(39/12) - (62/12) = -23/12

Therefore, 13/4 - 31/6 = -23/12.

**Calculation of 10/3:**

10/3 is an improper fraction, which means the numerator is greater than the denominator. We can convert it to a mixed number.

To do this, we divide the numerator (10) by the denominator (3).

10 ÷ 3 = 3 with a remainder of 1.

Therefore, 10/3 can be written as the mixed number: 3 1/3.

**Calculation of 0.087:**

0.087 is a decimal number. We can express it as a fraction by placing the digits after the decimal point over the appropriate power of 10.

0.087 = 87/1000.

**Calculation of 0.3717 ÷ 0.9:**

To divide decimals, we can move the decimal point of the divisor (0.9) to the right until it becomes a whole number.

In this case, we move the decimal point one place to the right, which gives us 9.

Now, we can divide 0.3717 by 9.

0.3717 ÷ 9 = 0.0413.

Therefore, 0.3717 ÷ 0.9 = 0.0413.

In summary:

- 13/4 - 31/6 = -23/12
- 10/3 = 3 1/3
- 0.087 = 87/1000
- 0.3717 ÷ 0.9 = 0.0413