-5/4-(-3/8)
=-5/4+3/8 [LCM of 4and 8 is 8]
=-10/8+3/8
=-7/8

Subtracting the rational number -3/8 from -5/4 requires finding a common denominator and then subtracting the numerators. Let's break down the steps in detail:

Step 1: Finding a common denominator
To subtract fractions, we need to have the same denominator. In this case, the denominators are already different (-8 and 4). To find a common denominator, we need to find the least common multiple (LCM) of these denominators, which is 8.

Step 2: Converting the fractions to have a common denominator
To convert -5/4 and -3/8 to have a common denominator of 8, we need to multiply the numerator and denominator of each fraction by a suitable factor.

For -5/4, we multiply both the numerator and denominator by 2 to get -10/8.
For -3/8, we don't need to make any changes since the denominator is already 8.

Now, the fractions are -10/8 and -3/8.

Step 3: Subtracting the fractions
Now that we have the same denominator, we can subtract the fractions by subtracting their numerators.

-10/8 - (-3/8) = -10/8 + 3/8

To add or subtract fractions with the same denominator, we simply add or subtract the numerators and keep the common denominator.

-10 + 3 = -7

The resulting fraction is -7/8.

Step 4: Simplifying the fraction (if necessary)
In this case, the fraction -7/8 is already in its simplest form because the numerator and denominator have no common factors other than 1.

Step 5: Final answer
The result of subtracting -3/8 from -5/4 is -7/8.

Summary:
To subtract -3/8 from -5/4, we first find a common denominator, which in this case is 8. Then, we convert the fractions to have this common denominator by multiplying the numerators and denominators accordingly. Next, we subtract the numerators and keep the common denominator to obtain the result, which is -7/8. Finally, if necessary, we simplify the fraction to its simplest form.