state true of false
Subtraction of rational number is commutative.

Answer

To determine whether the statement "Subtraction of rational numbers is commutative" is true or false, we can follow these steps:

### Step 1: Understand Commutative Property
The commutative property states that the order of the numbers does not affect the result of the operation. For example, in addition, \( a + b = b + a \). We need to check if this holds for subtraction.

### Step 2: Define Rational Numbers
Let’s take two rational numbers, \( \frac{a}{b} \) and \( \frac{c}{d} \). We will check if the subtraction of these numbers is commutative.

### Step 3: Perform Subtraction in Different Orders
1. First, calculate \( \frac{a}{b} - \frac{c}{d} \).
- To subtract these fractions, we need a common denominator. The common denominator for \( b \) and \( d \) is \( bd \).
- Thus, \( \frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd} \).

2. Now, calculate \( \frac{c}{d} - \frac{a}{b} \).
- Again, using the common denominator \( bd \), we have:
- \( \frac{c}{d} - \frac{a}{b} = \frac{cb - da}{bd} \).

### Step 4: Compare the Results
Now we need to compare the two results:
- From Step 3.1, we have \( \frac{ad - bc}{bd} \).
- From Step 3.2, we have \( \frac{cb - da}{bd} \).

For subtraction to be commutative, these two results must be equal:
\[ \frac{ad - bc}{bd} \neq \frac{cb - da}{bd} \]
This shows that the results are not equal unless \( ad - bc = cb - da \), which is not generally true.

### Conclusion
Since the results of the subtraction depend on the order of the numbers, we conclude that subtraction of rational numbers is **not commutative**. Therefore, the statement is **false**.