If `7 xx 5= 35 and 35 xx 3= 105`, then state True or False for the following statements
35 is a multiple of 105

Answer

To determine whether the statement "35 is a multiple of 105" is true or false, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Multiples**: A number A is said to be a multiple of another number B if A can be expressed as B multiplied by some integer. In other words, if A = B × n (where n is an integer), then A is a multiple of B.

2. **Identifying the Numbers**: Here, we need to check if 35 is a multiple of 105. This means we need to see if there exists an integer n such that:
\[ 35 = 105 \times n \]

3. **Dividing 35 by 105**: To check if 35 is a multiple of 105, we can divide 35 by 105:
\[ \frac{35}{105} \]

4. **Calculating the Division**: When we perform the division:
\[ \frac{35}{105} = \frac{1}{3} \approx 0.3333 \]
This result is not an integer.

5. **Conclusion**: Since the result of the division is not an integer, it indicates that 35 cannot be expressed as 105 multiplied by any integer. Therefore, 35 is not a multiple of 105.

### Final Answer:
The statement "35 is a multiple of 105" is **False**.

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