Evaluate in a way in which the multiplication process is simplified. Also, state the properties of multiplication used in the process.
a. `376 times 52" b. "76 times 98`

Answer

Let's solve the problems step-by-step, simplifying the multiplication process and stating the properties used.

### a. Evaluate `376 times 52`

1. **Break down the numbers**: We can express 52 as (50 + 2). This will simplify our multiplication.

\[ 376 \times 52 = 376 \times (50 + 2) \]

2. **Use the distributive property**: Apply the distributive property of multiplication over addition.

\[ 376 \times 52 = 376 \times 50 + 376 \times 2 \]

3. **Calculate each part**:
- First, calculate \(376 \times 50\):
\[ 376 \times 50 = 18800 \]
- Next, calculate \(376 \times 2\):
\[ 376 \times 2 = 752 \]

4. **Add the results**:
\[ 18800 + 752 = 19552 \]

5. **Final result**:
\[ 376 \times 52 = 19552 \]

**Properties used**:
- Distributive Property of Multiplication: \(a \times (b + c) = a \times b + a \times c\)

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### b. Evaluate `76 times 98`

1. **Break down the numbers**: We can express 98 as (100 - 2). This will simplify our multiplication.

\[ 76 \times 98 = 76 \times (100 - 2) \]

2. **Use the distributive property**: Apply the distributive property of multiplication over subtraction.

\[ 76 \times 98 = 76 \times 100 - 76 \times 2 \]

3. **Calculate each part**:
- First, calculate \(76 \times 100\):
\[ 76 \times 100 = 7600 \]
- Next, calculate \(76 \times 2\):
\[ 76 \times 2 = 152 \]

4. **Subtract the results**:
\[ 7600 - 152 = 7448 \]

5. **Final result**:
\[ 76 \times 98 = 7448 \]

**Properties used**:
- Distributive Property of Multiplication: \(a \times (b - c) = a \times b - a \times c\)

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