Question
Use the commutative and associative properties to solve the following problems.
2 x 2 x 5 x 5
2 x 2 x 5 x 5
Answers
GPT-4o mini
To solve the expression \(2 \times 2 \times 5 \times 5\) using the commutative and associative properties, we first rewrite the expression to group numbers in a way that simplifies calculation:
1. **Associative Property**: This property allows us to group numbers in a way that makes multiplication easier. We can group the numbers as follows:
\[
(2 \times 2) \times (5 \times 5)
\]
2. **Calculate each group**:
- \(2 \times 2 = 4\)
- \(5 \times 5 = 25\)
3. **Now, multiply the results**:
\[
4 \times 25
\]
4. **Calculate \(4 \times 25\)**:
- You can think of \(4 \times 25\) as \(100\) (since \(4 \times 25 = 100\)), or calculate it by breaking it down:
\[
4 \times 25 = 4 \times (20 + 5) = (4 \times 20) + (4 \times 5) = 80 + 20 = 100
\]
Thus, the final value of \(2 \times 2 \times 5 \times 5\) is \(100\).
1. **Associative Property**: This property allows us to group numbers in a way that makes multiplication easier. We can group the numbers as follows:
\[
(2 \times 2) \times (5 \times 5)
\]
2. **Calculate each group**:
- \(2 \times 2 = 4\)
- \(5 \times 5 = 25\)
3. **Now, multiply the results**:
\[
4 \times 25
\]
4. **Calculate \(4 \times 25\)**:
- You can think of \(4 \times 25\) as \(100\) (since \(4 \times 25 = 100\)), or calculate it by breaking it down:
\[
4 \times 25 = 4 \times (20 + 5) = (4 \times 20) + (4 \times 5) = 80 + 20 = 100
\]
Thus, the final value of \(2 \times 2 \times 5 \times 5\) is \(100\).