Middle School

Reflection and Discussion

Casey was given the problem 57 + 274. He knows that addition is commutative, so the answer to 57 + 274 is the same as 274 + 57. He wondered whether it was easier to solve 57 + 274 or 274 + 57.

What do you think?

Answer :

The correct answer is that it is easier to solve 274 + 57.

When adding two numbers, it is often easier to start with the larger number and then add the smaller number. This is because when adding larger place values (like hundreds and tens), it is straightforward to keep track of any carrying that needs to occur. In the case of 274 + 57, one can add the hundreds (200 + 0), the tens (70 + 50), and then the ones (4 + 7). This approach minimizes the chances of making mistakes with carrying over from one place value to the next.

Let's add both expressions to illustrate this:

For 57 + 274:

1. Start by adding the ones place: 7 + 4 = 11. Write down the 1 and carry over the 1 to the tens place.

2. Add the tens place: 5 + 7 + 1 (carried over) = 13. Write down the 3 and carry over the 1 to the hundreds place.

3. Add the hundreds place: 2 + 0 + 1 (carried over) = 3.

4. Combine the results: 331.

For 274 + 57:

1. Start by adding the ones place: 4 + 7 = 11. Write down the 1 and carry over the 1 to the tens place.

2. Add the tens place: 7 + 5 + 1 (carried over) = 13. Write down the 3 and carry over the 1 to the hundreds place.

3. Add the hundreds place: 2 + 0 + 1 (carried over) = 3.

4. Combine the results: 331.

Both methods yield the same result, which is 331. However, starting with the larger number (274 + 57) is generally considered easier because it involves adding a smaller number to a larger one, which can be more intuitive and reduces the likelihood of carrying errors

Answer:

it might be easier to solve 274+57 only because the bigger number is before the smaller number.But in the end, its all the same answer

Step-by-step explanation: