To simplify the addition of $74 + 12 + 53 + 13 + 14 + 12$, we can use the associative property and commutative property of addition. These properties allow us to group the numbers in a way that makes the addition easier and more efficient.

Step 1: Grouping terms for easier calculation

Look for pairs of numbers that add up to round numbers (like multiples of 10) or numbers that are easy to add mentally.

• $74 + 12 = 86$
• $53 + 13 = 66$
• $14 + 12 = 26$

Now, we have the expression:
$86 + 66 + 26$

Step 2: Adding the simpler groups

Now we add the results from Step 1:

• $86 + 66 = 152$
• $152 + 26 = 178$

So, the simplified sum is $178$.

How this simplifies the addition:

By grouping numbers that result in easier sums (like $74 + 12 = 86$), we reduced the number of operations needed. It avoids adding the numbers in a straight sequence, which might have been slower or more prone to errors if done without grouping.

Would you like further clarification or additional examples?

Here are some related questions that expand on this approach:

1. How can the commutative property of addition be used to rearrange numbers for easier mental math?
2. Can the distributive property help with simplifying addition in certain cases?
3. What happens if you have three numbers that are all multiples of 10? How can you simplify their addition?
4. Can the associative property help when dealing with larger numbers or more complex expressions?
5. What are some common strategies to simplify subtraction using properties of numbers?

Tip: When adding multiple numbers, always look for pairs that make round numbers, as they are easier to calculate quickly!