List three different ways to write 723 as the sum of three numbers. Explain why all three of your expressions are equal to 723.
To find three different ways to write 723 as the sum of three numbers, we can use a systematic approach. Let's call the three numbers x, y, and z.
1. Approach 1:
In this approach, we will let x be less than y and y be less than z.
Let's assume x = 200, y = 250, and z = 273.
So, 200 + 250 + 273 = 723.
2. Approach 2:
In this approach, we will let x be greater than y and y be greater than z.
Let's assume x = 300, y = 200, and z = 223.
So, 300 + 200 + 223 = 723.
3. Approach 3:
In this approach, we will use a combination of positive and negative integers.
Let's assume x = 400, y = -200, and z = 523.
So, 400 + (-200) + 523 = 723.
Now, let's explain why all three expressions are equal to 723.
In all three approaches, the sum of x, y, and z is equal to 723. This is because addition is commutative and associative.
In Approach 1, we can rearrange the numbers as (200 + 250) + 273, which gives us 723.
In Approach 2, we can rearrange the numbers as (300 + 200) + 223, which gives us 723.
In Approach 3, we can rearrange the numbers as 400 + (-200 + 523), which also gives us 723.
Thus, regardless of the specific values chosen for x, y, and z, the sum of the three numbers will always be equal to 723.