When it comes to simple arithmetic, most of us are accustomed to using positive numbers. However, as soon as we encounter negative numbers, things can get a bit more confusing. In this article, we will compare the calculation of 1+849-844-5 and show the similarities and differences between them.
First, let's define what integers are. Integers are whole numbers that can either be positive or negative, including zero. In our case, 1, 849, 844, and 5 are all integers. When we perform calculations with integers, we follow certain rules, also known as properties.
The first rule we will look at is the commutative property, which states that the order in which we add or multiply numbers does not change the result. This means that whether we calculate 1+849-844-5 or calculate 849+1-844-5, the answer will be the same, which is 1.
The next rule is the associative property, which states that when we add or multiply three or more numbers, we can group them differently without changing the result. For example, in 1+849-844-5, we can group (1+849) and (844-5) as (850-5), which again gives us the answer of 1.
Lastly, we have the distributive property, which states that multiplying a number by a sum is the same as multiplying the number by each term individually and adding the products. In our case, we can rewrite 1+849-844-5 as (1+849) - (844+5), which results in 850-849=1.
Now, let's take a closer look at negative numbers. When we add a negative number to a positive number, it is essentially the same as subtracting the positive number from the negative number. For example, (-5+3) is the same as (-5-3), which both equal -8. Similarly, subtracting a negative number is the same as adding a positive number. For instance, (-5-3) is the same as (-5+3), which both equal -8.
With that being said, let's compare 1+849-844-5 with 849-5-844+1. Using the rules we discussed, we can group (1-5) and (849-844) as -4 and 5, respectively, resulting in 849-844-4+5, which again gives us the answer of 1. We can also group (-844+1) and (849-5) as (-843+844) and 844, respectively, which also results in 1.
In conclusion, whether we use the commutative, associative, or distributive property, or apply the rules of negative numbers, the result is the same for both 1+849-844-5 and 849-5-844+1, which is 1. While it may seem confusing to perform calculations with integers at first, following these basic rules and properties will help us solve any equation with ease. So, next time you encounter a mix of positive and negative numbers, remember these properties and see how they can simplify the calculation for you.
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