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The sum is the result of adding two or more numbers together. In mathematics, summation is represented by the Greek letter sigma (Σ), which indicates adding a series of numbers.
Sigma (Σ) is the Greek capital letter for 'S' (for 'Sum'). It's a compact way to write "add all these numbers together."
i = 1 (bottom): Start at index 1
n = 5 (top): End at index 5
xᵢ: Add x₁ + x₂ + x₃ + x₄ + x₅
Order doesn't matter
Grouping doesn't matter
Adding zero doesn't change the number
Rent: $1200, Groceries: $450, Utilities: $180, Transportation: $250
Total: $1200 + $450 + $180 + $250 = $2,080
Scores: 85, 92, 78, 88, 95
Total Points: 85 + 92 + 78 + 88 + 95 = 438
Store A: 145 items, Store B: 203 items, Store C: 167 items, Store D: 189 items
Total Inventory: 145 + 203 + 167 + 189 = 704 items
Combine numbers that add to 10, 100, etc. for easier mental math
Keep a running sum to track progress and catch errors
Round numbers to estimate the sum, then verify your exact answer is close
Sigma (Σ) is the Greek letter used in mathematics to represent summation - adding a series of numbers together. It's a shorthand notation that means 'sum all these values.'
Add them the same way, but remember that adding a negative is the same as subtracting. For example: 10 + (-5) + 3 = 10 - 5 + 3 = 8.
In everyday language, 'sum' and 'total' mean the same thing - the result of adding numbers. 'Sum' is more commonly used in mathematics, while 'total' is used in everyday contexts.
Yes! Just add them as normal: 10 + 2.5 + 7.3 + 5 = 24.8. Line up the decimal points if doing it by hand.
The sum of an empty set is defined as zero. This is the 'additive identity' - the starting point before any numbers are added.
Several methods: (1) Add in reverse order, (2) Estimate by rounding first, (3) Use a calculator to verify, (4) Subtract your answer from the last running total to see if you get the last number.