If you add a positive number with another positive number, the sum is always a positive number; if you add two negative numbers, the sum is always a negative number. So when you have an algebra problem where you have to add signed numbers that are the same sign, remember this catchy “S” rule:
When the signs are the same, you find the sum, and the sign of the sum is the same.
This rule holds when a and b represent any two real numbers:
(+a) + (+b) = +(a + b)
(–a) + (–b) = –(a + b)
If a number doesn't have a sign, such as 6, it's a positive number, +6.
Here are some examples of adding numbers that have the same sign:
You have 3 apples and your friend gives you 4 apples.
(+3) + (+4) = +7
Because you've added +3 and +4, and the signs are the same, you first find the sum, which is 7. Because the signs of +3 and +4 are the same (both positive), the sum is also a positive number, and so the answer is +7.
You owe Jon $8 and have to borrow $2 more.
(–8) + (–2) = –10
Because you've added –8 and –2, and the signs are the same, you first find the sum, which is 10. Because the signs of –8 and –2 are the same (both negative), the sum is also a negative number, and so the answer is –10.
Even if you're adding more than just two numbers, the rule still holds: If the signs are the same, the sign of the sum is the same. Check out these examples:
(+8) + (+11) + (+5) = +24
(–14) + (–100) + (–3) = –117
(+4) + (+7) + (+2) + (+10) = +23
(–5) + (–2) + (–3) + (–1) = –11