Adding Integers
Every question with a fully worked solution.
- Adding Integers - Video - Adding Integers | How to Add Positive and Negative Integers Watch
Theory
To add an integer, start at the first number on a number line and jump by the second: right for a positive, left for a negative. This Year 7 maths page shows how to add integers on a number line, the rules for same signs and different signs, how to add three integers and how to find a missing number.
Adding a positive moves right: \(-3 + 8 = -3 + 3 + 5 = 5\).
Adding a negative is the same as subtracting, so it moves left: \(3 + (-8) = 3 - 8 = -5\).
The size (or magnitude) of an integer is its distance from zero. The size of \(-6\) is \(6\).
In \(3 + (-8)\) the \(+\) is an operation (add) and the \(-\) in \((-8)\) shows a position (left of zero). Brackets keep the two signs apart.
A number and its opposite add to zero: \(-7 + 7 = 0\).
Adding by the signs:
Same signs: add the sizes and keep the sign.
Different signs: subtract the sizes and keep the sign of the larger size.
How to add on a number line
- Start at the first number.
- Jump right for a positive, left for a negative.
- Cross zero in two steps: to \(0\), then the rest.
How to add with the sign rules
- Same signs: add the sizes and keep the sign.
- Different signs: subtract the smaller size from the larger, and use the sign of the larger size.
- Three or more numbers: work left to right, or add all the negatives and all the positives first.
How to find a missing number
- Add the numbers you know.
- Find the jump from that total to the answer: right is positive, left is negative.
- Check by putting your number back in.
| \(-4 + 6\) | \(=\) | \(-4 + 4 + 2\) |
| \(\) | \(=\) | \(2\) |
\(2\)
(i) \(-5 + (-8)\)
(ii) \(-14 + 9\)
(iii) \(11 + (-11)\)
| \(-5 + (-8)\) | \(=\) | \(-5 - 8 = -13\) |
| \(-14 + 9\) | \(=\) | \(-(14 - 9) = -5\) |
| \(11 + (-11)\) | \(=\) | \(0\) |
(i) Same signs: \(-13\)
(ii) Different signs, \(14 > 9\): \(-5\)
(iii) Opposites: \(0\)
| \(-9 + 17\) | \(=\) | \(8\) |
| \(8 + (-6)\) | \(=\) | \(2\) |
Work left to right: \(2\).
(i) \(-6 + (-2) + \square = 3\)
(ii) \(7 + \square = -4\)
(i) \(-6 + (-2) = -8\). From \(-8\) to \(3\): \(8\) up to \(0\), then \(3\) more, a jump of \(11\) right.
(ii) From \(7\) to \(-4\): \(7\) down to \(0\), then \(4\) more, a jump of \(11\) left.
| \(-8 + 11\) | \(=\) | \(3\) |
| \(7 + (-11)\) | \(=\) | \(-4\) |
(i) \(11\)
(ii) \(-11\)
| \(-28 + 45\) | \(=\) | \(17\) |
| \(17 + (-6)\) | \(=\) | \(11\) |
His balance is \(\$11\).
First undo the \(+10\) by adding its opposite, \(-10\). Then add the second offset.
| \(20 + (-10)\) | \(=\) | \(10\) |
| \(10 + (-5)\) | \(=\) | \(5\) |
It is hour \(5\), which is 5 am, in the second city.
Common pitfalls
Frequently asked questions
What happens when you add a negative number?
It is the same as subtracting. \(3 + (-8) = 3 - 8 = -5\).
What is the rule for adding two negatives?
Add the sizes and keep the negative sign. \(-5 + (-4) = -9\).
What if the signs are different?
Subtract the sizes and use the sign of the larger size. \(-13 + 5 = -8\).
What do a number and its opposite add to?
Zero. \(-7 + 7 = 0\).
How do you find a missing number in a sum?
Find the jump from the known total to the answer. From \(-8\) to \(3\) is \(11\) right, so the missing number is \(11\).