Addition and subtraction (1)
Positive and negative integers
Integers are whole numbers. They can be positive (above zero) or negative (below zero), like temperatures on a cold day. A number line helps you add and subtract them and find how far apart two integers are.
Positive and negative integers
An integer is a whole number. Positive integers are above zero and negative integers are below zero, written with a minus sign like -5. On a number line the numbers get smaller as you move left, so -10 is less than -5. That is why -10 °C is colder than -5 °C.
Adding and subtracting on a number line
To add, move RIGHT. To subtract, move LEFT. A temperature that rises means add; a temperature that falls means subtract. For example -30 + 5 moves 5 steps right, and -30 - 5 moves 5 steps left.
The difference between two integers
The difference tells you how far apart two integers are. Count the steps from the smaller number up to the larger one. A difference is ALWAYS positive. For 4 and -5, count 5 steps up to 0 and 4 more steps, giving a difference of 9.
Estimating, adding and subtracting large integers
Always estimate first by rounding each number, then do the exact calculation and check it is close to your estimate. For example 34 405 + 90 253 is about 30 000 + 90 000 = 120 000, so the exact answer should be near 120 000.
Worked examples
Adding to a negative number (temperature rises)
- The temperature is -30 °C and rises by 5 °C, so we add: -30 + 5.
- On a number line, start at -30 and move 5 steps to the RIGHT.
Answer: -30 + 5 = -25 °C
Subtracting from a negative number (temperature falls)
- The temperature is -30 °C and falls by 5 °C, so we subtract: -30 - 5.
- On a number line, start at -30 and move 5 steps to the LEFT.
Answer: -30 - 5 = -35 °C
Finding the difference between two integers
- Find the difference between 4 and -5.
- Count the steps from -5 up to 0 (that is 5), then from 0 up to 4 (that is 4).
- Add the steps: 5 + 4. Remember a difference is always positive.
Answer: The difference between 4 and -5 is 9.
Estimating a large calculation
- Estimate 34 405 + 90 253 before calculating.
- Round each number: 34 405 is about 30 000 and 90 253 is about 90 000.
- Add the rounded numbers: 30 000 + 90 000.
Answer: A good estimate is 120 000.
Adding large integers
- Faizah has 5398 points and scores 465 more, so we add: 5398 + 465.
- Line up the digits by place value and add the ones, tens, hundreds and thousands, carrying where needed.
Answer: 5398 + 465 = 5863 points
Where you see this in real life
- Reading temperatures below zero on a cold day, like -10 °C.
- Comparing how much deeper a sperm whale dives than an elephant seal.
- Adding up flight distances between cities such as Dubai to Singapore.
- Working out how many more points you need to reach a target score in a game.
Key words
- Integer
- A whole number, which can be positive, negative or zero.
- Positive number
- A number greater than zero.
- Negative number
- A number less than zero, written with a minus sign like -5.
- Difference
- How far apart two numbers are; it is always positive.
- Estimate
- A sensible answer found by rounding the numbers first.