Maths: Negative Numbers

Negative numbers can be tricky when children first encounter them in the Mathematics course. The real challenge can be in explaining what it means in real life. Every number can have a negative (–). The only number that is neither positive nor negative is zero. Positive and negative numbers can be written as fractions or mixed numbers. Below are the basics of negative numbers.

Basics

Any number above zero is a positive number. These are either written with a plus sign in front of them or no sign. On a number line these numbers are counted from zero to the right. Positive numbers get bigger the further you move to the right.

Any number below zero is a negative number and these are written with a minus sign in front of them e.g. -1 -2, -3 etc. On a number line negative numbers are counted from the zero to the left. Negative numbers get smaller the further you move to the left. Therefore –6 is smaller than –2.

Addition and Subtraction

When it comes to adding or subtracting negative numbers it is vital to remember that when two signs appear beside each other and are different then you must subtract. For example –7 + -6 is a subtraction sum. The opposite occurs when two signs are next to each other and are the same. For example – 7 + +6 is an addition sum.

Similarly, when multiplying and dividing, if the signs are different the answer is negative, and when the signs are the same the answer is positive. For example:

• +6 x – 4 the signs are different so the answer will be negative (-24)
• +6 x +4 the signs are the same so the answer will be positive (+24)

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Real Life Negative Numbers

To support your child in learning negative numbers it is important to try to introduce them in terms of real life situations. The following are real life stories you could use to explain negative numbers:

• You borrow 4 books from a library. Therefore you owe 4 books (-4). Once you have finished one book, you take it back, returning (subtracting) it (a borrowed book is a minus, thus a -1) and so you have subtracted one book you owe, and now owe only three.

  The sum is: -4 -(-1) = -4 + 1 = -3

• You borrow £5 from your friend John to buy lunch. You owe John £5 so this is -5. Later you get your wallet and pay John the £5 back so you can subtract your debit (a net credit, subtracting a negative is a positive). The sum is: -5 -(-5) = -5 +5 = 0, which is what you now owe.

Have a number line close at hand so that your child can either count to the left or count to the right depending on the question. Once your child starts to get a grasp of negative numbers there are many mental questions that you could ask to get them thinking quickly without the use of the number line. For instance, “If I have £50 in the bank and spend £70, how much do I now have?” or “If the temperature is 3 degrees and it cools down by 5 degrees what is the temperature now”?

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