1. October 4, 2012
Negative numbers and decimals
1. Adding and subtracting negative numbers
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2. Explanation October 4, 2012
Sally and Rajani both have some biscuits.
Sally has 3 and Rajani has 5, so Sally has two less than
Rajani.
Sally’s Rajani’s
What would you have two do for Sally, to remove the “2
lessness” she is experiencing?
You could give her 2 more biscuits.
In this way you are taking away the “2 lessness”, by
adding 2 more biscuits to her total.
You are subtracting her “minus 2”, a negative number,
which is the same as adding 2, a positive number.
3 – (-2) = 5
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3. Explanation October 4, 2012
What could you do to now make Rajani have 2 less?
You could take 2, a positive number, away from her.
Sally’s Rajani’s
In this way, you are adding a “2 lessness” to her, or
adding minus 2.
Adding a negative number is the same as subtracting a
positive number.
5 + (-2) = 3
If you imagine that positive numbers have a “+” sign in
front of them, this will help you.
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4. Explanation October 4, 2012
If you imagine that positive numbers have a “+” sign in
front of them, this will help you.
+5 + –2 = +3 When theses two signs are different,
+8 – +4 = +4 then subtract.
+5 – –2 = +7 When theses two signs are the
+8 + +4 = +12 same, then add.
So
5
+ + –2= 3 8 – –2 = 10
+ + 1 – 7 = –6
+
is also is also is also
Knowing this simple rule helps with some short cuts.
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5. Explanation October 4, 2012
Here you need to subtract from a minus number,
because the middle signs are different.
– 8 – +4 = – 12
A quick way is to add the numbers, then place a “–” in
front of the answer.
This always works when you subtract from a minus
number.
Here you need to add to a minus number, because the
middle signs are the same
–3 –+– 4 = +7
A quick way is to subtract the numbers, then give the
answer the same sign as the operation involving the
larger number.
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6. Explanation October 4, 2012
When you have a whole string of numbers to add and
subtract…
3–8+7+4+9–6–8–4
Add all the numbers you 3 8
need to add together. 7 6
Add all the numbers you 4 8
need to subtract together. 9 4
23 26
Your answer is the
difference between the –3
totals.
If the “add” total was bigger, the answer remains positive.
If the “subtract” total was bigger, add a minus sign.
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7. Revise October 4, 2012
Before completing some exercises, you need to
remember that…
Multiplying and dividing two negative, or two positive
numbers always gives a positive answer.
-3 × -9 = 27
Multiplying and dividing two numbers where one is
negative and the other positive always gives a negative
answer.
-12 ÷ 4 = -3
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