April 13, 2023

Negative numbers and decimals

1. Adding and subtracting negative numbers

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April 13, 2023

Sally and Rajani both have some biscuits.Sally has 3

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

and Rajani has 5, so Sally has two less thanRajani.

Explanation

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Sally’s Rajani’s

April 13, 2023

What could you do to now make Rajani have 2 less?You could take 2, a positive number, away from her.

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.

Explanation

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Sally’s Rajani’s

April 13, 2023

–

If you imagine that positive numbers have a “+” sign in front of them, this will help you.

+5 + – = +3 When theses two signs are different, then subtract.+8 – + = +4

+5 – = +7 When theses two signs are the same, then add.+8 + + = +

24

2124

Knowing this simple rule helps with some short cuts.

5 – = 3 8 – – =2 102 –1 =7++is also is alsois also

So

+ ++ 6–

Explanation

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April 13, 2023

– – + = 1248

Here you need to subtract from a minus number, because the middle signs are different.

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

A quick way is to subtract the numbers, then give the answer the same sign as the operation involving the larger number.

7+

Explanation

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April 13, 2023

8

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 need to add together.

Add all the numbers you need to subtract together.

Your answer is the difference between the totals.

If the “add” total was bigger, the answer remains positive.If the “subtract” total was bigger, add a minus sign.

3749

86

4

2623

3–

Explanation

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April 13, 2023

Before completing some exercises, you need to remember that… Multiplying and dividing two negative, or two positive numbers always gives a positive answer.

Multiplying and dividing two numbers where one is negative and the other positive always gives a negative answer.

-3 × -9 = 27

-12 ÷ 4 = -3

Revise

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