Åk 6–9
 
English/فارسی
2.4 Subtracting in different ways
How do you think when you calculation 12 – 7? It is an easy exercise and you probably aren’t even conscious of how you think?  Try to describe how you think.

Some students answered the question like this:

"I imagine that I had 12 and then I took away one at a time. 12, 11, 10, 9, 8, 7, 6, 5. The answer becomes five! ".

"I am buying a soda pop for 12 kr but only have 7 kr.  How much is missing for me to buy the soda pop? 8, 9, 10, 11, 12 – in total 5 crowns".




If you calculate with larger numbers, it can be a good idea to be able to use a written version of mental calculation which can be used both for subtraction as well as addition (the same method we used for addition in section 2.3).  Here are a few examples of how you can use written mental calculation to work with subtraction.



A Calculate every number by themselves
87 - 53 = (80 - 50) + (7 - 3) = 30 + 4 = 34

5,009 - 3,006 = (5,000 - 3,000) + (9 - 6) = 2,000 + 3 = 2,003

437 - 122 = (400 - 100) + (30 - 20) + (7 - 2) = 315



B  Filling out
405 – 398 = ?

From 398 until 400 there are two numbers, and from 400 until 405 there are 5 numbers.
405 – 398 = 2 + 5 = 7

30.3 – 29.5 = ?

From 29.5 until 30 there are 0.5, and from 30 until 30.3 there is 0.3.
30.3 – 29.5 = 0.5 + 0.3 = 0.8



C Increase the ones in every term

431 – 297 = ?

Increase both terms with the same number 3, so that you can take away 300 instead.

431 – 297 =
= (431 + 3) – (297 + 3) =
=  434 - 300 = 134



D Simplify one of the terms
87 - 53 = ?

87 – 53 = 87 – (50 + 3) =
87
– 50 - 3 = (87 – 50) - 3 = 37 - 3 = 34

This method means that the term we are going to subtract with is separated into two terms and then we subtract gradually. 53 is separated into 50 and 3. We subtract then the tens number first
(87 - 50 = 37) and then the ones (37 - 3 = 34).