calculating heights: accumulating some heights for calculating in total the total hts

[Ryan$]

Hi guys ; sorry about that but still confused on this thing about accumulating some heights for calculating in total the total height .... what's confused me is when I have for example height =80; and other height 20 20 20 20 ; so I imagine it as something with size 20 in real life and get stuck because in real life we always have errors and not measuring pieces exactly ...


so please is there any good way please please please to visualize "quantity"(number) of whatever thing that could help me understand the concept of accumulating quantities .... thanks! I always visualize quantity as something which makes it complex for me to solve problems..

 

[Denis]

Oh boy...

 

[Otis]

… [I've been given heights] 20 20 20 20 [to add]; so I imagine [each] as something with size 20 in real life and get stuck because in real life we always have errors and not measuring pieces exactly …]

Precision depends on context.

If your exercise models heights and you're given four heights as 20 units each, then consider each height as exactly 20 units high (regardless of the real world).

Don't think about changing given numbers or concerning yourself with reasonableness of models in any exercise -- unless you're specifically asked to do those sorts of things.

Many exercises model things in the real world by using ideal conditions and rounded measurements and exceptions to reality. These exercises are only for practice; focus on things like rules, basic formulas, properties, and methods. Be more concerned with accuracy (does your answer make sense), not precision (is it exact to the nth degree, using advanced rules for measurement taking, standard calibrations and the concept of significant figures).

Once you get into subjects using applied mathematics (eg: physics, biology, economics, engineering), then you'll be learning about precision and how it affects mathematics in the real world. Until then, remember that most real-world exercises you get now will be idealized, so as to focus more on meaning and less on how precise the answer needs to be.

Find the stacked height of four shipping containers, where each container measures 20 units high.

20 + 20 + 20 + 20 = 80

That's accurate! Who cares whether or not it's a precise model of heights in some actual, real-world situation. The exact answer to the exercise is: 80 units. Whether the measurements deviate in any significant way from reality is a question for somebody working in the real world to worry about. :cool:

 

[Ryan$]

once you wrote 20+20+20+20=80 I visualized it as
-------------------- + ------------------- +---------------------+---------------------=
-------------------------------------------------------------------------------------------

which every piece is 20 ...but what's confused me that the "+" between every piece may have also a space other than the size of the piece itself .. so it makes me confused!

 

[Otis]

once you wrote 20+20+20+20=80 I visualized it as

-------------------- + ------------------- + --------------------- + --------------------- =
-------------------------------------------------------------------------------------------

which every piece is 20 ...but what's confused me that the "+" between every piece may have also a space other than the size of the piece itself .. so it makes me confused!

In my example exercise (using shipping-container height), I gave ideal heights only (nice, Whole numbers). The shipping containers are imaginary, you're not given information about or asked to consider space between containers. Don't create variations to the given exercise. Use the numbers as given and add them. Done!

There's no "space" between exact numbers comprising a sum, either. Stop thinking about numbers that way. You're going to drive yourself insane. :shock: