Help with finalising knowledge on division

[Noaaaa]

Hi,

I didn't know where else to put this, so sorry if it's in the wrong place

I have just finished GCSE Maths and am looking to move on to A Level. My issue with maths has always been that my knowledge with some areas of division (mainly mental division, long division etc.) is not as strong as it should be. I can do the complicated areas, but when division comes up I struggle. The only resources I can find for this online are literally aimed at small children that I find way too basic - I can't seem to find the areas that I need.

Does anyone have any useful links / tips / places to go for resources to help my finalise my knowledge on division for when I move onto A Level Maths?

Thanks

 

[JeffM]

Unfortunately doing exact division by hand involves a tedious and convoluted algorithm (a fancy word for a detailed procedure.) Someone here can undoubtedly give you that algorithm in a concise form, but it has almost zero practical use in the age of hand calculators and has, as far as I know, almost no theoretical interest.

So why do you think this is important?

 

[lev888]

Hi,

I didn't know where else to put this, so sorry if it's in the wrong place

I have just finished GCSE Maths and am looking to move on to A Level. My issue with maths has always been that my knowledge with some areas of division (mainly mental division, long division etc.) is not as strong as it should be. I can do the complicated areas, but when division comes up I struggle. The only resources I can find for this online are literally aimed at small children that I find way too basic - I can't seem to find the areas that I need.

Does anyone have any useful links / tips / places to go for resources to help my finalise my knowledge on division for when I move onto A Level Maths?

Thanks

Can you provide a few examples of problems you found difficult?

 

[Noaaaa]

Can you provide a few examples of problems you found difficult?

Mainly it's just things such as dividing smaller numbers by bigger numbers (this sounds so basic lol) like 0.3 ÷ 253 for example. Or 0.4 ÷ 0.9, 1/3 ÷ 53 etc. I wouldn't even know where to start with doing problems ones like that

 

[JeffM]

Mainly it's just things such as dividing smaller numbers by bigger numbers (this sounds so basic lol) like 0.3 ÷ 253 for example. Or 0.4 ÷ 0.9, 1/3 ÷ 53 etc. I wouldn't even know where to start with doing problems ones like that

Ahh. Use the laws of exponents to turn the division into dividing a bigger number by a smaller. This used to be formally taught back when we did calculations by slide rule.

[MATH]\dfrac{0.4}{0.9} = \dfrac{4 * 10^{-1}}{9 * 10^{-1}}= \dfrac{40 * 10^{-2}}{9 * 10^{-1}} =\\ = \dfrac{40}{9} * 10^{\{(-2)-(-1)\}} = \dfrac{40}{9} * 10^{-1} \approx 4.444 * 10^{-1} = 0.4444.[/MATH]
Now here is something that you may not know. In algebra and calculus, we frequently prefer to keep things exact. There is no exact decimal representation of 1/3 divided by 53. It is approximately 0.0062893, but that is not exact. So we may well prefer to go

[MATH]\dfrac{1}{3} \div 53 = \dfrac{\dfrac{1}{3}}{53} = \dfrac{\dfrac{1}{3}}{\dfrac{53}{1}} = \\ \dfrac{1}{3} * \dfrac{1}{53} = \dfrac{1}{159}.[/MATH]That is an exact answer.

Now if you insist on reducing that to a decimal, look how easy it is using exponents and a fraction containing only whole numbers.

[MATH]\dfrac{1}{159} = \dfrac{1000 * 10^{-3}}{159} = \dfrac{1000}{159} * 10^{-3} \approx\\ 6.2893 * 10^{-3} = 0.0062893.[/MATH]

 

[Noaaaa]

Ahh. Use the laws of exponents to turn the division into dividing a bigger number by a smaller. This used to be formally taught back when we did calculations by slide rule.

[MATH]\dfrac{0.4}{0.9} = \dfrac{4 * 10^{-1}}{9 * 10^{-1}}= \dfrac{40 * 10^{-2}}{9 * 10^{-1}} =\\ = \dfrac{40}{9} * 10^{\{(-2)-(-1)\}} = \dfrac{40}{9} * 10^{-1} \approx 4.444 * 10^{-1} = 0.4444.[/MATH]
Now here is something that you may not know. In algebra and calculus, we frequently prefer to keep things exact. There is no exact decimal representation of 1/3 divided by 53. It is approximately 0.0062893, but that is not exact. So we may well prefer to go

[MATH]\dfrac{1}{3} \div 53 = \dfrac{\dfrac{1}{3}}{53} = \dfrac{\dfrac{1}{3}}{\dfrac{53}{1}} = \\ \dfrac{1}{3} * \dfrac{1}{53} = \dfrac{1}{159}.[/MATH]That is an exact answer.

Now if you insist on reducing that to a decimal, look how easy it is using exponents and a fraction containing only whole numbers.

[MATH]\dfrac{1}{159} = \dfrac{1000 * 10^{-3}}{159} = \dfrac{1000}{159} * 10^{-3} \approx\\ 6.2893 * 10^{-3} = 0.0062893.[/MATH]

Thanks, this really helps!