Finding a fraction of a number.

[christina.b]

Can anyone help please? I can find a fraction of a number, e.g 2/5 of 900 = 360. I did this by dividing 900 by 5 then multiplying my answer (180) by 2.

I am now stuck on a question that asks me something slightly different and I don't quite understand how to work it out. It's not much different from what I just mentioned, it's like it's just swapped around.
It says: A farmer has a 1200 hectare farm, of which 720 hectares are for vegetables. What fraction is this (in its lowest terms)?

Any help is appreciated.

 

[HallsofIvy]

A fraction is an "indicated division". "What fraction of 1200 hectares is 720 hectares?"

That will be \(\displaystyle \frac{720}{1200}\) and now you want to reduce. Probably the simplest way is to do it "step by step". Seeing that "0" at the end of both numbers, they are both divisible by 10: \(\displaystyle \frac{720}{1200}= \frac{(10)(72)}{(10)(120)}= \frac{72}{120}\) since the "10" in numerator and denominator will cancel. Now I observe that 72 and 120 are both even, 72= 2(36) and 120= 2(60) so \(\displaystyle \frac{72}{120}= \frac{(2)(36)}{(2)(60)}= \frac{36}{60}\). And 36 and 60 are both even: \(\displaystyle \frac{36}{60}= \frac{2(18)}{2(30)}= \frac{18}{30}\). And 18 and 30 are both even: \(\displaystyle \frac{18}{30}= \frac{(2)(9)}{(2)(15)}= \frac{9}{15}\). Those are NOT even but they are both multiples of 3: \(\displaystyle \frac{9}{15}= \frac{(3)(3)}{(3)(5)}= \frac{3}{5}\). Finally, 3 and 5 have no factors I common so \(\displaystyle \frac{3}{5}\) is the "final answer".

 

[christina.b]

A fraction is an "indicated division". "What fraction of 1200 hectares is 720 hectares?"

That will be \(\displaystyle \frac{720}{1200}\) and now you want to reduce. Probably the simplest way is to do it "step by step". Seeing that "0" at the end of both numbers, they are both divisible by 10: \(\displaystyle \frac{720}{1200}= \frac{(10)(72)}{(10)(120)}= \frac{72}{120}\) since the "10" in numerator and denominator will cancel. Now I observe that 72 and 120 are both even, 72= 2(36) and 120= 2(60) so \(\displaystyle \frac{72}{120}= \frac{(2)(36)}{(2)(60)}= \frac{36}{60}\). And 36 and 60 are both even: \(\displaystyle \frac{36}{60}= \frac{2(18)}{2(30)}= \frac{18}{30}\). And 18 and 30 are both even: \(\displaystyle \frac{18}{30}= \frac{(2)(9)}{(2)(15)}= \frac{9}{15}\). Those are NOT even but they are both multiples of 3: \(\displaystyle \frac{9}{15}= \frac{(3)(3)}{(3)(5)}= \frac{3}{5}\). Finally, 3 and 5 have no factors I common so \(\displaystyle \frac{3}{5}\) is the "final answer".

Thank you very much, really helpful.

 

[HallsofIvy]

If I were really good I would have noticed right at the start by both 720 and 1200 are divisible by 240 (their "greatest common divisor") but I've never been able to do that!