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Found this exercise in the BBC Bitesize website: Fractions of amounts

Asking which value is larger between $2/3$ of $24$ and $3/4$ of $20$.

My calculations brought me to:

$2/3$ of $24$ = $16/24$

while

$3/4$ of $ 20$ = $15/20$.

Making them with the same denominator I obtained:

$2/3$ of $24$ = $16/24$ = $80/120$

while

$3/4$ of $20$ = $15/20$ = $90/120$

It's clear for me that $3/4$ of $20$ is bigger than $2/3$ of $24$. But the answer is not correct as they define $16 > 15$.

I don't understand, am I missing something?

Thanks

-- Update -- I am sorry. I understand the answers .. but I don't understand.

This funny website (pizza fraction calculator) helped me figure how many pieces of a pizza would it be to cut 16 pieces out of 24 and 15 out of 20.

this is 16 pieces out of 24: enter image description here

and this is 15 pieces out of 20: enter image description here

Either I am blind or 15 pieces out of 20 seems to be more pizza for me.

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    The problem is asking about the results of "three quarters of $20$" and so on. "Three quarters of $20$" is $15$, not $15\over 20$. – 2017-01-06
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    I see, but can't you represent three quarters of 20 as 15/20 too? Thanks anyway, I understand your point – 2017-01-06
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    Updated question with 2 images – 2017-01-06
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    You have drawn 2/3 of one pizza. 2/3 of 24 means taking 2/3rds of *24 pizzas*. – 2017-01-06
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    @Rahul, I see. Thank you, I didn't think about that – 2017-01-06

3 Answers 3

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Hint $$\frac23 \times24=\frac{2\times 24}{3}=\frac{48}{3}=16$$ $$\frac34\times 20=\frac{3\times 20}{4}=\frac{60}{4}=15$$

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    Thanks for your answer. I obtained 16 and 15 but I thought I could represent them as fractions 16/24 and 15/20. – 2017-01-06
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    @Lino Why would you do that? $16\ne 16/24$ and $15\ne 15/20$. – 2017-01-06
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    Yes, 16 is different than 16/24, I agree, but I cannot see any difference in saying that 2/3 of 24 is = 16 (out of) 24 - 16/24 – 2017-01-06
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    @Lino Why are you adding an extra "out of"? It's just asking you what 2/3 of 24 is. It's not asking what 2/3 of 24 is out of 24 (which would just be 2/3 again, the 24 wouldn't matter). – 2017-01-06
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    If I ask you to get 16 pieces of a pizza with 24 pieces, how many pieces did you get (in fractions) out of 24 pieces? – 2017-01-06
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    @Lino I would have got 16 pieces. In a fraction it would be $16/1$. – 2017-01-06
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    I don't think it's correct. If you get one quarter of a pizza with 4 pieces you say you got 1/4 not 1/1. – 2017-01-06
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    @Lino The question is asking "if a pizza has 24 pieces, and you have 2/3 of the pizza, how many slices did you get?" and the answer is 16 slices – 2017-01-06
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    @Lino In the pizza example, you have 1/4 of the pizza but 1/1 of a slice. – 2017-01-06
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    I have updated the question with 2 images. Maybe I have more pieces of pizza but they are smaller and if I put them together they are less than the other case. still confused. – 2017-01-06
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    @Lino The question isn't asking how much pizza. It's asking how many slices. – 2017-01-06
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    Okay, then it's okay. There are more number of slices in 2/3 of 24. The question "which one is larger" is pretty confusing to me. Thanks for your time anyway! – 2017-01-06
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$$\frac {2}{3} \text { of } 24 =\frac {2}{3}\times 24 =16$$ $$\frac {3}{4} \text { of } 20 =\frac {3}{4}\times 20 =15$$

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    Thanks for your answer. I obtained 16 and 15 but I thought I could represent them as fractions 16/24 and 15/20. – 2017-01-06
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You have that $$\frac{2}{3}\cdot 24 = \frac{48}{3} = 16$$ and $$\frac34 \cdot 20 = 3\cdot\frac{20}{4} = 3\cdot 5 = 15. $$ That's why.

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    Thanks for your answer. I obtained 16 and 15 but I thought I could represent them as fractions 16/24 and 15/20. – 2017-01-06