Is the answer book wrong?
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Is the answer book wrong?
Alia ate 1/3 of a pizza for lunch. Later she ate 2/5 of the remaining pizza as a snack. How much of the pizza did she eat altogether?
A. 3/8
B. 3/5
C. 11/15
D. 4/5
E. 3/15
DC made the answer 3/5 (B)
Answer sheet says C 11/15, but I agree with DC!
Can anyone explain why it's C please?
TIA
A. 3/8
B. 3/5
C. 11/15
D. 4/5
E. 3/15
DC made the answer 3/5 (B)
Answer sheet says C 11/15, but I agree with DC!
Can anyone explain why it's C please?
TIA
Re: Is the answer book wrong?
Answer C is correct.
I think you’ve missed that she are 2/5 of the remaining pizza. So you need to work out what 2/5 of 2/3 is, to work out how much is eaten then work out how much is left.
I think you’ve missed that she are 2/5 of the remaining pizza. So you need to work out what 2/5 of 2/3 is, to work out how much is eaten then work out how much is left.
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Re: Is the answer book wrong?
These are our steps:
Ate 1/3 = 5/15
Ate 2/5 of remaining, so 2/5 x 2/3 = 4/15
Altogether ate 5/15 + 4/15 = 9/15 = 3/5
Am I missing something
Ate 1/3 = 5/15
Ate 2/5 of remaining, so 2/5 x 2/3 = 4/15
Altogether ate 5/15 + 4/15 = 9/15 = 3/5
Am I missing something
Re: Is the answer book wrong?
Yes
1/3 = 5 /15 so she has already eaten 5/15
Remaining is 10/15
2/5 of this is 6/15 (x both x 3)
so 5/15 + 6/15 = 11/15
1/3 = 5 /15 so she has already eaten 5/15
Remaining is 10/15
2/5 of this is 6/15 (x both x 3)
so 5/15 + 6/15 = 11/15
mad?
Re: Is the answer book wrong?
I think Sleepyhead is correct
Imagine the pizza had been precut into 15 slices
First she eats 1/3 of them ie 5 slices - there are now 10 slices left
Then she eats 2/5 of the 10 slices ie 4 slices (4/10 and 2/5 are equivalent fractions)
She's eaten 9 altogether which is 9/15 or 3/5 of the original pizza
You can see how they choose the "wrong" answers too to catch out the common mistakes
A: from incorrectly adding 1/3 + 2/5 (adding tops & bottoms of the fractions)
C: This would be correct if adding 1/3 +2/5 properly as you would convert both to 15ths 5/15 + 6/15, so without the words "of the remaining pizza"
D: ? not sure
E: adding 1+2 and multiplying the denominators together
Imagine the pizza had been precut into 15 slices
First she eats 1/3 of them ie 5 slices - there are now 10 slices left
Then she eats 2/5 of the 10 slices ie 4 slices (4/10 and 2/5 are equivalent fractions)
She's eaten 9 altogether which is 9/15 or 3/5 of the original pizza
You can see how they choose the "wrong" answers too to catch out the common mistakes
A: from incorrectly adding 1/3 + 2/5 (adding tops & bottoms of the fractions)
C: This would be correct if adding 1/3 +2/5 properly as you would convert both to 15ths 5/15 + 6/15, so without the words "of the remaining pizza"
D: ? not sure
E: adding 1+2 and multiplying the denominators together
Re: Is the answer book wrong?
One concept which is difficult to grasp with fractions is that the innocuous word "of" means "multiply"
so 2/5 OF 2/3 means 2/5 x 2/3 and multiplying fractions is the "easy" one, (2x2)/(5x3)
I think where you went astray mad is
But the 15ths here are different from the original 15ths: it's as if you divided the 2/3 of the original pizza into 15 new slices and had 6 of those - those are smaller than the imaginary 15 slices of the original pizza.
It would be much easier to explain with real pizza.....
so 2/5 OF 2/3 means 2/5 x 2/3 and multiplying fractions is the "easy" one, (2x2)/(5x3)
I think where you went astray mad is
What you've done there is express 2/5 as its equivalent fraction 6/15 by multiplying top & bottom by 3Remaining is 10/15
2/5 of this is 6/15 (x both x 3)
But the 15ths here are different from the original 15ths: it's as if you divided the 2/3 of the original pizza into 15 new slices and had 6 of those - those are smaller than the imaginary 15 slices of the original pizza.
It would be much easier to explain with real pizza.....
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Re: Is the answer book wrong?
Thanks all