I have a word problem with fractions.
Anna estimated that her brother Nick ate about 1/3 of an apple pie, her brother Matt ate 5/8 of the pie, and she ate about 1/4 of the pie. How might you convince Anna that her estimates do not make sense? Be sure to show every step of your work. Explain your answer in a detailed write up using I think the answer is, I think this because and I figured this out by...
Thank you.
1/3 = 8/24
5/8 = 15/24
1/4 = 6/24
________________________
Total=29/24
That's about 1 1/4 pies
To convince Anna that her estimates do not make sense, let's calculate the total fraction of the apple pie that was eaten by her family members.
First, we need to find a common denominator for the fractions involved. The least common denominator (LCD) for 1/3, 5/8, and 1/4 is 24.
To convert 1/3 to a fraction with the LCD of 24, we multiply the numerator and denominator by 8:
1/3 = (1 * 8) / (3 * 8) = 8/24
To convert 5/8 to a fraction with the LCD of 24, we multiply the numerator and denominator by 3:
5/8 = (5 * 3) / (8 * 3) = 15/24
To convert 1/4 to a fraction with the LCD of 24, we multiply the numerator and denominator by 6:
1/4 = (1 * 6) / (4 * 6) = 6/24
Now, let's add up the fractions:
8/24 + 15/24 + 6/24 = 29/24
However, this result is greater than 1 (the whole pie). In any situation, the sum of the fractions that represent parts of a whole cannot exceed 1. So, Anna's estimates do not make sense because the total fraction exceeds the whole pie.
To explain this to Anna, you can say:
"I think the answer is that your estimates do not make sense because the total fraction of the apple pie that was eaten by your family members is greater than 1. I figured this out by converting the fractions to a common denominator of 24. When adding them up, we get 29/24, which is more than the whole pie. In any situation, the sum of the fractions representing parts of a whole cannot exceed 1. Therefore, your estimates are not accurate."