Question

comparing fractions martin decided to buy 2 bags of grapes weighing $5 \frac{2}{3}$ pounds each, instead of the 3 bags weighing $4 \frac{1}{5}$ pounds each, because the bigger bags were on sale. did he end up with more grapes or less grapes by buying the bigger bags? \bigcirc he ended up with about $\frac{1}{2}$ pound less grapes. \bigcirc he ended up with about $\frac{1}{2}$ pound more grapes. \bigcirc he ended up with about 1 pound less grapes. \bigcirc he ended up with about 1 pound more grapes.

Explanation:

Step1: Calculate total for 2 bags of $\frac{2}{3}$ lb

Total = $2\times\frac{2}{3}=\frac{4}{3}\approx1.33$ lb

Step2: Calculate total for 3 bags of $\frac{1}{5}$ lb

Total = $3\times\frac{1}{5}=\frac{3}{5}=0.6$ lb

Step3: Find the difference

Difference = $\frac{4}{3}-\frac{3}{5}=\frac{20 - 9}{15}=\frac{11}{15}\approx0.73$, close to $\frac{1}{2}$ (0.5) but wait, maybe approximate: $\frac{2}{3}\approx0.67$, 2 bags: ~1.34; $\frac{1}{5}=0.2$, 3 bags: 0.6. Difference: 1.34 - 0.6 = 0.74, about $\frac{1}{2}$ less? Wait no, wait the question: "Did he end up with more grapes or less grapes by buying the bigger bags?" Wait, no: he decided to buy 2 bags of $\frac{2}{3}$ instead of 3 bags of $\frac{1}{5}$. Wait, original plan: 3 bags of $\frac{1}{5}$? Wait no, the text: "buy 2 bags of grapes weighing $\frac{2}{3}$ pounds each, instead of the 3 bags weighing $\frac{1}{5}$ pounds each". So calculate both totals.

Wait, let's re - calculate:

Total for 2 bags of $\frac{2}{3}$: $2\times\frac{2}{3}=\frac{4}{3}\approx1.333$ pounds.

Total for 3 bags of $\frac{1}{5}$: $3\times\frac{1}{5}=\frac{3}{5} = 0.6$ pounds.

Now find the difference: $\frac{4}{3}-\frac{3}{5}=\frac{20 - 9}{15}=\frac{11}{15}\approx0.733$, which is about $\frac{1}{2}$ (0.5) but wait, maybe the options: "He ended up with about $\frac{1}{2}$ pound less grapes" – no, wait, wait: wait, maybe I misread. Wait, the options:

1. He ended up with about $\frac{1}{2}$ pound less grapes.

2. He ended up with about $\frac{1}{2}$ pound more grapes.

3. He ended up with about 1 pound less grapes.

4. He ended up with about 1 pound more grapes.

Wait, $\frac{4}{3}\approx1.33$, $\frac{3}{5}=0.6$, difference is $1.33 - 0.6 = 0.73$, which is closer to $\frac{1}{2}$ (0.5) but wait, maybe the problem has a typo or approximate. Wait, $\frac{2}{3}\approx0.67$, 2 bags: 1.34; $\frac{1}{5}=0.2$, 3 bags: 0.6. 1.34 - 0.6 = 0.74, which is about $\frac{1}{2}$ more? Wait no, wait: he bought 2 bags instead of 3 bags. Wait, no: he changed from 3 bags of $\frac{1}{5}$ to 2 bags of $\frac{2}{3}$. So the amount he got: 2 bags of $\frac{2}{3}$ is more than 3 bags of $\frac{1}{5}$? Wait, $\frac{4}{3}\approx1.33$, $\frac{3}{5}=0.6$, so 1.33 > 0.6, so he ended up with more? Wait, no, the options: wait the first option: "He ended up with about $\frac{1}{2}$ pound less grapes" – no, that can't be. Wait, maybe I misread the weights. Wait, maybe the bigger bags are $\frac{1}{5}$? No, the text: "bigger bags were on sale", so $\frac{2}{3}$ is bigger than $\frac{1}{5}$. So he bought 2 bags of $\frac{2}{3}$ (bigger) instead of 3 bags of $\frac{1}{5}$ (smaller). So total with bigger bags: $2\times\frac{2}{3}=\frac{4}{3}\approx1.33$; total with smaller bags: $3\times\frac{1}{5}=\frac{3}{5}=0.6$. So the difference is $\frac{4}{3}-\frac{3}{5}=\frac{11}{15}\approx0.73$, which is about $\frac{1}{2}$ (0.5) but closer to $\frac{1}{2}$ more? Wait, no, $\frac{11}{15}\approx0.73$, which is about $\frac{1}{2}$ (0.5) but the options: "about $\frac{1}{2}$ pound more" or less? Wait, he bought bigger bags, so he should have more? Wait, no, wait: 2 bags of $\frac{2}{3}$: ~1.33; 3 bags of $\frac{1}{5}$: 0.6. So 1.33 - 0.6 = 0.73, which is about $\frac{1}{2}$ pound more (since $\frac{1}{2}=0.5$, 0.73 is close to 0.5, maybe approximate as $\frac{1}{2}$). So the correct option is "He ended up with about $\frac{1}{2}$ pound more grapes". Wait, but let's check the options again. Wait, the first option: "He ended up with about $\frac{1}{2}$ pound less grapes" – no. Second: "He ended up with about $\frac{1}{2}$ pound more grapes" – yes. Third: 1 pound less – no. Fourth: 1 pound more – 0.73 is less than 1. So the answer is the second option.

Answer:

He ended up with about $\frac{1}{2}$ pound more grapes (the second option among the given choices).