Question

estimating with compatible fractions
on another day, martin bought $12 \frac{3}{5}$ pounds of grapes for a picnic. his friend bought $\frac{3}{8}$ of that amount. use compatible fractions to estimate how many pounds of grapes martin’s friend bought.
$12 \frac{3}{5} \
ightarrow \boldsymbol{\bigtriangledown}$
$\frac{3}{8} \
ightarrow \boldsymbol{\bigtriangledown}$
martin’s friend bought about $\boldsymbol{\bigtriangledown}$ pounds of grapes.

Explanation:

Step1: Estimate \( 12\frac{3}{5} \)

\( 12\frac{3}{5} \) is close to 12 (or we can also consider it close to 13, but for compatible fractions with \( \frac{3}{8} \), let's see. Wait, actually, maybe we can round \( 12\frac{3}{5} \) to a whole number or a number that is easy to multiply with \( \frac{3}{8} \). \( 12\frac{3}{5}=12.6 \), which is close to 12 or 13. But maybe a better compatible fraction: let's see, \( 12\frac{3}{5} \) can be estimated as 12 (since \( \frac{3}{5} \) is less than \( \frac{1}{2} \)? Wait, no, \( \frac{3}{5}=0.6 \), which is more than 0.5. Wait, maybe 13? Wait, but maybe the problem is to use compatible fractions, so let's check the fraction \( \frac{3}{8} \). Wait, maybe we need to multiply \( 12\frac{3}{5} \times \frac{3}{8} \) and estimate. Let's first estimate \( 12\frac{3}{5} \). Let's take \( 12\frac{3}{5} \approx 12 \) (or maybe 13, but let's see). Wait, maybe the first box is for estimating \( 12\frac{3}{5} \), and the second for \( \frac{3}{8} \), then multiply. Wait, \( \frac{3}{8} \) is close to \( \frac{1}{3} \)? No, maybe \( \frac{3}{8} \approx \frac{1}{2} \)? No, \( \frac{3}{8}=0.375 \), close to \( \frac{1}{3} \) (0.333) or \( \frac{3}{8} \) itself. Wait, maybe the problem is to estimate \( 12\frac{3}{5} \times \frac{3}{8} \). Let's estimate \( 12\frac{3}{5} \) as 12 (or 13). Let's try 12: \( 12 \times \frac{3}{8} = \frac{36}{8}=4.5 \). If we take \( 12\frac{3}{5} \approx 13 \), \( 13 \times \frac{3}{8}=\frac{39}{8}=4.875 \). But maybe the compatible fraction for \( 12\frac{3}{5} \) is 12 (or 13), and for \( \frac{3}{8} \) is \( \frac{1}{3} \)? No, maybe the first box: \( 12\frac{3}{5} \approx 12 \) (or 13), and the second \( \frac{3}{8} \approx \frac{1}{3} \)? Wait, no, maybe the problem is simpler. Wait, maybe the first step is to estimate \( 12\frac{3}{5} \) as 12 (or 13), and \( \frac{3}{8} \) as \( \frac{1}{2} \)? No, let's re-read the problem: "Use compatible fractions to estimate how many pounds of grapes Martin’s friend bought." So Martin bought \( 12\frac{3}{5} \) pounds, friend bought \( \frac{3}{8} \) of that amount. So we need to estimate \( 12\frac{3}{5} \times \frac{3}{8} \).

First, estimate \( 12\frac{3}{5} \): \( 12\frac{3}{5} \) is close to 12 (since \( \frac{3}{5}=0.6 \), but maybe 12 is a whole number, or 13? Wait, maybe the first box is for \( 12\frac{3}{5} \) estimation: let's say \( 12\frac{3}{5} \approx 12 \) (or 13). Then \( \frac{3}{8} \approx \frac{1}{3} \)? No, \( \frac{3}{8} \) is 0.375, which is close to \( \frac{1}{3} \) (0.333) or \( \frac{3}{8} \) itself. Wait, maybe the first box: \( 12\frac{3}{5} \approx 12 \), second box: \( \frac{3}{8} \approx \frac{3}{8} \), then multiply: \( 12 \times \frac{3}{8} = \frac{36}{8}=4.5 \). Or if we take \( 12\frac{3}{5} \approx 13 \), \( 13 \times \frac{3}{8}=\frac{39}{8}=4.875 \). But maybe the intended compatible fractions are \( 12\frac{3}{5} \approx 12 \) (or 13) and \( \frac{3}{8} \approx \frac{1}{2} \)? No, \( \frac{3}{8} \) is less than \( \frac{1}{2} \). Wait, maybe the first box is \( 12\frac{3}{5} \approx 12 \), second box \( \frac{3}{8} \approx \frac{3}{8} \), then the product is \( 12 \times \frac{3}{8}=4.5 \), so about 4.5 pounds, or maybe 4 or 5. Wait, maybe the first box: \( 12\frac{3}{5} \) estimated as 12 (or 13), second box \( \frac{3}{8} \) estimated as \( \frac{3}{8} \), then the product is estimated. Let's check the problem again: "On another day, Martin bought \( 12\frac{3}{5} \) pounds of grapes for a picnic. His friend bought \( \frac{3}{8} \) of that amount. Use compatible fractions to estimate how many pounds of grapes Martin’s friend bought."

So step 1: Estimate \( 12\frac{3}{5} \). Let's take \( 12\frac{3}{5} \approx 12 \) (since \( \frac{3}{5} \) is 0.6, but maybe 12 is a whole number, or 13? Wait, maybe 12 is better. Step 2: Estimate \( \frac{3}{8} \). \( \frac{3}{8} \approx \frac{3}{8} \) (or maybe \( \frac{1}{3} \), but \( \frac{3}{8} \) is 0.375, \( \frac{1}{3} \) is ~0.333, close). Then multiply: \( 12 \times \frac{3}{8} = \frac{36}{8} = 4.5 \). So Martin's friend bought about 4.5 pounds, or maybe 4 or 5. But let's see the boxes. The first box is for \( 12\frac{3}{5} \) estimation, second for \( \frac{3}{8} \), then the result.

Wait, maybe the first box: \( 12\frac{3}{5} \approx 12 \) (or 13), second box: \( \frac{3}{8} \approx \frac{3}{8} \), then the product is \( 12 \times \frac{3}{8}=4.5 \), so about 4.5 pounds. So the first box (estimating \( 12\frac{3}{5} \)): maybe 12, second box (estimating \( \frac{3}{8} \)): maybe \( \frac{3}{8} \) or \( \frac{1}{3} \), but let's go with the first estimation.

Step1: Estimate \( 12\frac{3}{5} \)

\( 12\frac{3}{5} \approx 12 \) (or 13, but let's take 12 for simplicity)

Step2: Estimate \( \frac{3}{8} \)

\( \frac{3}{8} \approx \frac{3}{8} \) (or \( \frac{1}{3} \), but we'll use \( \frac{3}{8} \))

Step3: Multiply the estimates

\( 12 \times \frac{3}{8} = \frac{36}{8} = 4.5 \)

Alternatively, if we take \( 12\frac{3}{5} \approx 13 \) (since \( \frac{3}{5}=0.6 \), so 12.6 is close to 13), then \( 13 \times \frac{3}{8} = \frac{39}{8} = 4.875 \), which is about 5. But maybe the intended answer is 4.5 or 5. But let's check the problem again. The first box is for \( 12\frac{3}{5} \), second for \( \frac{3}{8} \), then the result.

So the first box: \( 12\frac{3}{5} \) estimated as 12 (or 13), second box: \( \frac{3}{8} \) estimated as \( \frac{3}{8} \) (or \( \frac{1}{2} \)? No, \( \frac{3}{8} \) is 0.375, \( \frac{1}{2} \) is 0.5). Wait, maybe the problem is to use compatible fractions, so \( 12\frac{3}{5} \) can be written as \( \frac{63}{5} \), and \( \frac{3}{8} \), but compatible fractions for multiplication. Maybe \( 12\frac{3}{5} \approx 12 \) (since 12 and 8 are compatible, as 12 is divisible by 4, 8 is divisible by 4). 12 and 8 have a common factor of 4. So \( 12 \times \frac{3}{8} = \frac{12}{8} \times 3 = \frac{3}{2} \times 3 = 4.5 \). So that's a compatible fraction because 12 and 8 are both divisible by 4, making the multiplication easier.

So step 1: Estimate \( 12\frac{3}{5} \) as 12 (compatible with 8 in the denominator of \( \frac{3}{8} \) because 12 and 8 have a common factor). Step 2: Keep \( \frac{3}{8} \) as is (or estimate, but 3/8 is already simple). Step 3: Multiply 12 * 3/8 = 4.5.

So the first box (for \( 12\frac{3}{5} \)): 12, second box (for \( \frac{3}{8} \)): 3/8, then the result is 4.5 (or about 4 or 5). But the problem says "about" how many pounds, so 4.5 or 5. But let's see the options (the boxes). The first box: \( 12\frac{3}{5} \) → 12 (or 13), second box: \( \frac{3}{8} \) → 3/8 (or 1/3), then the result: 4.5 (or 5).

Answer:

First box (estimating \( 12\frac{3}{5} \)): \( 12 \) (or \( 13 \))
Second box (estimating \( \frac{3}{8} \)): \( \frac{3}{8} \) (or \( \frac{1}{3} \))
Martin’s friend bought about \( 4.5 \) (or \( 5 \)) pounds of grapes.

(If we take the first estimation as 12 and second as 3/8, the answer is \( 4.5 \), which is \( \frac{9}{2} \) or 4.5. So the final answer is about \( 4.5 \) pounds, or 5 pounds if we estimated \( 12\frac{3}{5} \) as 13.)