Question

calculate the product of 2 1/2 and 3 1/3. 5/6 17/6 4/5 7/8

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(2\frac{1}{2}\) to an improper fraction, we multiply the whole number (2) by the denominator (2) and add the numerator (1). So, \(2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2}\).

To convert \(3\frac{1}{3}\) to an improper fraction, we multiply the whole number (3) by the denominator (3) and add the numerator (1). So, \(3\frac{1}{3}=\frac{3\times3+1}{3}=\frac{10}{3}\).

Step2: Multiply the two improper fractions

Now, we multiply \(\frac{5}{2}\) and \(\frac{10}{3}\). The formula for multiplying fractions is \(\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}\).

So, \(\frac{5}{2}\times\frac{10}{3}=\frac{5\times10}{2\times3}=\frac{50}{6}\).

Step3: Simplify the resulting fraction

We can simplify \(\frac{50}{6}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

\(\frac{50\div2}{6\div2}=\frac{25}{3}\). Wait, but let's check the options. Wait, maybe I made a mistake. Wait, no, let's re - calculate.

Wait, \(2\frac{1}{2}=\frac{5}{2}\) and \(3\frac{1}{3}=\frac{10}{3}\). Then \(\frac{5}{2}\times\frac{10}{3}=\frac{5\times10}{2\times3}=\frac{50}{6}=\frac{25}{3}\approx8.33\). But the options given are \(\frac{5}{6}\), \(\frac{17}{6}\), \(\frac{4}{5}\), \(\frac{7}{8}\). Wait, this means I must have made a mistake. Wait, no, maybe the question was misread. Wait, the question says "product of \(2\frac{1}{2}\) and \(3\frac{1}{3}\)". Wait, maybe the options are wrong or I misread the numbers. Wait, no, let's check again.

Wait, \(2\frac{1}{2}=\frac{5}{2}\), \(3\frac{1}{3}=\frac{10}{3}\). \(\frac{5}{2}\times\frac{10}{3}=\frac{50}{6}=\frac{25}{3}\approx8.33\). But none of the options match. Wait, maybe the question is "sum" instead of "product"? Let's check the sum. \(2\frac{1}{2}+3\frac{1}{3}=\frac{5}{2}+\frac{10}{3}=\frac{15 + 20}{6}=\frac{35}{6}\approx5.83\), still not matching. Wait, maybe the numbers are \(2\frac{1}{3}\) and \(3\frac{1}{2}\)? No, the user provided the question as "Calculate the product of \(2\frac{1}{2}\) and \(3\frac{1}{3}\)". Wait, maybe there is a mistake in the options. But according to the calculation, the product is \(\frac{25}{3}\approx8.33\), which is not in the options. But let's check the options again. The options are \(\frac{5}{6}\), \(\frac{17}{6}\), \(\frac{4}{5}\), \(\frac{7}{8}\). None of these are equal to \(\frac{25}{3}\). Wait, maybe I made a mistake in conversion. Wait, \(2\frac{1}{2}=\frac{5}{2}\), \(3\frac{1}{3}=\frac{10}{3}\). \(\frac{5}{2}\times\frac{10}{3}=\frac{50}{6}=\frac{25}{3}\approx8.33\). There is a discrepancy here. But since the options are given, maybe the question was supposed to be multiplying \(1\frac{1}{2}\) and \(1\frac{1}{3}\)? Let's try that. \(1\frac{1}{2}=\frac{3}{2}\), \(1\frac{1}{3}=\frac{4}{3}\). Then \(\frac{3}{2}\times\frac{4}{3} = 2=\frac{12}{6}\), still not matching. Alternatively, maybe the numbers are \(2\frac{1}{3}\) and \(1\frac{1}{2}\). \(2\frac{1}{3}=\frac{7}{3}\), \(1\frac{1}{2}=\frac{3}{2}\). \(\frac{7}{3}\times\frac{3}{2}=\frac{7}{2}=\frac{21}{6}\), not matching. Wait, maybe the question is "divide" instead of "product"? \(2\frac{1}{2}\div3\frac{1}{3}=\frac{5}{2}\div\frac{10}{3}=\frac{5}{2}\times\frac{3}{10}=\frac{15}{20}=\frac{3}{4}\), not matching.

Wait, maybe the original problem has a typo, but based on the given options, none of them is the correct product of \(2\frac{1}{2}\) and \(3\frac{1}{3}\). But since the user provided these options, maybe I misread the mixed numbers. Let's check the options again. The options are \(\frac{5}{6}\), \(\frac{17}{6}\), \(\frac{4}{5}\), \(\frac{7}{8}\). Let's see, if we multiply \(\frac{5}{6}\) is too small, \(\frac{17}{6}\approx2.83\), \(\frac{4}{5} = 0.8\), \(\frac{7}{8}=0.875\). None of these is equal to \(\frac{25}{3}\approx8.33\). So there must be an error in the problem or the options. But assuming that maybe the question was to multiply \(1\frac{1}{2}\) and \(\frac{5}{9}\) (but that's not the case). Alternatively, maybe the mixed numbers are \(1\frac{1}{3}\) and \(1\frac{1}{2}\). \(1\frac{1}{3}=\frac{4}{3}\), \(1\frac{1}{2}=\frac{3}{2}\), product is 2, not in options.

Wait, maybe the user made a mistake in the problem statement. But according to the given problem, the correct product of \(2\frac{1}{2}\) and \(3\frac{1}{3}\) is \(\frac{25}{3}\) or \(8\frac{1}{3}\), which is not in the options. But since the options are provided, maybe there is a mistake in my calculation. Wait, no, the formula for multiplying mixed numbers is correct. Convert to improper fractions and multiply.

Answer:

None of the given options is the correct product of \(2\frac{1}{2}\) and \(3\frac{1}{3}\). The correct product is \(\frac{25}{3}\) (or \(8\frac{1}{3}\)).