Question

1. simplify if necessary.

1\frac{3}{4} \times 2\frac{1}{5}
type a response

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(1\frac{3}{4}\) to an improper fraction, we multiply the whole number (1) by the denominator (4) and add the numerator (3): \(1\times4 + 3 = 7\), so \(1\frac{3}{4}=\frac{7}{4}\).

To convert \(2\frac{1}{5}\) to an improper fraction, we multiply the whole number (2) by the denominator (5) and add the numerator (1): \(2\times5 + 1 = 11\), so \(2\frac{1}{5}=\frac{11}{5}\).

Step2: Multiply the improper fractions

Now we multiply \(\frac{7}{4}\) and \(\frac{11}{5}\). When multiplying fractions, we multiply the numerators together and the denominators together: \(\frac{7}{4}\times\frac{11}{5}=\frac{7\times11}{4\times5}=\frac{77}{20}\).

Step3: Convert the improper fraction to a mixed number (if needed)

To convert \(\frac{77}{20}\) to a mixed number, we divide 77 by 20. 20 times 3 is 60, and 77 minus 60 is 17. So \(\frac{77}{20}=3\frac{17}{20}\).

Answer:

\(3\frac{17}{20}\)