Question

1. simplify if necessary.

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

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert \(1\frac{1}{3}\) to an improper fraction, we multiply the whole number (1) by the denominator (3) and add the numerator (1). So, \(1\frac{1}{3}=\frac{1\times3 + 1}{3}=\frac{4}{3}\).

To convert \(2\frac{3}{4}\) to an improper fraction, we multiply the whole number (2) by the denominator (4) and add the numerator (3). So, \(2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}\).

Step2: Multiply the improper fractions

Now we multiply \(\frac{4}{3}\) and \(\frac{11}{4}\). When multiplying fractions, we multiply the numerators together and the denominators together: \(\frac{4}{3}\times\frac{11}{4}=\frac{4\times11}{3\times4}\).

Step3: Simplify the fraction

We can cancel out the common factor of 4 in the numerator and the denominator: \(\frac{4\times11}{3\times4}=\frac{11}{3}\).

Step4: Convert back to a mixed number (if needed)

\(\frac{11}{3}\) as a mixed number is \(3\frac{2}{3}\) (since \(11\div3 = 3\) with a remainder of \(2\)).

Answer:

\(3\frac{2}{3}\) (or \(\frac{11}{3}\))