Question

1. simplify if necessary.

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

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(1\frac{3}{4}\) can be converted to an improper fraction. To do this, multiply the whole number part (1) by the denominator (4) and add the numerator (3). So, \(1\times4 + 3=7\), and the improper fraction is \(\frac{7}{4}\). Now the expression becomes \(\frac{2}{3}\times\frac{7}{4}\).

Step2: Multiply the fractions

When multiplying fractions, multiply the numerators together and the denominators together. So, \(\frac{2\times7}{3\times4}=\frac{14}{12}\).

Step3: Simplify the fraction

We can simplify \(\frac{14}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \(\frac{14\div2}{12\div2}=\frac{7}{6}\), or as a mixed number \(1\frac{1}{6}\). But \(\frac{7}{6}\) is also correct in improper fraction form. However, let's check the multiplication again. Wait, \(\frac{2}{3}\times\frac{7}{4}\), we can cancel the 2 and 4 first. 2 and 4 have a common factor of 2, so 2 ÷ 2 = 1, 4 ÷ 2 = 2. Then we have \(\frac{1\times7}{3\times2}=\frac{7}{6}\), which is \(1\frac{1}{6}\).

Answer:

\(\frac{7}{6}\) (or \(1\frac{1}{6}\))