Question

multiply
2\frac{3}{4} \times \frac{8}{9}

1. mixed

to improper

1. \cross out\
2. multiply numerators
3. multiply denominators
4. simplify

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \( 2\frac{3}{4} \) can be converted to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 2\frac{3}{4} \), we have \( a = 2 \), \( b = 3 \), \( c = 4 \). Then \( 2\times4 + 3 = 8 + 3 = 11 \), so \( 2\frac{3}{4}=\frac{11}{4} \).

Step2: Multiply the two fractions

Now we have \( \frac{11}{4} \times \frac{8}{9} \). When multiplying fractions, we multiply the numerators together and the denominators together. So \( \frac{11\times8}{4\times9}=\frac{88}{36} \).

Step3: Simplify the fraction

We can simplify \( \frac{88}{36} \) by dividing both the numerator and the denominator by their greatest common divisor. The GCD of 88 and 36 is 4. So \( \frac{88\div4}{36\div4}=\frac{22}{9} \). We can also convert this back to a mixed number: \( \frac{22}{9}=2\frac{4}{9} \).

Answer:

\( 2\frac{4}{9} \) (or \( \frac{22}{9} \))