4/5 x 1 1/6 as a fraction

Steps to Solve

1. Convert the mixed number to an improper fraction

A mixed number consists of a whole number and a fraction. We need to convert $1 \frac{1}{6}$ into an improper fraction.

To do this:

• Multiply the whole number (1) by the denominator (6)
• Add the numerator (1)

This can be expressed mathematically as: $$ 1 \frac{1}{6} = \frac{1 \times 6 + 1}{6} = \frac{7}{6} $$

2. Set up the multiplication of the two fractions

Now we have two fractions to multiply:

• The first fraction is $\frac{4}{5}$
• The second fraction, converted from the mixed number, is $\frac{7}{6}$

We can set this up as: $$ \frac{4}{5} \times \frac{7}{6} $$

3. Multiply the numerators and the denominators

Multiply the numerators together and the denominators together: $$ \text{Numerator: } 4 \times 7 = 28 $$ $$ \text{Denominator: } 5 \times 6 = 30 $$

So, we have: $$ \frac{4}{5} \times \frac{7}{6} = \frac{28}{30} $$

4. Simplify the resulting fraction

Now, we can simplify $\frac{28}{30}$ by finding the greatest common divisor of 28 and 30.

The GCD is 2. Thus, we divide both the numerator and denominator by 2: $$ \frac{28 \div 2}{30 \div 2} = \frac{14}{15} $$

5. Final Answer in Fraction Form

The final product of the two fractions is $\frac{14}{15}$.