Question

1. \\(13 \frac{5}{9} \div 5 = \underline{\quad\quad}\\)

Explanation:

Convert the mixed number to an improper fraction

We convert the mixed number \(13\frac{5}{9}\) using Improper Fractions.
Multiply the whole number by the denominator and add the numerator:

$$ 13 \times 9 + 5 = 117 + 5 = 122 $$

This gives the improper fraction:

$$ 13\frac{5}{9} = \frac{122}{9} $$

Set up the division problem

We write the whole number divisor \(5\) as a fraction:

$$ 5 = \frac{5}{1} $$

Now we write the division expression:

$$ \frac{122}{9} \div \frac{5}{1} $$

Multiply by the reciprocal

We apply Fraction Division by multiplying by the Reciprocals of the divisor:

$$ \frac{122}{9} \times \frac{1}{5} $$

Calculate the product

Multiply the numerators and the denominators:

$$ \frac{122 \times 1}{9 \times 5} = \frac{122}{45} $$

Convert back to a mixed number

We divide \(122\) by \(45\) to find the whole number and remainder:

$$ 122 \div 45 = 2 \text{ remainder } 32 $$

This gives the final mixed number:

$$ 2\frac{32}{45} $$

We check if we can apply Simplifying Fractions, but \(32\) and \(45\) share no common factors.

Answer:

\(13\frac{5}{9} \div 5 =\) <blank>\(2\frac{32}{45}\)</blank>