5 1/4 divided by 5/8

Steps to Solve

1. Convert the mixed number to an improper fraction

To convert the mixed number $5 \frac{1}{4}$ to an improper fraction, we multiply the whole number (5) by the denominator (4) and add the numerator (1). The formula is:

$$ \text{Improper Fraction} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} $$

2. Find the reciprocal of the fraction

Next, we need to find the reciprocal of the fraction $\frac{5}{8}$. The reciprocal is obtained by swapping the numerator and denominator:

$$ \text{Reciprocal of } \frac{5}{8} = \frac{8}{5} $$

3. Multiply the improper fraction by the reciprocal

Now, we will multiply the improper fraction $\frac{21}{4}$ by the reciprocal $\frac{8}{5}$:

$$ \frac{21}{4} \times \frac{8}{5} = \frac{21 \times 8}{4 \times 5} $$

4. Simplify the product

Calculate the multiplication and simplify:

$$ \frac{21 \times 8}{4 \times 5} = \frac{168}{20} $$

Now, reduce the fraction by finding the greatest common divisor (GCD) of 168 and 20:

$$ \frac{168 \div 4}{20 \div 4} = \frac{42}{5} $$

5. Convert back to a mixed number (if needed)

Finally, if required, convert the improper fraction $\frac{42}{5}$ back to a mixed number.

Divide 42 by 5:

$$ 42 \div 5 = 8 \text{ R } 2 $$

So, $\frac{42}{5}$ can be written as:

$$ 8 \frac{2}{5} $$