$\frac{5}{4} \div 10=$

Full solution

\frac{5}{4} \div 10=

Understand the division problem: Understand the division problem. $\newline$ We need to divide the fraction $\frac{5}{4}$ by the number $10$ .
Convert whole number to fraction: Convert the whole number into a fraction. $\newline$ To divide by a whole number, we can convert the whole number into a fraction by putting it over $1$ . $\newline$ $10$ becomes $\frac{10}{1}$ .
Change division to multiplication: Change the division into multiplication by the reciprocal. $\newline$ Instead of dividing by $\frac{10}{1}$ , we multiply by the reciprocal of $\frac{10}{1}$ , which is $\frac{1}{10}$ . $\newline$ $(\frac{5}{4}) \div (\frac{10}{1})$ becomes $(\frac{5}{4}) \times (\frac{1}{10})$ .
Multiply numerators and denominators: Multiply the numerators and denominators. $\newline$ Multiply the numerators: $5 \times 1 = 5$ . $\newline$ Multiply the denominators: $4 \times 10 = 40$ . $\newline$ So, $(\frac{5}{4}) \times (\frac{1}{10}) = \frac{5}{40}$ .
Simplify the fraction: Simplify the fraction if possible. $\newline$ $5$ and $40$ have a common factor of $5$ . $\newline$ Divide both the numerator and the denominator by $5$ . $\newline$ $5 \div 5 = 1$ and $40 \div 5 = 8$ . $\newline$ So, $\frac{5}{40}$ simplifies to $\frac{1}{8}$ .