To solve the problem [tex]\(\frac{4}{5} \div 10\)[/tex], follow these steps:
1. Understand the Problem:
- You are given a fraction [tex]\(\frac{4}{5}\)[/tex].
- You need to divide this fraction by 10.
2. Convert Division by 10 into Multiplication:
- Dividing by a number is the same as multiplying by its reciprocal.
- The reciprocal of 10 is [tex]\(\frac{1}{10}\)[/tex].
- Therefore, [tex]\(\frac{4}{5} \div 10\)[/tex] can be written as [tex]\(\frac{4}{5} \times \frac{1}{10}\)[/tex].
3. Multiply the Fractions:
- When multiplying fractions, multiply the numerators (top numbers) together and the denominators (bottom numbers) together:
[tex]\[
\frac{4}{5} \times \frac{1}{10} = \frac{4 \times 1}{5 \times 10} = \frac{4}{50}
\][/tex]
4. Simplify the Result:
- To simplify the fraction [tex]\(\frac{4}{50}\)[/tex], find the greatest common divisor (GCD) of the numerator and the denominator.
- The GCD of 4 and 50 is 2. Divide both the numerator and the denominator by 2:
[tex]\[
\frac{4 \div 2}{50 \div 2} = \frac{2}{25}
\][/tex]
5. Convert to Decimal (if needed):
- To convert the simplified fraction into a decimal, divide the numerator by the denominator:
[tex]\[
\frac{2}{25} = 0.08
\][/tex]
Thus, the result of [tex]\(\frac{4}{5} \div 10\)[/tex] is [tex]\(0.08\)[/tex].
