5 1/4 divided by 5/8
Understand the Problem
The question is asking us to perform the division of the mixed number 5 1/4 by the fraction 5/8. To solve this, we will first convert the mixed number into an improper fraction, and then we will multiply by the reciprocal of the second fraction.
Answer
The answer is $8 \frac{2}{5}$.
Answer for screen readers
The result of dividing $5 \frac{1}{4}$ by $\frac{5}{8}$ is $\frac{42}{5}$ or as a mixed number, $8 \frac{2}{5}$.
Steps to Solve
- 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:
$$ \text{Improper Fraction} = \frac{(5 \times 4) + 1}{4} = \frac{20 + 1}{4} = \frac{21}{4} $$
- 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:
$$ \text{Reciprocal of } \frac{5}{8} = \frac{8}{5} $$
- Multiply the improper fraction by the reciprocal
Now, we will multiply the improper fraction $\frac{21}{4}$ by the reciprocal $\frac{8}{5}$:
$$ \frac{21}{4} \times \frac{8}{5} = \frac{21 \times 8}{4 \times 5} $$
- 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:
$$ \frac{168 \div 4}{20 \div 4} = \frac{42}{5} $$
- 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:
$$ 8 \frac{2}{5} $$
The result of dividing $5 \frac{1}{4}$ by $\frac{5}{8}$ is $\frac{42}{5}$ or as a mixed number, $8 \frac{2}{5}$.
More Information
Dividing fractions involves multiplying by the reciprocal, which is a fundamental property of fractions. Additionally, converting mixed numbers into improper fractions simplifies the process.
Tips
- Forgetting to convert the mixed number to an improper fraction before dividing.
- Not flipping the second fraction to its reciprocal correctly.
- Failing to simplify the result fully after multiplication.