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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

  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:

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

  1. 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:

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

  1. Multiply the improper fraction by the reciprocal

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

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

  1. 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:

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

  1. 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.
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