Finding Fractions in Mixed Numbers: Step-by-Step

The question asks us to determine how many times the fraction $\frac{1}{8}\$$ is contained within the mixed number $37\frac{1}{2}\$$ . This is equivalent to solving the division problem:

$37\frac{1}{2}÷\frac{1}{8}\$$

Step 1: Convert Mixed Number to Improper Fraction

First, we convert the mixed number $37\frac{1}{2}\$$ into an improper fraction. The formula is:

$\text{Improper Fraction}=\frac{(\text{Whole Number}\times \text{Denominator})+\text{Numerator}}{\text{Denominator}}\$$

Applying this:

$37\frac{1}{2}=\frac{(37\times 2)+1}{2}=\frac{74+1}{2}=\frac{75}{2}\$$

Step 2: Divide by the Fraction

Now we need to divide the improper fraction $\frac{75}{2}\$$ by $\frac{1}{8}\$$ . Dividing by a fraction is the same as multiplying by its reciprocal (the fraction flipped upside down).

The reciprocal of $\frac{1}{8}\$$ is $\frac{8}{1}\$$ .

So, the calculation becomes:

$\frac{75}{2}\times \frac{8}{1}\$$

Step 3: Simplify and Calculate the Result

Multiply the numerators together and the denominators together:

$\frac{75\times 8}{2\times 1}=\frac{600}{2}\$$

Finally, perform the division:

$\frac{600}{2}=300\$$

Therefore, there are 300 eighths ( $\frac{1}{8}\$$ 's) in $37\frac{1}{2}\$$ .