To solve [tex]\(\frac{1}{4} \div \frac{8}{3}\)[/tex], follow these steps:
### Step 1: Understand the Division of Fractions
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
### Step 2: Find the Reciprocal
Identify the reciprocal of [tex]\(\frac{8}{3}\)[/tex]. The reciprocal of [tex]\(\frac{8}{3}\)[/tex] is [tex]\(\frac{3}{8}\)[/tex].
### Step 3: Rewrite the Problem as Multiplication
Rewrite the division problem [tex]\(\frac{1}{4} \div \frac{8}{3}\)[/tex] as multiplication of [tex]\(\frac{1}{4}\)[/tex] and the reciprocal of [tex]\(\frac{8}{3}\)[/tex]:
[tex]\[
\frac{1}{4} \times \frac{3}{8}
\][/tex]
### Step 4: Multiply the Fractions
To multiply the fractions, multiply the numerators together and the denominators together:
Numerator:
[tex]\[
1 \times 3 = 3
\][/tex]
Denominator:
[tex]\[
4 \times 8 = 32
\][/tex]
So, the product of the fractions is:
[tex]\[
\frac{3}{32}
\][/tex]
### Step 5: Simplify the Fraction (if needed)
In this case, [tex]\(\frac{3}{32}\)[/tex] is already in its simplest form, as the greatest common divisor of 3 and 32 is 1.
Thus, the result of [tex]\(\frac{1}{4} \div \frac{8}{3}\)[/tex] is [tex]\(\frac{3}{32}\)[/tex].
When written as a decimal, [tex]\(\frac{3}{32}\)[/tex] is:
[tex]\[
0.09375
\][/tex]
Therefore:
[tex]\[
\frac{1}{4} \div \frac{8}{3} = 0.09375
\][/tex]
