The quotient in lowest terms is 0.22 or [tex]\frac{2}{9}[/tex]
Solution:
Given that we have to divide and write the quotient in lowest terms
Given expression is:
[tex]\frac{1}{4} \div 1\frac{1}{8}[/tex]
Let us first convert the mixed number to fraction
Follow these 3 steps to convert a mixed number to an improper fraction:
Multiply the whole number by the denominator
Add the answer from Step 1 to the numerator
Write answer from Step 2 over the denominator
Therefore,
[tex]1\frac{1}{8} = \frac{8 \times 1 + 1}{8} = \frac{9}{8}[/tex]
Thus the expression becomes,
[tex]\rightarrow \frac{1}{4} \div \frac{9}{8}[/tex]
Convert the problem to multiplication by changing the division sign to multiplication and inverting the fraction to the right of the sign
[tex]\rightarrow \frac{1}{4} \times \frac{8}{9}[/tex]
Simplify the above expression by cancelling terms
[tex]\rightarrow \frac{1}{4} \times \frac{8}{9} = \frac{2}{9} = 0.22[/tex]
Thus the quotient in lowest terms is 0.22 or [tex]\frac{2}{9}[/tex]
