Alright, let's break down the subtraction of the fractions [tex]\( \frac{2}{3} - \frac{1}{4} \)[/tex] step-by-step:
1. Find a Common Denominator:
The denominators of the fractions are 3 and 4. To subtract these fractions, we first need to find a common denominator. The smallest common multiple of 3 and 4 is 12.
2. Convert Each Fraction to Equivalent Fractions with the Common Denominator:
- For [tex]\( \frac{2}{3} \)[/tex]:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
- For [tex]\( \frac{1}{4} \)[/tex]:
[tex]\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\][/tex]
3. Subtract the Fractions:
Now that both fractions have the same denominator, we can subtract the numerators:
[tex]\[
\frac{8}{12} - \frac{3}{12} = \frac{8 - 3}{12} = \frac{5}{12}
\][/tex]
The numerical value of [tex]\(\frac{5}{12}\)[/tex] is approximately [tex]\(0.41666666666666663\)[/tex].
So, [tex]\( \frac{2}{3} - \frac{1}{4} \)[/tex] simplifies to [tex]\( \frac{5}{12} \)[/tex] or approximately [tex]\( 0.41666666666666663 \)[/tex].
