To solve the expression [tex]\(\frac{4}{3} - \frac{5}{2}\)[/tex], we can follow these steps:
1. Write down the fractions:
[tex]\[
\frac{4}{3}, \quad \frac{5}{2}
\][/tex]
2. Find a common denominator: The denominators are 3 and 2. The common denominator for these two values is their least common multiple (LCM), which is 6.
3. Convert each fraction to the common denominator:
- [tex]\(\frac{4}{3}\)[/tex] to [tex]\(\frac{?}{6}\)[/tex]:
[tex]\[
\frac{4}{3} = \frac{4 \times 2}{3 \times 2} = \frac{8}{6}
\][/tex]
- [tex]\(\frac{5}{2}\)[/tex] to [tex]\(\frac{?}{6}\)[/tex]:
[tex]\[
\frac{5}{2} = \frac{5 \times 3}{2 \times 3} = \frac{15}{6}
\][/tex]
4. Perform the subtraction with the converted fractions:
[tex]\[
\frac{8}{6} - \frac{15}{6} = \frac{8 - 15}{6} = \frac{-7}{6}
\][/tex]
5. Convert the fraction back to a decimal, if needed:
[tex]\[
\frac{-7}{6} \approx -1.1666666666666667 \, \text{(in decimal form)}
\][/tex]
So, the result of subtracting [tex]\(\frac{5}{2}\)[/tex] from [tex]\(\frac{4}{3}\)[/tex] is [tex]\(\frac{-7}{6}\)[/tex], which is approximately [tex]\(-1.1666666666666667\)[/tex] in decimal form.
