Answer: [tex]\frac{31}{12}[/tex]
Step-by-step explanation:
We have the following expression:
[tex]4-2\frac{2}{3}+1\frac{1}{4}[/tex]
As we can see, the second and the third term are mixed fractions, which are a combination of an integer and a fraction, and to convert it into an improper fraction and be able to solve the expression more easily, we must do the following:
Mixed fraction: [tex]a\frac{b}{c}[/tex]
Converting Mixed fraction to improper fraction: [tex]\frac{(a)(c)+b}{c}[/tex]
So, for both mixed fractions we have:
[tex]2\frac{2}{3}=\frac{8}{3}[/tex]
[tex]1\frac{1}{4}=\frac{5}{4}[/tex]
Then the expression is rewritten as:
[tex]4-\frac{8}{3}+\frac{5}{4}[/tex]
Calculating the least common multiple (l.c.m) with the denominators, being the l.c.m=12:
[tex]\frac{48-32+15}{12}[/tex]
Solving:
[tex]\frac{31}{12}[/tex]
Hence:
[tex]4-2\frac{2}{3}+1\frac{1}{4}=\frac{31}{12}[/tex]
