[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
- [tex] \sf \: 3 ( \frac { 3 } { 4 } ) + 4 ( \frac { 1 } { 2 } - \frac { 3 } { 8 } ) + 2 = ? \\ [/tex]
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \sf \: 3 ( \frac { 3 } { 4 } ) + 4 ( \frac { 1 } { 2 } - \frac { 3 } { 8 } ) + 2 \\ [/tex]
- Express [tex]\sf3\times \left(\frac{3}{4}\right)[/tex] as a single fraction.
[tex] \sf\frac{3\times 3}{4}+4\left(\frac{1}{2}-\frac{3}{8}\right)+2 \\ [/tex]
- The least common multiple of 2 and 8 is 8. Convert 1 / 2 and 3 / 8 to fractions with denominator 8.
[tex] \sf\frac{9}{4}+4\left(\frac{4}{8}-\frac{3}{8}\right)+2 \\ [/tex]
- Because 4 / 8 and 3 / 8 have the same denominator, subtract them by subtracting their numerators.
[tex] \sf\frac{9}{4}+4\times \left(\frac{4-3}{8}\right)+2 \\ [/tex]
- Subtract 3 from 4 to get 1.
[tex] \sf\frac{9}{4}+4\times \left(\frac{1}{8}\right)+2 \\ [/tex]
- Multiply 4 and 1 / 8 to get 4 / 8.
[tex] \sf\frac{9}{4}+\frac{4}{8}+2 \\ [/tex]
- Reduce the fraction 4 / 8 to its lowest terms by extracting and cancelling out 4.
[tex] \sf\frac{9}{4}+\frac{1}{2}+2 \\ [/tex]
- The least common multiple of 4 and 2 is 4. Convert 9 / 4 and 1 / 2 to fractions with denominator 4.
[tex] \sf\frac{9}{4}+\frac{2}{4}+2 \\ [/tex]
- Because 9 / 4 and 2 / 4 have the same denominator, add them by adding their numerators.
[tex] \sf\frac{9+2}{4}+2 \\ [/tex]
[tex] \sf\frac{11}{4}+2 \\ [/tex]
- Convert 2 to fraction 8 / 4.
[tex] \sf\frac{11}{4}+\frac{8}{4} \\ [/tex]
[tex] = \boxed{ \bf \frac{19}{4}} \\ = \underline{\bf4.75}[/tex]
