Question

Could someone please answer with a step by step explanation?

Answer 1

`\huge \boxed{\mathfrak{Question} \downarrow}`

• 
  `\sf \: 3 ( \frac { 3 } { 4 } ) + 4 ( \frac { 1 } { 2 } - \frac { 3 } { 8 } ) + 2 = ? \\`

`\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}`

`\sf \: 3 ( \frac { 3 } { 4 } ) + 4 ( \frac { 1 } { 2 } - \frac { 3 } { 8 } ) + 2 \\`

• Express
  `\sf3* \left((3)/(4)\right)` as a single fraction.

`\sf(3* 3)/(4)+4\left((1)/(2)-(3)/(8)\right)+2 \\`

• The least common multiple of 2 and 8 is 8. Convert 1 / 2 and 3 / 8 to fractions with denominator 8.

`\sf(9)/(4)+4\left((4)/(8)-(3)/(8)\right)+2 \\`

• Because 4 / 8 and 3 / 8 have the same denominator, subtract them by subtracting their numerators.

`\sf(9)/(4)+4* \left((4-3)/(8)\right)+2 \\`

• Subtract 3 from 4 to get 1.

`\sf(9)/(4)+4* \left((1)/(8)\right)+2 \\`

• Multiply 4 and 1 / 8 to get 4 / 8.

`\sf(9)/(4)+(4)/(8)+2 \\`

• Reduce the fraction 4 / 8 to its lowest terms by extracting and cancelling out 4.

`\sf(9)/(4)+(1)/(2)+2 \\`

• The least common multiple of 4 and 2 is 4. Convert 9 / 4 and 1 / 2 to fractions with denominator 4.

`\sf(9)/(4)+(2)/(4)+2 \\`

• Because 9 / 4 and 2 / 4 have the same denominator, add them by adding their numerators.

`\sf(9+2)/(4)+2 \\`

• Add 9 and 2 to get 11.

`\sf(11)/(4)+2 \\`

• Convert 2 to fraction 8 / 4.

`\sf(11)/(4)+(8)/(4) \\`

• Add 11 and 8 to get 19.

`= \boxed{ \bf (19)/(4)} \\ = \underline{\bf4.75}`