Algebra Examples

$2 \frac{3}{4} + (1 \frac{1}{2} + 3.8)$

Step 1

Remove parentheses.

$2 \frac{3}{4} + 1 \frac{1}{2} + 3.8$

Step 2

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 2.1

A mixed number is an addition of its whole and fractional parts.

$2 + \frac{3}{4} + 1 \frac{1}{2} + 3.8$

Step 2.2

Add $2$ and $\frac{3}{4}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$2 \cdot \frac{4}{4} + \frac{3}{4} + 1 \frac{1}{2} + 3.8$

Step 2.2.2

Combine $2$ and $\frac{4}{4}$ .

$\frac{2 \cdot 4}{4} + \frac{3}{4} + 1 \frac{1}{2} + 3.8$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 4 + 3}{4} + 1 \frac{1}{2} + 3.8$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{8 + 3}{4} + 1 \frac{1}{2} + 3.8$

Step 2.2.4.2

Add $8$ and $3$ .

$\frac{11}{4} + 1 \frac{1}{2} + 3.8$

Step 3

Convert $1 \frac{1}{2}$ to an improper fraction.

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Step 3.1

A mixed number is an addition of its whole and fractional parts.

$\frac{11}{4} + 1 + \frac{1}{2} + 3.8$

Step 3.2

Add $1$ and $\frac{1}{2}$ .

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Step 3.2.1

Write $1$ as a fraction with a common denominator.

$\frac{11}{4} + \frac{2}{2} + \frac{1}{2} + 3.8$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{11}{4} + \frac{2 + 1}{2} + 3.8$

Step 3.2.3

Add $2$ and $1$ .

$\frac{11}{4} + \frac{3}{2} + 3.8$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{11}{4} + \frac{3}{2} \cdot \frac{2}{2} + 3.8$

Step 4.2

Multiply $\frac{3}{2}$ by $\frac{2}{2}$ .

$\frac{11}{4} + \frac{3 \cdot 2}{2 \cdot 2} + 3.8$

Step 4.3

Write $3.8$ as a fraction with denominator $1$ .

$\frac{11}{4} + \frac{3 \cdot 2}{2 \cdot 2} + \frac{3.8}{1}$

Step 4.4

Multiply $\frac{3.8}{1}$ by $\frac{4}{4}$ .

$\frac{11}{4} + \frac{3 \cdot 2}{2 \cdot 2} + \frac{3.8}{1} \cdot \frac{4}{4}$

Step 4.5

Multiply $\frac{3.8}{1}$ by $\frac{4}{4}$ .

$\frac{11}{4} + \frac{3 \cdot 2}{2 \cdot 2} + \frac{3.8 \cdot 4}{4}$

Step 4.6

Multiply $2$ by $2$ .

$\frac{11}{4} + \frac{3 \cdot 2}{4} + \frac{3.8 \cdot 4}{4}$

Step 5

Combine the numerators over the common denominator.

$\frac{11 + 3 \cdot 2 + 3.8 \cdot 4}{4}$

Step 6

Simplify each term.

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Step 6.1

Multiply $3$ by $2$ .

$\frac{11 + 6 + 3.8 \cdot 4}{4}$

Step 6.2

Multiply $3.8$ by $4$ .

$\frac{11 + 6 + 15.2}{4}$

Step 7

Simplify the expression.

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Step 7.1

Add $11$ and $6$ .

$\frac{17 + 15.2}{4}$

Step 7.2

Add $17$ and $15.2$ .

$\frac{32.2}{4}$

Step 7.3

Divide $32.2$ by $4$ .

$8.05$