Basic Math Examples

$4 \frac{1}{6} + 2 \frac{3}{4} + \frac{2}{3}$

Step 1

Convert $4 \frac{1}{6}$ to an improper fraction.

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Step 1.1

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

$4 + \frac{1}{6} + 2 \frac{3}{4} + \frac{2}{3}$

Step 1.2

Add $4$ and $\frac{1}{6}$ .

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Step 1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$4 \cdot \frac{6}{6} + \frac{1}{6} + 2 \frac{3}{4} + \frac{2}{3}$

Step 1.2.2

Combine $4$ and $\frac{6}{6}$ .

$\frac{4 \cdot 6}{6} + \frac{1}{6} + 2 \frac{3}{4} + \frac{2}{3}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 6 + 1}{6} + 2 \frac{3}{4} + \frac{2}{3}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $6$ .

$\frac{24 + 1}{6} + 2 \frac{3}{4} + \frac{2}{3}$

Step 1.2.4.2

Add $24$ and $1$ .

$\frac{25}{6} + 2 \frac{3}{4} + \frac{2}{3}$

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.

$\frac{25}{6} + 2 + \frac{3}{4} + \frac{2}{3}$

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 $\frac{4}{4}$ .

$\frac{25}{6} + 2 \cdot \frac{4}{4} + \frac{3}{4} + \frac{2}{3}$

Step 2.2.2

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

$\frac{25}{6} + \frac{2 \cdot 4}{4} + \frac{3}{4} + \frac{2}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{25}{6} + \frac{2 \cdot 4 + 3}{4} + \frac{2}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{25}{6} + \frac{8 + 3}{4} + \frac{2}{3}$

Step 2.2.4.2

Add $8$ and $3$ .

$\frac{25}{6} + \frac{11}{4} + \frac{2}{3}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{25}{6}$ by $\frac{2}{2}$ .

$\frac{25}{6} \cdot \frac{2}{2} + \frac{11}{4} + \frac{2}{3}$

Step 3.2

Multiply $\frac{25}{6}$ by $\frac{2}{2}$ .

$\frac{25 \cdot 2}{6 \cdot 2} + \frac{11}{4} + \frac{2}{3}$

Step 3.3

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$\frac{25 \cdot 2}{6 \cdot 2} + \frac{11}{4} \cdot \frac{3}{3} + \frac{2}{3}$

Step 3.4

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$\frac{25 \cdot 2}{6 \cdot 2} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{2}{3}$

Step 3.5

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{25 \cdot 2}{6 \cdot 2} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{2}{3} \cdot \frac{4}{4}$

Step 3.6

Multiply $\frac{2}{3}$ by $\frac{4}{4}$ .

$\frac{25 \cdot 2}{6 \cdot 2} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.7

Reorder the factors of $6 \cdot 2$ .

$\frac{25 \cdot 2}{2 \cdot 6} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.8

Multiply $2$ by $6$ .

$\frac{25 \cdot 2}{12} + \frac{11 \cdot 3}{4 \cdot 3} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.9

Reorder the factors of $4 \cdot 3$ .

$\frac{25 \cdot 2}{12} + \frac{11 \cdot 3}{3 \cdot 4} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.10

Multiply $3$ by $4$ .

$\frac{25 \cdot 2}{12} + \frac{11 \cdot 3}{12} + \frac{2 \cdot 4}{3 \cdot 4}$

Step 3.11

Multiply $3$ by $4$ .

$\frac{25 \cdot 2}{12} + \frac{11 \cdot 3}{12} + \frac{2 \cdot 4}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{25 \cdot 2 + 11 \cdot 3 + 2 \cdot 4}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $25$ by $2$ .

$\frac{50 + 11 \cdot 3 + 2 \cdot 4}{12}$

Step 5.2

Multiply $11$ by $3$ .

$\frac{50 + 33 + 2 \cdot 4}{12}$

Step 5.3

Multiply $2$ by $4$ .

$\frac{50 + 33 + 8}{12}$

Step 6

Simplify by adding numbers.

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Step 6.1

Add $50$ and $33$ .

$\frac{83 + 8}{12}$

Step 6.2

Add $83$ and $8$ .

$\frac{91}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{91}{12}$

Decimal Form:

$7.58\overline{3}$

Mixed Number Form:

$7 \frac{7}{12}$