Basic Math Examples

$\frac{2}{3} + 1 \frac{4}{7} + 5 \frac{1}{2} - \frac{1}{3}$

Step 1

Convert $1 \frac{4}{7}$ to an improper fraction.

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Step 1.1

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

$\frac{2}{3} + 1 + \frac{4}{7} + 5 \frac{1}{2} - \frac{1}{3}$

Step 1.2

Add $1$ and $\frac{4}{7}$ .

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Step 1.2.1

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

$\frac{2}{3} + \frac{7}{7} + \frac{4}{7} + 5 \frac{1}{2} - \frac{1}{3}$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{2}{3} + \frac{7 + 4}{7} + 5 \frac{1}{2} - \frac{1}{3}$

Step 1.2.3

Add $7$ and $4$ .

$\frac{2}{3} + \frac{11}{7} + 5 \frac{1}{2} - \frac{1}{3}$

Step 2

Convert $5 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$\frac{2}{3} + \frac{11}{7} + 5 + \frac{1}{2} - \frac{1}{3}$

Step 2.2

Add $5$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{2}{3} + \frac{11}{7} + 5 \cdot \frac{2}{2} + \frac{1}{2} - \frac{1}{3}$

Step 2.2.2

Combine $5$ and $\frac{2}{2}$ .

$\frac{2}{3} + \frac{11}{7} + \frac{5 \cdot 2}{2} + \frac{1}{2} - \frac{1}{3}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{2}{3} + \frac{11}{7} + \frac{5 \cdot 2 + 1}{2} - \frac{1}{3}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $2$ .

$\frac{2}{3} + \frac{11}{7} + \frac{10 + 1}{2} - \frac{1}{3}$

Step 2.2.4.2

Add $10$ and $1$ .

$\frac{2}{3} + \frac{11}{7} + \frac{11}{2} - \frac{1}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 - 1}{3} + \frac{11}{7} + \frac{11}{2}$

Step 4

Subtract $1$ from $2$ .

$\frac{1}{3} + \frac{11}{7} + \frac{11}{2}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{1}{3}$ by $\frac{14}{14}$ .

$\frac{1}{3} \cdot \frac{14}{14} + \frac{11}{7} + \frac{11}{2}$

Step 5.2

Multiply $\frac{1}{3}$ by $\frac{14}{14}$ .

$\frac{14}{3 \cdot 14} + \frac{11}{7} + \frac{11}{2}$

Step 5.3

Multiply $\frac{11}{7}$ by $\frac{6}{6}$ .

$\frac{14}{3 \cdot 14} + \frac{11}{7} \cdot \frac{6}{6} + \frac{11}{2}$

Step 5.4

Multiply $\frac{11}{7}$ by $\frac{6}{6}$ .

$\frac{14}{3 \cdot 14} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11}{2}$

Step 5.5

Multiply $\frac{11}{2}$ by $\frac{21}{21}$ .

$\frac{14}{3 \cdot 14} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11}{2} \cdot \frac{21}{21}$

Step 5.6

Multiply $\frac{11}{2}$ by $\frac{21}{21}$ .

$\frac{14}{3 \cdot 14} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11 \cdot 21}{2 \cdot 21}$

Step 5.7

Multiply $3$ by $14$ .

$\frac{14}{42} + \frac{11 \cdot 6}{7 \cdot 6} + \frac{11 \cdot 21}{2 \cdot 21}$

Step 5.8

Reorder the factors of $7 \cdot 6$ .

$\frac{14}{42} + \frac{11 \cdot 6}{6 \cdot 7} + \frac{11 \cdot 21}{2 \cdot 21}$

Step 5.9

Multiply $6$ by $7$ .

$\frac{14}{42} + \frac{11 \cdot 6}{42} + \frac{11 \cdot 21}{2 \cdot 21}$

Step 5.10

Multiply $2$ by $21$ .

$\frac{14}{42} + \frac{11 \cdot 6}{42} + \frac{11 \cdot 21}{42}$

Step 6

Combine the numerators over the common denominator.

$\frac{14 + 11 \cdot 6 + 11 \cdot 21}{42}$

Step 7

Simplify each term.

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Step 7.1

Multiply $11$ by $6$ .

$\frac{14 + 66 + 11 \cdot 21}{42}$

Step 7.2

Multiply $11$ by $21$ .

$\frac{14 + 66 + 231}{42}$

Step 8

Simplify by adding numbers.

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Step 8.1

Add $14$ and $66$ .

$\frac{80 + 231}{42}$

Step 8.2

Add $80$ and $231$ .

$\frac{311}{42}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{311}{42}$

Decimal Form:

$7.40476190 \dots$

Mixed Number Form:

$7 \frac{17}{42}$