Basic Math Examples

$18 \frac{6}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 1

Convert $18 \frac{6}{7}$ to an improper fraction.

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Step 1.1

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

$18 + \frac{6}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 1.2

Add $18$ and $\frac{6}{7}$ .

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Step 1.2.1

To write $18$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$18 \cdot \frac{7}{7} + \frac{6}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 1.2.2

Combine $18$ and $\frac{7}{7}$ .

$\frac{18 \cdot 7}{7} + \frac{6}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{18 \cdot 7 + 6}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $18$ by $7$ .

$\frac{126 + 6}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 1.2.4.2

Add $126$ and $6$ .

$\frac{132}{7} + 13 \frac{5}{7} + 16 \frac{2}{7}$

Step 2

Convert $13 \frac{5}{7}$ to an improper fraction.

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Step 2.1

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

$\frac{132}{7} + 13 + \frac{5}{7} + 16 \frac{2}{7}$

Step 2.2

Add $13$ and $\frac{5}{7}$ .

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Step 2.2.1

To write $13$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{132}{7} + 13 \cdot \frac{7}{7} + \frac{5}{7} + 16 \frac{2}{7}$

Step 2.2.2

Combine $13$ and $\frac{7}{7}$ .

$\frac{132}{7} + \frac{13 \cdot 7}{7} + \frac{5}{7} + 16 \frac{2}{7}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{132}{7} + \frac{13 \cdot 7 + 5}{7} + 16 \frac{2}{7}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $13$ by $7$ .

$\frac{132}{7} + \frac{91 + 5}{7} + 16 \frac{2}{7}$

Step 2.2.4.2

Add $91$ and $5$ .

$\frac{132}{7} + \frac{96}{7} + 16 \frac{2}{7}$

Step 3

Convert $16 \frac{2}{7}$ to an improper fraction.

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Step 3.1

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

$\frac{132}{7} + \frac{96}{7} + 16 + \frac{2}{7}$

Step 3.2

Add $16$ and $\frac{2}{7}$ .

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Step 3.2.1

To write $16$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{132}{7} + \frac{96}{7} + 16 \cdot \frac{7}{7} + \frac{2}{7}$

Step 3.2.2

Combine $16$ and $\frac{7}{7}$ .

$\frac{132}{7} + \frac{96}{7} + \frac{16 \cdot 7}{7} + \frac{2}{7}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{132}{7} + \frac{96}{7} + \frac{16 \cdot 7 + 2}{7}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $16$ by $7$ .

$\frac{132}{7} + \frac{96}{7} + \frac{112 + 2}{7}$

Step 3.2.4.2

Add $112$ and $2$ .

$\frac{132}{7} + \frac{96}{7} + \frac{114}{7}$

Step 4

Combine the numerators over the common denominator.

$\frac{132 + 96 + 114}{7}$

Step 5

Simplify by adding numbers.

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Step 5.1

Add $132$ and $96$ .

$\frac{228 + 114}{7}$

Step 5.2

Add $228$ and $114$ .

$\frac{342}{7}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{342}{7}$

Decimal Form:

$48.85714285 \dots$

Mixed Number Form:

$48 \frac{6}{7}$