Basic Math Examples

$2 (7) (2 \frac{1}{7}) + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 1

Convert $2 \frac{1}{7}$ to an improper fraction.

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Step 1.1

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

$2 (7) (2 + \frac{1}{7}) + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 1.2

Add $2$ and $\frac{1}{7}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 (7) (2 \cdot \frac{7}{7} + \frac{1}{7}) + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 1.2.2

Combine $2$ and $\frac{7}{7}$ .

$2 (7) (\frac{2 \cdot 7}{7} + \frac{1}{7}) + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 1.2.3

Combine the numerators over the common denominator.

$2 (7) \frac{2 \cdot 7 + 1}{7} + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $7$ .

$2 (7) \frac{14 + 1}{7} + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 1.2.4.2

Add $14$ and $1$ .

$2 (7) \frac{15}{7} + 2 (7) (4 \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 2

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$2 (7) \frac{15}{7} + 2 (7) (4 + \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 2.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.2.1

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

$2 (7) \frac{15}{7} + 2 (7) (4 \cdot \frac{2}{2} + \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 2.2.2

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

$2 (7) \frac{15}{7} + 2 (7) (\frac{4 \cdot 2}{2} + \frac{1}{2}) + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 2.2.3

Combine the numerators over the common denominator.

$2 (7) \frac{15}{7} + 2 (7) \frac{4 \cdot 2 + 1}{2} + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $4$ by $2$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{8 + 1}{2} + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 2.2.4.2

Add $8$ and $1$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (2 \frac{1}{7}) (4 \frac{1}{2})$

Step 3

Convert $2 \frac{1}{7}$ to an improper fraction.

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Step 3.1

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

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (2 + \frac{1}{7}) (4 \frac{1}{2})$

Step 3.2

Add $2$ and $\frac{1}{7}$ .

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Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (2 \cdot \frac{7}{7} + \frac{1}{7}) (4 \frac{1}{2})$

Step 3.2.2

Combine $2$ and $\frac{7}{7}$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{2 \cdot 7}{7} + \frac{1}{7}) (4 \frac{1}{2})$

Step 3.2.3

Combine the numerators over the common denominator.

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 \frac{2 \cdot 7 + 1}{7} (4 \frac{1}{2})$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $7$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 \frac{14 + 1}{7} (4 \frac{1}{2})$

Step 3.2.4.2

Add $14$ and $1$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) (4 \frac{1}{2})$

Step 4

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 4.1

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

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) (4 + \frac{1}{2})$

Step 4.2

Add $4$ and $\frac{1}{2}$ .

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Step 4.2.1

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

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) (4 \cdot \frac{2}{2} + \frac{1}{2})$

Step 4.2.2

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

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) (\frac{4 \cdot 2}{2} + \frac{1}{2})$

Step 4.2.3

Combine the numerators over the common denominator.

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{4 \cdot 2 + 1}{2}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $4$ by $2$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{8 + 1}{2}$

Step 4.2.4.2

Add $8$ and $1$ .

$2 (7) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5

Simplify each term.

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Step 5.1

Multiply $2$ by $7$ .

$14 (\frac{15}{7}) + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.2

Cancel the common factor of $7$ .

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Step 5.2.1

Factor $7$ out of $14$ .

$7 (2) \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.2.2

Cancel the common factor.

$7 \cdot 2 \frac{15}{7} + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.2.3

Rewrite the expression.

$2 \cdot 15 + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.3

Multiply $2$ by $15$ .

$30 + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.4

Multiply $2$ by $7$ .

$30 + 14 (\frac{9}{2}) + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.5

Cancel the common factor of $2$ .

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Step 5.5.1

Factor $2$ out of $14$ .

$30 + 2 (7) \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.5.2

Cancel the common factor.

$30 + 2 \cdot 7 \frac{9}{2} + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.5.3

Rewrite the expression.

$30 + 7 \cdot 9 + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.6

Multiply $7$ by $9$ .

$30 + 63 + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.7

Cancel the common factor of $2$ .

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Step 5.7.1

Cancel the common factor.

$30 + 63 + 2 (\frac{15}{7}) \frac{9}{2}$

Step 5.7.2

Rewrite the expression.

$30 + 63 + \frac{15}{7} \cdot 9$

Step 5.8

Combine $\frac{15}{7}$ and $9$ .

$30 + 63 + \frac{15 \cdot 9}{7}$

Step 5.9

Multiply $15$ by $9$ .

$30 + 63 + \frac{135}{7}$

Step 6

Find the common denominator.

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Step 6.1

Write $30$ as a fraction with denominator $1$ .

$\frac{30}{1} + 63 + \frac{135}{7}$

Step 6.2

Multiply $\frac{30}{1}$ by $\frac{7}{7}$ .

$\frac{30}{1} \cdot \frac{7}{7} + 63 + \frac{135}{7}$

Step 6.3

Multiply $\frac{30}{1}$ by $\frac{7}{7}$ .

$\frac{30 \cdot 7}{7} + 63 + \frac{135}{7}$

Step 6.4

Write $63$ as a fraction with denominator $1$ .

$\frac{30 \cdot 7}{7} + \frac{63}{1} + \frac{135}{7}$

Step 6.5

Multiply $\frac{63}{1}$ by $\frac{7}{7}$ .

$\frac{30 \cdot 7}{7} + \frac{63}{1} \cdot \frac{7}{7} + \frac{135}{7}$

Step 6.6

Multiply $\frac{63}{1}$ by $\frac{7}{7}$ .

$\frac{30 \cdot 7}{7} + \frac{63 \cdot 7}{7} + \frac{135}{7}$

Step 7

Combine the numerators over the common denominator.

$\frac{30 \cdot 7 + 63 \cdot 7 + 135}{7}$

Step 8

Simplify each term.

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Step 8.1

Multiply $30$ by $7$ .

$\frac{210 + 63 \cdot 7 + 135}{7}$

Step 8.2

Multiply $63$ by $7$ .

$\frac{210 + 441 + 135}{7}$

Step 9

Simplify by adding numbers.

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Step 9.1

Add $210$ and $441$ .

$\frac{651 + 135}{7}$

Step 9.2

Add $651$ and $135$ .

$\frac{786}{7}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$\frac{786}{7}$

Decimal Form:

$112.28571428 \dots$

Mixed Number Form:

$112 \frac{2}{7}$