Basic Math Examples

$6 \frac{2}{7} \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 1

Convert $6 \frac{2}{7}$ to an improper fraction.

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Step 1.1

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

$(6 + \frac{2}{7}) \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 1.2

Add $6$ and $\frac{2}{7}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$(6 \cdot \frac{7}{7} + \frac{2}{7}) \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 1.2.2

Combine $6$ and $\frac{7}{7}$ .

$(\frac{6 \cdot 7}{7} + \frac{2}{7}) \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{6 \cdot 7 + 2}{7} \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $7$ .

$\frac{42 + 2}{7} \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 1.2.4.2

Add $42$ and $2$ .

$\frac{44}{7} \cdot 2 \frac{3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 2

Convert $2 \frac{3}{8}$ to an improper fraction.

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Step 2.1

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

$\frac{44}{7} \cdot (2 + \frac{3}{8}) + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 2.2

Add $2$ and $\frac{3}{8}$ .

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Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{44}{7} \cdot (2 \cdot \frac{8}{8} + \frac{3}{8}) + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 2.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{44}{7} \cdot (\frac{2 \cdot 8}{8} + \frac{3}{8}) + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{44}{7} \cdot \frac{2 \cdot 8 + 3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $8$ .

$\frac{44}{7} \cdot \frac{16 + 3}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 2.2.4.2

Add $16$ and $3$ .

$\frac{44}{7} \cdot \frac{19}{8} + 2 \frac{1}{2} \cdot 2 \frac{3}{8}$

Step 3

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

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Step 3.1

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

$\frac{44}{7} \cdot \frac{19}{8} + (2 + \frac{1}{2}) \cdot 2 \frac{3}{8}$

Step 3.2

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

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Step 3.2.1

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

$\frac{44}{7} \cdot \frac{19}{8} + (2 \cdot \frac{2}{2} + \frac{1}{2}) \cdot 2 \frac{3}{8}$

Step 3.2.2

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

$\frac{44}{7} \cdot \frac{19}{8} + (\frac{2 \cdot 2}{2} + \frac{1}{2}) \cdot 2 \frac{3}{8}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{44}{7} \cdot \frac{19}{8} + \frac{2 \cdot 2 + 1}{2} \cdot 2 \frac{3}{8}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply $2$ by $2$ .

$\frac{44}{7} \cdot \frac{19}{8} + \frac{4 + 1}{2} \cdot 2 \frac{3}{8}$

Step 3.2.4.2

Add $4$ and $1$ .

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot 2 \frac{3}{8}$

Step 4

Convert $2 \frac{3}{8}$ to an improper fraction.

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Step 4.1

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

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot (2 + \frac{3}{8})$

Step 4.2

Add $2$ and $\frac{3}{8}$ .

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Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot (2 \cdot \frac{8}{8} + \frac{3}{8})$

Step 4.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot (\frac{2 \cdot 8}{8} + \frac{3}{8})$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot \frac{2 \cdot 8 + 3}{8}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply $2$ by $8$ .

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot \frac{16 + 3}{8}$

Step 4.2.4.2

Add $16$ and $3$ .

$\frac{44}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5

Simplify each term.

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Step 5.1

Cancel the common factor of $4$ .

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Step 5.1.1

Factor $4$ out of $44$ .

$\frac{4 (11)}{7} \cdot \frac{19}{8} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.1.2

Factor $4$ out of $8$ .

$\frac{4 \cdot 11}{7} \cdot \frac{19}{4 \cdot 2} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.1.3

Cancel the common factor.

$\frac{4 \cdot 11}{7} \cdot \frac{19}{4 \cdot 2} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.1.4

Rewrite the expression.

$\frac{11}{7} \cdot \frac{19}{2} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.2

Multiply $\frac{11}{7}$ by $\frac{19}{2}$ .

$\frac{11 \cdot 19}{7 \cdot 2} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.3

Multiply $11$ by $19$ .

$\frac{209}{7 \cdot 2} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.4

Multiply $7$ by $2$ .

$\frac{209}{14} + \frac{5}{2} \cdot \frac{19}{8}$

Step 5.5

Multiply $\frac{5}{2} \cdot \frac{19}{8}$ .

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Step 5.5.1

Multiply $\frac{5}{2}$ by $\frac{19}{8}$ .

$\frac{209}{14} + \frac{5 \cdot 19}{2 \cdot 8}$

Step 5.5.2

Multiply $5$ by $19$ .

$\frac{209}{14} + \frac{95}{2 \cdot 8}$

Step 5.5.3

Multiply $2$ by $8$ .

$\frac{209}{14} + \frac{95}{16}$

Step 6

To write $\frac{209}{14}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{209}{14} \cdot \frac{8}{8} + \frac{95}{16}$

Step 7

To write $\frac{95}{16}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{209}{14} \cdot \frac{8}{8} + \frac{95}{16} \cdot \frac{7}{7}$

Step 8

Write each expression with a common denominator of $112$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{209}{14}$ by $\frac{8}{8}$ .

$\frac{209 \cdot 8}{14 \cdot 8} + \frac{95}{16} \cdot \frac{7}{7}$

Step 8.2

Multiply $14$ by $8$ .

$\frac{209 \cdot 8}{112} + \frac{95}{16} \cdot \frac{7}{7}$

Step 8.3

Multiply $\frac{95}{16}$ by $\frac{7}{7}$ .

$\frac{209 \cdot 8}{112} + \frac{95 \cdot 7}{16 \cdot 7}$

Step 8.4

Multiply $16$ by $7$ .

$\frac{209 \cdot 8}{112} + \frac{95 \cdot 7}{112}$

Step 9

Combine the numerators over the common denominator.

$\frac{209 \cdot 8 + 95 \cdot 7}{112}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $209$ by $8$ .

$\frac{1672 + 95 \cdot 7}{112}$

Step 10.2

Multiply $95$ by $7$ .

$\frac{1672 + 665}{112}$

Step 10.3

Add $1672$ and $665$ .

$\frac{2337}{112}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{2337}{112}$

Decimal Form:

$20.86607142 \dots$

Mixed Number Form:

$20 \frac{97}{112}$