Basic Math Examples

$3 \frac{1}{4} \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 1

Convert $3 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$(3 + \frac{1}{4}) \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 1.2

Add $3$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(3 \cdot \frac{4}{4} + \frac{1}{4}) \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 1.2.2

Combine $3$ and $\frac{4}{4}$ .

$(\frac{3 \cdot 4}{4} + \frac{1}{4}) \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 4 + 1}{4} \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $4$ .

$\frac{12 + 1}{4} \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 1.2.4.2

Add $12$ and $1$ .

$\frac{13}{4} \cdot 100 + 3 \frac{1}{7} \cdot 12$

Step 2

Convert $3 \frac{1}{7}$ to an improper fraction.

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Step 2.1

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

$\frac{13}{4} \cdot 100 + (3 + \frac{1}{7}) \cdot 12$

Step 2.2

Add $3$ and $\frac{1}{7}$ .

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Step 2.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{13}{4} \cdot 100 + (3 \cdot \frac{7}{7} + \frac{1}{7}) \cdot 12$

Step 2.2.2

Combine $3$ and $\frac{7}{7}$ .

$\frac{13}{4} \cdot 100 + (\frac{3 \cdot 7}{7} + \frac{1}{7}) \cdot 12$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{13}{4} \cdot 100 + \frac{3 \cdot 7 + 1}{7} \cdot 12$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $3$ by $7$ .

$\frac{13}{4} \cdot 100 + \frac{21 + 1}{7} \cdot 12$

Step 2.2.4.2

Add $21$ and $1$ .

$\frac{13}{4} \cdot 100 + \frac{22}{7} \cdot 12$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $4$ .

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Step 3.1.1

Factor $4$ out of $100$ .

$\frac{13}{4} \cdot (4 (25)) + \frac{22}{7} \cdot 12$

Step 3.1.2

Cancel the common factor.

$\frac{13}{4} \cdot (4 \cdot 25) + \frac{22}{7} \cdot 12$

Step 3.1.3

Rewrite the expression.

$13 \cdot 25 + \frac{22}{7} \cdot 12$

Step 3.2

Multiply $13$ by $25$ .

$325 + \frac{22}{7} \cdot 12$

Step 3.3

Multiply $\frac{22}{7} \cdot 12$ .

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Step 3.3.1

Combine $\frac{22}{7}$ and $12$ .

$325 + \frac{22 \cdot 12}{7}$

Step 3.3.2

Multiply $22$ by $12$ .

$325 + \frac{264}{7}$

Step 4

To write $325$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$325 \cdot \frac{7}{7} + \frac{264}{7}$

Step 5

Combine $325$ and $\frac{7}{7}$ .

$\frac{325 \cdot 7}{7} + \frac{264}{7}$

Step 6

Combine the numerators over the common denominator.

$\frac{325 \cdot 7 + 264}{7}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $325$ by $7$ .

$\frac{2275 + 264}{7}$

Step 7.2

Add $2275$ and $264$ .

$\frac{2539}{7}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{2539}{7}$

Decimal Form:

$362.71428571 \dots$

Mixed Number Form:

$362 \frac{5}{7}$