Basic Math Examples

$4 \frac{1}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 1

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

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Step 1.1

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

$4 + \frac{1}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 1.2

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

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Step 1.2.1

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

$4 \cdot \frac{3}{3} + \frac{1}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 1.2.2

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

$\frac{4 \cdot 3}{3} + \frac{1}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 1}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $4$ by $3$ .

$\frac{12 + 1}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 1.2.4.2

Add $12$ and $1$ .

$\frac{13}{3} - 2 \frac{3}{4} + \frac{5}{12}$

Step 2

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{13}{3} - (2 + \frac{3}{4}) + \frac{5}{12}$

Step 2.2

Add $2$ and $\frac{3}{4}$ .

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Step 2.2.1

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

$\frac{13}{3} - (2 \cdot \frac{4}{4} + \frac{3}{4}) + \frac{5}{12}$

Step 2.2.2

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

$\frac{13}{3} - (\frac{2 \cdot 4}{4} + \frac{3}{4}) + \frac{5}{12}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{13}{3} - \frac{2 \cdot 4 + 3}{4} + \frac{5}{12}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $2$ by $4$ .

$\frac{13}{3} - \frac{8 + 3}{4} + \frac{5}{12}$

Step 2.2.4.2

Add $8$ and $3$ .

$\frac{13}{3} - \frac{11}{4} + \frac{5}{12}$

Step 3

Find the common denominator.

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Step 3.1

Multiply $\frac{13}{3}$ by $\frac{4}{4}$ .

$\frac{13}{3} \cdot \frac{4}{4} - \frac{11}{4} + \frac{5}{12}$

Step 3.2

Multiply $\frac{13}{3}$ by $\frac{4}{4}$ .

$\frac{13 \cdot 4}{3 \cdot 4} - \frac{11}{4} + \frac{5}{12}$

Step 3.3

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$\frac{13 \cdot 4}{3 \cdot 4} - (\frac{11}{4} \cdot \frac{3}{3}) + \frac{5}{12}$

Step 3.4

Multiply $\frac{11}{4}$ by $\frac{3}{3}$ .

$\frac{13 \cdot 4}{3 \cdot 4} - \frac{11 \cdot 3}{4 \cdot 3} + \frac{5}{12}$

Step 3.5

Multiply $3$ by $4$ .

$\frac{13 \cdot 4}{12} - \frac{11 \cdot 3}{4 \cdot 3} + \frac{5}{12}$

Step 3.6

Reorder the factors of $4 \cdot 3$ .

$\frac{13 \cdot 4}{12} - \frac{11 \cdot 3}{3 \cdot 4} + \frac{5}{12}$

Step 3.7

Multiply $3$ by $4$ .

$\frac{13 \cdot 4}{12} - \frac{11 \cdot 3}{12} + \frac{5}{12}$

Step 4

Combine the numerators over the common denominator.

$\frac{13 \cdot 4 - 11 \cdot 3 + 5}{12}$

Step 5

Simplify each term.

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Step 5.1

Multiply $13$ by $4$ .

$\frac{52 - 11 \cdot 3 + 5}{12}$

Step 5.2

Multiply $- 11$ by $3$ .

$\frac{52 - 33 + 5}{12}$

Step 6

Simplify the expression.

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Step 6.1

Subtract $33$ from $52$ .

$\frac{19 + 5}{12}$

Step 6.2

Add $19$ and $5$ .

$\frac{24}{12}$

Step 6.3

Divide $24$ by $12$ .

$2$