Basic Math Examples

$4 \frac{1}{3} - 2 \frac{3}{4}$

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.

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

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

$\frac{3}{3}$ .

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

Step 1.2.2

Combine

$4$ and

$\frac{3}{3}$ .

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

Step 1.2.3

Combine the numerators over the common denominator.

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$4$ by

$3$ .

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

Step 1.2.4.2

Add

$12$ and

$1$ .

$\frac{13}{3} - 2 \frac{3}{4}$

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.

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

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

$\frac{4}{4}$ .

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

Step 2.2.2

Combine

$2$ and

$\frac{4}{4}$ .

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

Step 2.2.3

Combine the numerators over the common denominator.

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

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$2$ by

$4$ .

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

Step 2.2.4.2

Add

$8$ and

$3$ .

$\frac{13}{3} - \frac{11}{4}$

Step 3

To write

$\frac{13}{3}$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{13}{3} \cdot \frac{4}{4} - \frac{11}{4}$

Step 4

To write

$- \frac{11}{4}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{13}{3} \cdot \frac{4}{4} - \frac{11}{4} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

$12$ , by multiplying each by an appropriate factor of

$1$ .

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Step 5.1

Multiply

$\frac{13}{3}$ by

$\frac{4}{4}$ .

$\frac{13 \cdot 4}{3 \cdot 4} - \frac{11}{4} \cdot \frac{3}{3}$

Step 5.2

Multiply

$3$ by

$4$ .

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

Step 5.3

Multiply

$\frac{11}{4}$ by

$\frac{3}{3}$ .

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

Step 5.4

Multiply

$4$ by

$3$ .

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply

$13$ by

$4$ .

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

Step 7.2

Multiply

$- 11$ by

$3$ .

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

Step 7.3

Subtract

$33$ from

$52$ .

$\frac{19}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{19}{12}$

Decimal Form:

$1.58\overline{3}$

Mixed Number Form:

$1 \frac{7}{12}$