Basic Math Examples

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

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

Step 1

Convert

3 \frac{1}{3}

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

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Step 1.1

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

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

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

Step 1.2

Add

3

$3$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

3

$3$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.2

Combine

3

$3$ and

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 1.2.3

Combine the numerators over the common denominator.

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

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

3

$3$ by

3

$3$ .

\frac{9 + 1}{3} + 2 \frac{3}{4}

$\frac{9 + 1}{3} + 2 \frac{3}{4}$

Step 1.2.4.2

Add

9

$9$ and

1

$1$ .

\frac{10}{3} + 2 \frac{3}{4}

$\frac{10}{3} + 2 \frac{3}{4}$

\frac{10}{3} + 2 \frac{3}{4}

$\frac{10}{3} + 2 \frac{3}{4}$

\frac{10}{3} + 2 \frac{3}{4}

$\frac{10}{3} + 2 \frac{3}{4}$

\frac{10}{3} + 2 \frac{3}{4}

$\frac{10}{3} + 2 \frac{3}{4}$

Step 2

Convert

2 \frac{3}{4}

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

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Step 2.1

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

\frac{10}{3} + 2 + \frac{3}{4}

$\frac{10}{3} + 2 + \frac{3}{4}$

Step 2.2

Add

2

$2$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 2.2.1

To write

2

$2$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{10}{3} + 2 \cdot \frac{4}{4} + \frac{3}{4}

$\frac{10}{3} + 2 \cdot \frac{4}{4} + \frac{3}{4}$

Step 2.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{10}{3} + \frac{2 \cdot 4}{4} + \frac{3}{4}

$\frac{10}{3} + \frac{2 \cdot 4}{4} + \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{10}{3} + \frac{2 \cdot 4 + 3}{4}

$\frac{10}{3} + \frac{2 \cdot 4 + 3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{10}{3} + \frac{8 + 3}{4}

$\frac{10}{3} + \frac{8 + 3}{4}$

Step 2.2.4.2

Add

8

$8$ and

3

$3$ .

\frac{10}{3} + \frac{11}{4}

$\frac{10}{3} + \frac{11}{4}$

\frac{10}{3} + \frac{11}{4}

$\frac{10}{3} + \frac{11}{4}$

\frac{10}{3} + \frac{11}{4}

$\frac{10}{3} + \frac{11}{4}$

\frac{10}{3} + \frac{11}{4}

$\frac{10}{3} + \frac{11}{4}$

Step 3

To write

\frac{10}{3}

$\frac{10}{3}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{10}{3} \cdot \frac{4}{4} + \frac{11}{4}

$\frac{10}{3} \cdot \frac{4}{4} + \frac{11}{4}$

Step 4

To write

\frac{11}{4}

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

\frac{3}{3}

$\frac{3}{3}$ .

\frac{10}{3} \cdot \frac{4}{4} + \frac{11}{4} \cdot \frac{3}{3}

$\frac{10}{3} \cdot \frac{4}{4} + \frac{11}{4} \cdot \frac{3}{3}$

Step 5

Write each expression with a common denominator of

12

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

1

$1$ .

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Step 5.1

Multiply

\frac{10}{3}

$\frac{10}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{10 \cdot 4}{3 \cdot 4} + \frac{11}{4} \cdot \frac{3}{3}

$\frac{10 \cdot 4}{3 \cdot 4} + \frac{11}{4} \cdot \frac{3}{3}$

Step 5.2

Multiply

3

$3$ by

4

$4$ .

\frac{10 \cdot 4}{12} + \frac{11}{4} \cdot \frac{3}{3}

$\frac{10 \cdot 4}{12} + \frac{11}{4} \cdot \frac{3}{3}$

Step 5.3

Multiply

\frac{11}{4}

$\frac{11}{4}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{10 \cdot 4}{12} + \frac{11 \cdot 3}{4 \cdot 3}

$\frac{10 \cdot 4}{12} + \frac{11 \cdot 3}{4 \cdot 3}$

Step 5.4

Multiply

4

$4$ by

3

$3$ .

\frac{10 \cdot 4}{12} + \frac{11 \cdot 3}{12}

$\frac{10 \cdot 4}{12} + \frac{11 \cdot 3}{12}$

\frac{10 \cdot 4}{12} + \frac{11 \cdot 3}{12}

$\frac{10 \cdot 4}{12} + \frac{11 \cdot 3}{12}$

Step 6

Combine the numerators over the common denominator.

\frac{10 \cdot 4 + 11 \cdot 3}{12}

$\frac{10 \cdot 4 + 11 \cdot 3}{12}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

10

$10$ by

4

$4$ .

\frac{40 + 11 \cdot 3}{12}

$\frac{40 + 11 \cdot 3}{12}$

Step 7.2

Multiply

11

$11$ by

3

$3$ .

\frac{40 + 33}{12}

$\frac{40 + 33}{12}$

Step 7.3

Add

40

$40$ and

33

$33$ .

\frac{73}{12}

$\frac{73}{12}$

\frac{73}{12}

$\frac{73}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{73}{12}

$\frac{73}{12}$

Decimal Form:

6.08 ¯ 3

$6.08\overline{3}$

Mixed Number Form:

6 \frac{1}{12}

$6 \frac{1}{12}$