Basic Math Examples

2 \frac{3}{4} + 5 \frac{3}{5}

$2 \frac{3}{4} + 5 \frac{3}{5}$

Step 1

Convert

2 \frac{3}{4}

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

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Step 1.1

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

2 + \frac{3}{4} + 5 \frac{3}{5}

$2 + \frac{3}{4} + 5 \frac{3}{5}$

Step 1.2

Add

2

$2$ and

\frac{3}{4}

$\frac{3}{4}$ .

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Step 1.2.1

To write

2

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

\frac{4}{4}

$\frac{4}{4}$ .

2 \cdot \frac{4}{4} + \frac{3}{4} + 5 \frac{3}{5}

$2 \cdot \frac{4}{4} + \frac{3}{4} + 5 \frac{3}{5}$

Step 1.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{2 \cdot 4}{4} + \frac{3}{4} + 5 \frac{3}{5}

$\frac{2 \cdot 4}{4} + \frac{3}{4} + 5 \frac{3}{5}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 4 + 3}{4} + 5 \frac{3}{5}

$\frac{2 \cdot 4 + 3}{4} + 5 \frac{3}{5}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{8 + 3}{4} + 5 \frac{3}{5}

$\frac{8 + 3}{4} + 5 \frac{3}{5}$

Step 1.2.4.2

Add

8

$8$ and

3

$3$ .

\frac{11}{4} + 5 \frac{3}{5}

$\frac{11}{4} + 5 \frac{3}{5}$

\frac{11}{4} + 5 \frac{3}{5}

$\frac{11}{4} + 5 \frac{3}{5}$

\frac{11}{4} + 5 \frac{3}{5}

$\frac{11}{4} + 5 \frac{3}{5}$

\frac{11}{4} + 5 \frac{3}{5}

$\frac{11}{4} + 5 \frac{3}{5}$

Step 2

Convert

5 \frac{3}{5}

$5 \frac{3}{5}$ to an improper fraction.

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Step 2.1

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

\frac{11}{4} + 5 + \frac{3}{5}

$\frac{11}{4} + 5 + \frac{3}{5}$

Step 2.2

Add

5

$5$ and

\frac{3}{5}

$\frac{3}{5}$ .

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Step 2.2.1

To write

5

$5$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{11}{4} + 5 \cdot \frac{5}{5} + \frac{3}{5}

$\frac{11}{4} + 5 \cdot \frac{5}{5} + \frac{3}{5}$

Step 2.2.2

Combine

5

$5$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{11}{4} + \frac{5 \cdot 5}{5} + \frac{3}{5}

$\frac{11}{4} + \frac{5 \cdot 5}{5} + \frac{3}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{11}{4} + \frac{5 \cdot 5 + 3}{5}

$\frac{11}{4} + \frac{5 \cdot 5 + 3}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

5

$5$ by

5

$5$ .

\frac{11}{4} + \frac{25 + 3}{5}

$\frac{11}{4} + \frac{25 + 3}{5}$

Step 2.2.4.2

Add

25

$25$ and

3

$3$ .

\frac{11}{4} + \frac{28}{5}

$\frac{11}{4} + \frac{28}{5}$

\frac{11}{4} + \frac{28}{5}

$\frac{11}{4} + \frac{28}{5}$

\frac{11}{4} + \frac{28}{5}

$\frac{11}{4} + \frac{28}{5}$

\frac{11}{4} + \frac{28}{5}

$\frac{11}{4} + \frac{28}{5}$

Step 3

To write

\frac{11}{4}

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{11}{4} \cdot \frac{5}{5} + \frac{28}{5}

$\frac{11}{4} \cdot \frac{5}{5} + \frac{28}{5}$

Step 4

To write

\frac{28}{5}

$\frac{28}{5}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{11}{4} \cdot \frac{5}{5} + \frac{28}{5} \cdot \frac{4}{4}

$\frac{11}{4} \cdot \frac{5}{5} + \frac{28}{5} \cdot \frac{4}{4}$

Step 5

Write each expression with a common denominator of

20

$20$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{11}{4}

$\frac{11}{4}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{11 \cdot 5}{4 \cdot 5} + \frac{28}{5} \cdot \frac{4}{4}

$\frac{11 \cdot 5}{4 \cdot 5} + \frac{28}{5} \cdot \frac{4}{4}$

Step 5.2

Multiply

4

$4$ by

5

$5$ .

\frac{11 \cdot 5}{20} + \frac{28}{5} \cdot \frac{4}{4}

$\frac{11 \cdot 5}{20} + \frac{28}{5} \cdot \frac{4}{4}$

Step 5.3

Multiply

\frac{28}{5}

$\frac{28}{5}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{11 \cdot 5}{20} + \frac{28 \cdot 4}{5 \cdot 4}

$\frac{11 \cdot 5}{20} + \frac{28 \cdot 4}{5 \cdot 4}$

Step 5.4

Multiply

5

$5$ by

4

$4$ .

\frac{11 \cdot 5}{20} + \frac{28 \cdot 4}{20}

$\frac{11 \cdot 5}{20} + \frac{28 \cdot 4}{20}$

\frac{11 \cdot 5}{20} + \frac{28 \cdot 4}{20}

$\frac{11 \cdot 5}{20} + \frac{28 \cdot 4}{20}$

Step 6

Combine the numerators over the common denominator.

\frac{11 \cdot 5 + 28 \cdot 4}{20}

$\frac{11 \cdot 5 + 28 \cdot 4}{20}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

11

$11$ by

5

$5$ .

\frac{55 + 28 \cdot 4}{20}

$\frac{55 + 28 \cdot 4}{20}$

Step 7.2

Multiply

28

$28$ by

4

$4$ .

\frac{55 + 112}{20}

$\frac{55 + 112}{20}$

Step 7.3

Add

55

$55$ and

112

$112$ .

\frac{167}{20}

$\frac{167}{20}$

\frac{167}{20}

$\frac{167}{20}$