Basic Math Examples

2 \frac{1}{4} + 3 \frac{1}{5}

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

Step 1

Convert

2 \frac{1}{4}

$2 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

2 + \frac{1}{4} + 3 \frac{1}{5}

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

Step 1.2

Add

2

$2$ and

\frac{1}{4}

$\frac{1}{4}$ .

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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{1}{4} + 3 \frac{1}{5}

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

Step 1.2.2

Combine

2

$2$ and

\frac{4}{4}

$\frac{4}{4}$ .

\frac{2 \cdot 4}{4} + \frac{1}{4} + 3 \frac{1}{5}

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

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 4 + 1}{4} + 3 \frac{1}{5}

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

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

4

$4$ .

\frac{8 + 1}{4} + 3 \frac{1}{5}

$\frac{8 + 1}{4} + 3 \frac{1}{5}$

Step 1.2.4.2

Add

8

$8$ and

1

$1$ .

\frac{9}{4} + 3 \frac{1}{5}

$\frac{9}{4} + 3 \frac{1}{5}$

\frac{9}{4} + 3 \frac{1}{5}

$\frac{9}{4} + 3 \frac{1}{5}$

\frac{9}{4} + 3 \frac{1}{5}

$\frac{9}{4} + 3 \frac{1}{5}$

\frac{9}{4} + 3 \frac{1}{5}

$\frac{9}{4} + 3 \frac{1}{5}$

Step 2

Convert

3 \frac{1}{5}

$3 \frac{1}{5}$ to an improper fraction.

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Step 2.1

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

\frac{9}{4} + 3 + \frac{1}{5}

$\frac{9}{4} + 3 + \frac{1}{5}$

Step 2.2

Add

3

$3$ and

\frac{1}{5}

$\frac{1}{5}$ .

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Step 2.2.1

To write

3

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{4} + 3 \cdot \frac{5}{5} + \frac{1}{5}

$\frac{9}{4} + 3 \cdot \frac{5}{5} + \frac{1}{5}$

Step 2.2.2

Combine

3

$3$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{4} + \frac{3 \cdot 5}{5} + \frac{1}{5}

$\frac{9}{4} + \frac{3 \cdot 5}{5} + \frac{1}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{9}{4} + \frac{3 \cdot 5 + 1}{5}

$\frac{9}{4} + \frac{3 \cdot 5 + 1}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

3

$3$ by

5

$5$ .

\frac{9}{4} + \frac{15 + 1}{5}

$\frac{9}{4} + \frac{15 + 1}{5}$

Step 2.2.4.2

Add

15

$15$ and

1

$1$ .

\frac{9}{4} + \frac{16}{5}

$\frac{9}{4} + \frac{16}{5}$

\frac{9}{4} + \frac{16}{5}

$\frac{9}{4} + \frac{16}{5}$

\frac{9}{4} + \frac{16}{5}

$\frac{9}{4} + \frac{16}{5}$

\frac{9}{4} + \frac{16}{5}

$\frac{9}{4} + \frac{16}{5}$

Step 3

To write

\frac{9}{4}

$\frac{9}{4}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{4} \cdot \frac{5}{5} + \frac{16}{5}

$\frac{9}{4} \cdot \frac{5}{5} + \frac{16}{5}$

Step 4

To write

\frac{16}{5}

$\frac{16}{5}$ as a fraction with a common denominator, multiply by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{9}{4} \cdot \frac{5}{5} + \frac{16}{5} \cdot \frac{4}{4}

$\frac{9}{4} \cdot \frac{5}{5} + \frac{16}{5} \cdot \frac{4}{4}$

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{9}{4}

$\frac{9}{4}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9 \cdot 5}{4 \cdot 5} + \frac{16}{5} \cdot \frac{4}{4}

$\frac{9 \cdot 5}{4 \cdot 5} + \frac{16}{5} \cdot \frac{4}{4}$

Step 5.2

Multiply

4

$4$ by

5

$5$ .

\frac{9 \cdot 5}{20} + \frac{16}{5} \cdot \frac{4}{4}

$\frac{9 \cdot 5}{20} + \frac{16}{5} \cdot \frac{4}{4}$

Step 5.3

Multiply

\frac{16}{5}

$\frac{16}{5}$ by

\frac{4}{4}

$\frac{4}{4}$ .

\frac{9 \cdot 5}{20} + \frac{16 \cdot 4}{5 \cdot 4}

$\frac{9 \cdot 5}{20} + \frac{16 \cdot 4}{5 \cdot 4}$

Step 5.4

Multiply

5

$5$ by

4

$4$ .

\frac{9 \cdot 5}{20} + \frac{16 \cdot 4}{20}

$\frac{9 \cdot 5}{20} + \frac{16 \cdot 4}{20}$

\frac{9 \cdot 5}{20} + \frac{16 \cdot 4}{20}

$\frac{9 \cdot 5}{20} + \frac{16 \cdot 4}{20}$

Step 6

Combine the numerators over the common denominator.

\frac{9 \cdot 5 + 16 \cdot 4}{20}

$\frac{9 \cdot 5 + 16 \cdot 4}{20}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

9

$9$ by

5

$5$ .

\frac{45 + 16 \cdot 4}{20}

$\frac{45 + 16 \cdot 4}{20}$

Step 7.2

Multiply

16

$16$ by

4

$4$ .

\frac{45 + 64}{20}

$\frac{45 + 64}{20}$

Step 7.3

Add

45

$45$ and

64

$64$ .

\frac{109}{20}

$\frac{109}{20}$

\frac{109}{20}

$\frac{109}{20}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{109}{20}

$\frac{109}{20}$

Decimal Form:

5.45

$5.45$

Mixed Number Form:

5 \frac{9}{20}

$5 \frac{9}{20}$