Basic Math Examples

1 \frac{1}{8} + 2 \frac{2}{5}

$1 \frac{1}{8} + 2 \frac{2}{5}$

Step 1

Convert

1 \frac{1}{8}

$1 \frac{1}{8}$ to an improper fraction.

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Step 1.1

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

1 + \frac{1}{8} + 2 \frac{2}{5}

$1 + \frac{1}{8} + 2 \frac{2}{5}$

Step 1.2

Add

1

$1$ and

\frac{1}{8}

$\frac{1}{8}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{8}{8} + \frac{1}{8} + 2 \frac{2}{5}

$\frac{8}{8} + \frac{1}{8} + 2 \frac{2}{5}$

Step 1.2.2

Combine the numerators over the common denominator.

\frac{8 + 1}{8} + 2 \frac{2}{5}

$\frac{8 + 1}{8} + 2 \frac{2}{5}$

Step 1.2.3

Add

8

$8$ and

1

$1$ .

\frac{9}{8} + 2 \frac{2}{5}

$\frac{9}{8} + 2 \frac{2}{5}$

\frac{9}{8} + 2 \frac{2}{5}

$\frac{9}{8} + 2 \frac{2}{5}$

\frac{9}{8} + 2 \frac{2}{5}

$\frac{9}{8} + 2 \frac{2}{5}$

Step 2

Convert

2 \frac{2}{5}

$2 \frac{2}{5}$ 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}{8} + 2 + \frac{2}{5}

$\frac{9}{8} + 2 + \frac{2}{5}$

Step 2.2

Add

2

$2$ and

\frac{2}{5}

$\frac{2}{5}$ .

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Step 2.2.1

To write

2

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

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{8} + 2 \cdot \frac{5}{5} + \frac{2}{5}

$\frac{9}{8} + 2 \cdot \frac{5}{5} + \frac{2}{5}$

Step 2.2.2

Combine

2

$2$ and

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{8} + \frac{2 \cdot 5}{5} + \frac{2}{5}

$\frac{9}{8} + \frac{2 \cdot 5}{5} + \frac{2}{5}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{9}{8} + \frac{2 \cdot 5 + 2}{5}

$\frac{9}{8} + \frac{2 \cdot 5 + 2}{5}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

5

$5$ .

\frac{9}{8} + \frac{10 + 2}{5}

$\frac{9}{8} + \frac{10 + 2}{5}$

Step 2.2.4.2

Add

10

$10$ and

2

$2$ .

\frac{9}{8} + \frac{12}{5}

$\frac{9}{8} + \frac{12}{5}$

\frac{9}{8} + \frac{12}{5}

$\frac{9}{8} + \frac{12}{5}$

\frac{9}{8} + \frac{12}{5}

$\frac{9}{8} + \frac{12}{5}$

\frac{9}{8} + \frac{12}{5}

$\frac{9}{8} + \frac{12}{5}$

Step 3

To write

\frac{9}{8}

$\frac{9}{8}$ as a fraction with a common denominator, multiply by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9}{8} \cdot \frac{5}{5} + \frac{12}{5}

$\frac{9}{8} \cdot \frac{5}{5} + \frac{12}{5}$

Step 4

To write

\frac{12}{5}

$\frac{12}{5}$ as a fraction with a common denominator, multiply by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{9}{8} \cdot \frac{5}{5} + \frac{12}{5} \cdot \frac{8}{8}

$\frac{9}{8} \cdot \frac{5}{5} + \frac{12}{5} \cdot \frac{8}{8}$

Step 5

Write each expression with a common denominator of

40

$40$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{9}{8}

$\frac{9}{8}$ by

\frac{5}{5}

$\frac{5}{5}$ .

\frac{9 \cdot 5}{8 \cdot 5} + \frac{12}{5} \cdot \frac{8}{8}

$\frac{9 \cdot 5}{8 \cdot 5} + \frac{12}{5} \cdot \frac{8}{8}$

Step 5.2

Multiply

8

$8$ by

5

$5$ .

\frac{9 \cdot 5}{40} + \frac{12}{5} \cdot \frac{8}{8}

$\frac{9 \cdot 5}{40} + \frac{12}{5} \cdot \frac{8}{8}$

Step 5.3

Multiply

\frac{12}{5}

$\frac{12}{5}$ by

\frac{8}{8}

$\frac{8}{8}$ .

\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{5 \cdot 8}

$\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{5 \cdot 8}$

Step 5.4

Multiply

5

$5$ by

8

$8$ .

\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{40}

$\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{40}$

\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{40}

$\frac{9 \cdot 5}{40} + \frac{12 \cdot 8}{40}$

Step 6

Combine the numerators over the common denominator.

\frac{9 \cdot 5 + 12 \cdot 8}{40}

$\frac{9 \cdot 5 + 12 \cdot 8}{40}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply

9

$9$ by

5

$5$ .

\frac{45 + 12 \cdot 8}{40}

$\frac{45 + 12 \cdot 8}{40}$

Step 7.2

Multiply

12

$12$ by

8

$8$ .

\frac{45 + 96}{40}

$\frac{45 + 96}{40}$

Step 7.3

Add

45

$45$ and

96

$96$ .

\frac{141}{40}

$\frac{141}{40}$

\frac{141}{40}

$\frac{141}{40}$

Step 8

The result can be shown in multiple forms.

Exact Form:

\frac{141}{40}

$\frac{141}{40}$

Decimal Form:

3.525

$3.525$

Mixed Number Form:

3 \frac{21}{40}

$3 \frac{21}{40}$