Basic Math Examples

2 \frac{1}{3} \cdot 1 \frac{5}{8}

$2 \frac{1}{3} \cdot 1 \frac{5}{8}$

Step 1

Convert

2 \frac{1}{3}

$2 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

(2 + \frac{1}{3}) \cdot 1 \frac{5}{8}

$(2 + \frac{1}{3}) \cdot 1 \frac{5}{8}$

Step 1.2

Add

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

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Step 1.2.1

To write

2

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

\frac{3}{3}

$\frac{3}{3}$ .

(2 \cdot \frac{3}{3} + \frac{1}{3}) \cdot 1 \frac{5}{8}

$(2 \cdot \frac{3}{3} + \frac{1}{3}) \cdot 1 \frac{5}{8}$

Step 1.2.2

Combine

2

$2$ and

\frac{3}{3}

$\frac{3}{3}$ .

(\frac{2 \cdot 3}{3} + \frac{1}{3}) \cdot 1 \frac{5}{8}

$(\frac{2 \cdot 3}{3} + \frac{1}{3}) \cdot 1 \frac{5}{8}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{2 \cdot 3 + 1}{3} \cdot 1 \frac{5}{8}

$\frac{2 \cdot 3 + 1}{3} \cdot 1 \frac{5}{8}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

2

$2$ by

3

$3$ .

\frac{6 + 1}{3} \cdot 1 \frac{5}{8}

$\frac{6 + 1}{3} \cdot 1 \frac{5}{8}$

Step 1.2.4.2

Add

6

$6$ and

1

$1$ .

\frac{7}{3} \cdot 1 \frac{5}{8}

$\frac{7}{3} \cdot 1 \frac{5}{8}$

\frac{7}{3} \cdot 1 \frac{5}{8}

$\frac{7}{3} \cdot 1 \frac{5}{8}$

\frac{7}{3} \cdot 1 \frac{5}{8}

$\frac{7}{3} \cdot 1 \frac{5}{8}$

\frac{7}{3} \cdot 1 \frac{5}{8}

$\frac{7}{3} \cdot 1 \frac{5}{8}$

Step 2

Convert

1 \frac{5}{8}

$1 \frac{5}{8}$ to an improper fraction.

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Step 2.1

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

\frac{7}{3} \cdot (1 + \frac{5}{8})

$\frac{7}{3} \cdot (1 + \frac{5}{8})$

Step 2.2

Add

1

$1$ and

\frac{5}{8}

$\frac{5}{8}$ .

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Step 2.2.1

Write

1

$1$ as a fraction with a common denominator.

\frac{7}{3} \cdot (\frac{8}{8} + \frac{5}{8})

$\frac{7}{3} \cdot (\frac{8}{8} + \frac{5}{8})$

Step 2.2.2

Combine the numerators over the common denominator.

\frac{7}{3} \cdot \frac{8 + 5}{8}

$\frac{7}{3} \cdot \frac{8 + 5}{8}$

Step 2.2.3

Add

8

$8$ and

5

$5$ .

\frac{7}{3} \cdot \frac{13}{8}

$\frac{7}{3} \cdot \frac{13}{8}$

\frac{7}{3} \cdot \frac{13}{8}

$\frac{7}{3} \cdot \frac{13}{8}$

\frac{7}{3} \cdot \frac{13}{8}

$\frac{7}{3} \cdot \frac{13}{8}$

Step 3

Multiply

\frac{7}{3} \cdot \frac{13}{8}

$\frac{7}{3} \cdot \frac{13}{8}$ .

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Step 3.1

Multiply

\frac{7}{3}

$\frac{7}{3}$ by

\frac{13}{8}

$\frac{13}{8}$ .

\frac{7 \cdot 13}{3 \cdot 8}

$\frac{7 \cdot 13}{3 \cdot 8}$

Step 3.2

Multiply

7

$7$ by

13

$13$ .

\frac{91}{3 \cdot 8}

$\frac{91}{3 \cdot 8}$

Step 3.3

Multiply

3

$3$ by

8

$8$ .

\frac{91}{24}

$\frac{91}{24}$

\frac{91}{24}

$\frac{91}{24}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{91}{24}

$\frac{91}{24}$

Decimal Form:

3.791 ¯ 6

$3.791\overline{6}$

Mixed Number Form:

3 \frac{19}{24}

$3 \frac{19}{24}$