Basic Math Examples

6 \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}

$6 \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 1

Convert

6 \frac{7}{16}

$6 \frac{7}{16}$ to an improper fraction.

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Step 1.1

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

6 + \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}

$6 + \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 1.2

Add

6

$6$ and

\frac{7}{16}

$\frac{7}{16}$ .

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Step 1.2.1

To write

6

$6$ as a fraction with a common denominator, multiply by

\frac{16}{16}

$\frac{16}{16}$ .

6 \cdot \frac{16}{16} + \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}

$6 \cdot \frac{16}{16} + \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 1.2.2

Combine

6

$6$ and

\frac{16}{16}

$\frac{16}{16}$ .

\frac{6 \cdot 16}{16} + \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{6 \cdot 16}{16} + \frac{7}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 1.2.3

Combine the numerators over the common denominator.

\frac{6 \cdot 16 + 7}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{6 \cdot 16 + 7}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

6

$6$ by

16

$16$ .

\frac{96 + 7}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{96 + 7}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 1.2.4.2

Add

96

$96$ and

7

$7$ .

\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}$

\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}$

\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}$

\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + 2 \frac{1}{48}$

Step 2

Convert

2 \frac{1}{48}

$2 \frac{1}{48}$ to an improper fraction.

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Step 2.1

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

\frac{103}{16} + \frac{3}{24} + 2 + \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + 2 + \frac{1}{48}$

Step 2.2

Add

2

$2$ and

\frac{1}{48}

$\frac{1}{48}$ .

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Step 2.2.1

To write

2

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

\frac{48}{48}

$\frac{48}{48}$ .

\frac{103}{16} + \frac{3}{24} + 2 \cdot \frac{48}{48} + \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + 2 \cdot \frac{48}{48} + \frac{1}{48}$

Step 2.2.2

Combine

2

$2$ and

\frac{48}{48}

$\frac{48}{48}$ .

\frac{103}{16} + \frac{3}{24} + \frac{2 \cdot 48}{48} + \frac{1}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{2 \cdot 48}{48} + \frac{1}{48}$

Step 2.2.3

Combine the numerators over the common denominator.

\frac{103}{16} + \frac{3}{24} + \frac{2 \cdot 48 + 1}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{2 \cdot 48 + 1}{48}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

2

$2$ by

48

$48$ .

\frac{103}{16} + \frac{3}{24} + \frac{96 + 1}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{96 + 1}{48}$

Step 2.2.4.2

Add

96

$96$ and

1

$1$ .

\frac{103}{16} + \frac{3}{24} + \frac{97}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{97}{48}$

\frac{103}{16} + \frac{3}{24} + \frac{97}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{97}{48}$

\frac{103}{16} + \frac{3}{24} + \frac{97}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{97}{48}$

\frac{103}{16} + \frac{3}{24} + \frac{97}{48}

$\frac{103}{16} + \frac{3}{24} + \frac{97}{48}$

Step 3

Find the common denominator.

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Step 3.1

Multiply

\frac{103}{16}

$\frac{103}{16}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{103}{16} \cdot \frac{3}{3} + \frac{3}{24} + \frac{97}{48}

$\frac{103}{16} \cdot \frac{3}{3} + \frac{3}{24} + \frac{97}{48}$

Step 3.2

Multiply

\frac{103}{16}

$\frac{103}{16}$ by

\frac{3}{3}

$\frac{3}{3}$ .

\frac{103 \cdot 3}{16 \cdot 3} + \frac{3}{24} + \frac{97}{48}

$\frac{103 \cdot 3}{16 \cdot 3} + \frac{3}{24} + \frac{97}{48}$

Step 3.3

Multiply

\frac{3}{24}

$\frac{3}{24}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{103 \cdot 3}{16 \cdot 3} + \frac{3}{24} \cdot \frac{2}{2} + \frac{97}{48}

$\frac{103 \cdot 3}{16 \cdot 3} + \frac{3}{24} \cdot \frac{2}{2} + \frac{97}{48}$

Step 3.4

Multiply

\frac{3}{24}

$\frac{3}{24}$ by

\frac{2}{2}

$\frac{2}{2}$ .

\frac{103 \cdot 3}{16 \cdot 3} + \frac{3 \cdot 2}{24 \cdot 2} + \frac{97}{48}

$\frac{103 \cdot 3}{16 \cdot 3} + \frac{3 \cdot 2}{24 \cdot 2} + \frac{97}{48}$

Step 3.5

Reorder the factors of

16 \cdot 3

$16 \cdot 3$ .

\frac{103 \cdot 3}{3 \cdot 16} + \frac{3 \cdot 2}{24 \cdot 2} + \frac{97}{48}

$\frac{103 \cdot 3}{3 \cdot 16} + \frac{3 \cdot 2}{24 \cdot 2} + \frac{97}{48}$

Step 3.6

Multiply

3

$3$ by

16

$16$ .

\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{24 \cdot 2} + \frac{97}{48}

$\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{24 \cdot 2} + \frac{97}{48}$

Step 3.7

Reorder the factors of

24 \cdot 2

$24 \cdot 2$ .

\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{2 \cdot 24} + \frac{97}{48}

$\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{2 \cdot 24} + \frac{97}{48}$

Step 3.8

Multiply

2

$2$ by

24

$24$ .

\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{48} + \frac{97}{48}

$\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{48} + \frac{97}{48}$

\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{48} + \frac{97}{48}

$\frac{103 \cdot 3}{48} + \frac{3 \cdot 2}{48} + \frac{97}{48}$

Step 4

Combine the numerators over the common denominator.

\frac{103 \cdot 3 + 3 \cdot 2 + 97}{48}

$\frac{103 \cdot 3 + 3 \cdot 2 + 97}{48}$

Step 5

Simplify each term.

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Step 5.1

Multiply

103

$103$ by

3

$3$ .

\frac{309 + 3 \cdot 2 + 97}{48}

$\frac{309 + 3 \cdot 2 + 97}{48}$

Step 5.2

Multiply

3

$3$ by

2

$2$ .

\frac{309 + 6 + 97}{48}

$\frac{309 + 6 + 97}{48}$

\frac{309 + 6 + 97}{48}

$\frac{309 + 6 + 97}{48}$

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Add

309

$309$ and

6

$6$ .

\frac{315 + 97}{48}

$\frac{315 + 97}{48}$

Step 6.2

Add

315

$315$ and

97

$97$ .

\frac{412}{48}

$\frac{412}{48}$

Step 6.3

Cancel the common factor of

412

$412$ and

48

$48$ .

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Step 6.3.1

Factor

4

$4$ out of

412

$412$ .

\frac{4 (103)}{48}

$\frac{4 (103)}{48}$

Step 6.3.2

Cancel the common factors.

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Step 6.3.2.1

Factor

4

$4$ out of

48

$48$ .

\frac{4 \cdot 103}{4 \cdot 12}

$\frac{4 \cdot 103}{4 \cdot 12}$

Step 6.3.2.2

Cancel the common factor.

$\frac{4 \cdot 103}{4 \cdot 12}$

Step 6.3.2.3

Rewrite the expression.

$\frac{103}{12}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{103}{12}$

Decimal Form:

$8.58\overline{3}$

Mixed Number Form:

$8 \frac{7}{12}$