Simplify 8 3/4+6 11/16*1/(6^2)

$8 \frac{3}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Step 1

Convert

$8 \frac{3}{4}$ to an improper fraction.

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

$8 + \frac{3}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Add

$8$ and

$\frac{3}{4}$ .

To write

$8$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$8 \cdot \frac{4}{4} + \frac{3}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Combine

$8$ and

$\frac{4}{4}$ .

$\frac{8 \cdot 4}{4} + \frac{3}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Combine the numerators over the common denominator.

$\frac{8 \cdot 4 + 3}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Simplify the numerator.

Multiply

$8$ by

$4$ .

$\frac{32 + 3}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Add

$32$ and

$3$ .

$\frac{35}{4} + 6 \frac{11}{16} \cdot \frac{1}{6^{2}}$

Step 2

Convert

$6 \frac{11}{16}$ to an improper fraction.

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

$\frac{35}{4} + (6 + \frac{11}{16}) \cdot \frac{1}{6^{2}}$

Add

$6$ and

$\frac{11}{16}$ .

To write

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

$\frac{16}{16}$ .

$\frac{35}{4} + (6 \cdot \frac{16}{16} + \frac{11}{16}) \cdot \frac{1}{6^{2}}$

Combine

$6$ and

$\frac{16}{16}$ .

$\frac{35}{4} + (\frac{6 \cdot 16}{16} + \frac{11}{16}) \cdot \frac{1}{6^{2}}$

Combine the numerators over the common denominator.

$\frac{35}{4} + \frac{6 \cdot 16 + 11}{16} \cdot \frac{1}{6^{2}}$

Simplify the numerator.

Multiply

$6$ by

$16$ .

$\frac{35}{4} + \frac{96 + 11}{16} \cdot \frac{1}{6^{2}}$

Add

$96$ and

$11$ .

$\frac{35}{4} + \frac{107}{16} \cdot \frac{1}{6^{2}}$

Step 3

Simplify each term.

Combine.

$\frac{35}{4} + \frac{107 \cdot 1}{16 \cdot 6^{2}}$

Multiply

$107$ by

$1$ .

$\frac{35}{4} + \frac{107}{16 \cdot 6^{2}}$

Raise

$6$ to the power of

$2$ .

$\frac{35}{4} + \frac{107}{16 \cdot 36}$

Multiply

$16$ by

$36$ .

$\frac{35}{4} + \frac{107}{576}$

Step 4

To write

$\frac{35}{4}$ as a fraction with a common denominator, multiply by

$\frac{144}{144}$ .

$\frac{35}{4} \cdot \frac{144}{144} + \frac{107}{576}$

Step 5

Write each expression with a common denominator of

$576$ , by multiplying each by an appropriate factor of

$1$ .

Multiply

$\frac{35}{4}$ by

$\frac{144}{144}$ .

$\frac{35 \cdot 144}{4 \cdot 144} + \frac{107}{576}$

Multiply

$4$ by

$144$ .

$\frac{35 \cdot 144}{576} + \frac{107}{576}$

Step 6

Combine the numerators over the common denominator.

$\frac{35 \cdot 144 + 107}{576}$

Step 7

Simplify the numerator.

Multiply

$35$ by

$144$ .

$\frac{5040 + 107}{576}$

Add

$5040$ and

$107$ .

$\frac{5147}{576}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{5147}{576}$

Decimal Form:

$8.935763\overline{8}$

Mixed Number Form:

$8 \frac{539}{576}$

Simplify 8 3/4+6 11/16*1/(6^2)

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