Basic Math Examples

${(- \frac{3}{4})}^{2} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- \frac{3}{4}$ .

${(- 1)}^{2} {(\frac{3}{4})}^{2} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.1.2

Apply the product rule to $\frac{3}{4}$ .

${(- 1)}^{2} \frac{3^{2}}{4^{2}} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.2

Raise $- 1$ to the power of $2$ .

$1 \frac{3^{2}}{4^{2}} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.3

Multiply $\frac{3^{2}}{4^{2}}$ by $1$ .

$\frac{3^{2}}{4^{2}} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.4

Raise $3$ to the power of $2$ .

$\frac{9}{4^{2}} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.5

Raise $4$ to the power of $2$ .

$\frac{9}{16} - \frac{7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.6

Cancel the common factor of $7$ .

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Step 1.6.1

Move the leading negative in $- \frac{7}{8}$ into the numerator.

$\frac{9}{16} + \frac{- 7}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.6.2

Factor $7$ out of $- 7$ .

$\frac{9}{16} + \frac{7 (- 1)}{8} \cdot \frac{8}{21} + \frac{11}{12}$

Step 1.6.3

Factor $7$ out of $21$ .

$\frac{9}{16} + \frac{7 \cdot - 1}{8} \cdot \frac{8}{7 \cdot 3} + \frac{11}{12}$

Step 1.6.4

Cancel the common factor.

$\frac{9}{16} + \frac{7 \cdot - 1}{8} \cdot \frac{8}{7 \cdot 3} + \frac{11}{12}$

Step 1.6.5

Rewrite the expression.

$\frac{9}{16} + \frac{- 1}{8} \cdot \frac{8}{3} + \frac{11}{12}$

Step 1.7

Cancel the common factor of $8$ .

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Step 1.7.1

Cancel the common factor.

$\frac{9}{16} + \frac{- 1}{8} \cdot \frac{8}{3} + \frac{11}{12}$

Step 1.7.2

Rewrite the expression.

$\frac{9}{16} - 1 \cdot \frac{1}{3} + \frac{11}{12}$

Step 1.8

Rewrite $- 1 (\frac{1}{3})$ as $- (\frac{1}{3})$ .

$\frac{9}{16} - \frac{1}{3} + \frac{11}{12}$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{9}{16}$ by $\frac{3}{3}$ .

$\frac{9}{16} \cdot \frac{3}{3} - \frac{1}{3} + \frac{11}{12}$

Step 2.2

Multiply $\frac{9}{16}$ by $\frac{3}{3}$ .

$\frac{9 \cdot 3}{16 \cdot 3} - \frac{1}{3} + \frac{11}{12}$

Step 2.3

Multiply $\frac{1}{3}$ by $\frac{16}{16}$ .

$\frac{9 \cdot 3}{16 \cdot 3} - (\frac{1}{3} \cdot \frac{16}{16}) + \frac{11}{12}$

Step 2.4

Multiply $\frac{1}{3}$ by $\frac{16}{16}$ .

$\frac{9 \cdot 3}{16 \cdot 3} - \frac{16}{3 \cdot 16} + \frac{11}{12}$

Step 2.5

Multiply $\frac{11}{12}$ by $\frac{4}{4}$ .

$\frac{9 \cdot 3}{16 \cdot 3} - \frac{16}{3 \cdot 16} + \frac{11}{12} \cdot \frac{4}{4}$

Step 2.6

Multiply $\frac{11}{12}$ by $\frac{4}{4}$ .

$\frac{9 \cdot 3}{16 \cdot 3} - \frac{16}{3 \cdot 16} + \frac{11 \cdot 4}{12 \cdot 4}$

Step 2.7

Reorder the factors of $16 \cdot 3$ .

$\frac{9 \cdot 3}{3 \cdot 16} - \frac{16}{3 \cdot 16} + \frac{11 \cdot 4}{12 \cdot 4}$

Step 2.8

Multiply $3$ by $16$ .

$\frac{9 \cdot 3}{48} - \frac{16}{3 \cdot 16} + \frac{11 \cdot 4}{12 \cdot 4}$

Step 2.9

Multiply $3$ by $16$ .

$\frac{9 \cdot 3}{48} - \frac{16}{48} + \frac{11 \cdot 4}{12 \cdot 4}$

Step 2.10

Reorder the factors of $12 \cdot 4$ .

$\frac{9 \cdot 3}{48} - \frac{16}{48} + \frac{11 \cdot 4}{4 \cdot 12}$

Step 2.11

Multiply $4$ by $12$ .

$\frac{9 \cdot 3}{48} - \frac{16}{48} + \frac{11 \cdot 4}{48}$

Step 3

Combine the numerators over the common denominator.

$\frac{9 \cdot 3 - 16 + 11 \cdot 4}{48}$

Step 4

Simplify each term.

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Step 4.1

Multiply $9$ by $3$ .

$\frac{27 - 16 + 11 \cdot 4}{48}$

Step 4.2

Multiply $11$ by $4$ .

$\frac{27 - 16 + 44}{48}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Subtract $16$ from $27$ .

$\frac{11 + 44}{48}$

Step 5.2

Add $11$ and $44$ .

$\frac{55}{48}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{55}{48}$

Decimal Form:

$1.1458\overline{3}$

Mixed Number Form:

$1 \frac{7}{48}$