Basic Math Examples

$| \frac{{(2 - 1 \frac{3}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 1

Convert $1 \frac{3}{5}$ to an improper fraction.

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Step 1.1

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

$| \frac{{(2 - (1 + \frac{3}{5}))}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 1.2

Add $1$ and $\frac{3}{5}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$| \frac{{(2 - (\frac{5}{5} + \frac{3}{5}))}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 1.2.2

Combine the numerators over the common denominator.

$| \frac{{(2 - \frac{5 + 3}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 1.2.3

Add $5$ and $3$ .

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 2

Convert $7 \frac{1}{2}$ to an improper fraction.

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Step 2.1

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

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 + \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 2.2

Add $7$ and $\frac{1}{2}$ .

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Step 2.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(7 \cdot \frac{2}{2} + \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 2.2.2

Combine $7$ and $\frac{2}{2}$ .

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{7 \cdot 2}{2} + \frac{1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 2.2.3

Combine the numerators over the common denominator.

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{7 \cdot 2 + 1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $7$ by $2$ .

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{14 + 1}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 2.2.4.2

Add $14$ and $1$ .

$| \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 3

Multiply the numerator and denominator of the fraction by $5$ .

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Step 3.1

Multiply $\frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 - \frac{6}{5}}$ by $\frac{5}{5}$ .

$| \frac{5}{5} \cdot \frac{{(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 - \frac{6}{5}} |$

Step 3.2

Combine.

$| \frac{5 ({(2 - \frac{8}{5})}^{2} + (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2})}{5 (5 - \frac{6}{5})} |$

Step 4

Apply the distributive property.

$| \frac{5 {(2 - \frac{8}{5})}^{2} + 5 ((\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2})}{5 \cdot 5 + 5 (- \frac{6}{5})} |$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Move the leading negative in $- \frac{6}{5}$ into the numerator.

$| \frac{5 {(2 - \frac{8}{5})}^{2} + 5 ((\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2})}{5 \cdot 5 + 5 (\frac{- 6}{5})} |$

Step 5.2

Cancel the common factor.

$| \frac{5 {(2 - \frac{8}{5})}^{2} + 5 ((\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2})}{5 \cdot 5 + 5 (\frac{- 6}{5})} |$

Step 5.3

Rewrite the expression.

$| \frac{5 {(2 - \frac{8}{5})}^{2} + 5 ((\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2})}{5 \cdot 5 - 6} |$

Step 6

Simplify the numerator.

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Step 6.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$| \frac{5 {(2 \cdot \frac{5}{5} - \frac{8}{5})}^{2} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.2

Combine $2$ and $\frac{5}{5}$ .

$| \frac{5 {(\frac{2 \cdot 5}{5} - \frac{8}{5})}^{2} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.3

Combine the numerators over the common denominator.

$| \frac{5 {(\frac{2 \cdot 5 - 8}{5})}^{2} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.4

Simplify the numerator.

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Step 6.4.1

Multiply $2$ by $5$ .

$| \frac{5 {(\frac{10 - 8}{5})}^{2} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.4.2

Subtract $8$ from $10$ .

$| \frac{5 {(\frac{2}{5})}^{2} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.5

Apply the product rule to $\frac{2}{5}$ .

$| \frac{5 \frac{2^{2}}{5^{2}} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.6

Cancel the common factor of $5$ .

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Step 6.6.1

Factor $5$ out of $5^{2}$ .

$| \frac{5 \frac{2^{2}}{5 \cdot 5} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.6.2

Cancel the common factor.

$| \frac{5 \frac{2^{2}}{5 \cdot 5} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.6.3

Rewrite the expression.

$| \frac{\frac{2^{2}}{5} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.7

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

$| \frac{\frac{4}{5} + 5 (\frac{5}{8} - \frac{3}{4}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.8

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$| \frac{\frac{4}{5} + 5 (\frac{5}{8} - \frac{3}{4} \cdot \frac{2}{2}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.9

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.9.1

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

$| \frac{\frac{4}{5} + 5 (\frac{5}{8} - \frac{3 \cdot 2}{4 \cdot 2}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.9.2

Multiply $4$ by $2$ .

$| \frac{\frac{4}{5} + 5 (\frac{5}{8} - \frac{3 \cdot 2}{8}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.10

Combine the numerators over the common denominator.

$| \frac{\frac{4}{5} + 5 \frac{5 - 3 \cdot 2}{8} {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.11

Simplify the numerator.

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Step 6.11.1

Multiply $- 3$ by $2$ .

$| \frac{\frac{4}{5} + 5 \frac{5 - 6}{8} {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.11.2

Subtract $6$ from $5$ .

$| \frac{\frac{4}{5} + 5 (\frac{- 1}{8}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.12

Move the negative in front of the fraction.

$| \frac{\frac{4}{5} + 5 (- \frac{1}{8}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.13

Multiply $5 (- \frac{1}{8})$ .

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Step 6.13.1

Multiply $- 1$ by $5$ .

$| \frac{\frac{4}{5} - 5 (\frac{1}{8}) {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.13.2

Combine $- 5$ and $\frac{1}{8}$ .

$| \frac{\frac{4}{5} + \frac{- 5}{8} {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.14

Move the negative in front of the fraction.

$| \frac{\frac{4}{5} - \frac{5}{8} {(\frac{6}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.15

Cancel the common factor of $3$ .

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Step 6.15.1

Factor $3$ out of $6$ .

$| \frac{\frac{4}{5} - \frac{5}{8} {(\frac{3 (2)}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.15.2

Cancel the common factor.

$| \frac{\frac{4}{5} - \frac{5}{8} {(\frac{3 \cdot 2}{5} \cdot \frac{1}{3})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.15.3

Rewrite the expression.

$| \frac{\frac{4}{5} - \frac{5}{8} {(\frac{2}{5})}^{4} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.16

Apply the product rule to $\frac{2}{5}$ .

$| \frac{\frac{4}{5} - \frac{5}{8} \cdot \frac{2^{4}}{5^{4}} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.17

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

$| \frac{\frac{4}{5} - \frac{5}{8} \cdot \frac{16}{5^{4}} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.18

Raise $5$ to the power of $4$ .

$| \frac{\frac{4}{5} - \frac{5}{8} \cdot \frac{16}{625} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.19

Cancel the common factor of $5$ .

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Step 6.19.1

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$| \frac{\frac{4}{5} + \frac{- 5}{8} \cdot \frac{16}{625} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.19.2

Factor $5$ out of $- 5$ .

$| \frac{\frac{4}{5} + \frac{5 (- 1)}{8} \cdot \frac{16}{625} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.19.3

Factor $5$ out of $625$ .

$| \frac{\frac{4}{5} + \frac{5 \cdot - 1}{8} \cdot \frac{16}{5 \cdot 125} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.19.4

Cancel the common factor.

$| \frac{\frac{4}{5} + \frac{5 \cdot - 1}{8} \cdot \frac{16}{5 \cdot 125} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.19.5

Rewrite the expression.

$| \frac{\frac{4}{5} + \frac{- 1}{8} \cdot \frac{16}{125} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.20

Cancel the common factor of $8$ .

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Step 6.20.1

Factor $8$ out of $16$ .

$| \frac{\frac{4}{5} + \frac{- 1}{8} \cdot \frac{8 (2)}{125} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.20.2

Cancel the common factor.

$| \frac{\frac{4}{5} + \frac{- 1}{8} \cdot \frac{8 \cdot 2}{125} \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.20.3

Rewrite the expression.

$| \frac{\frac{4}{5} - 1 (\frac{2}{125}) \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.21

Rewrite $- 1 (\frac{2}{125})$ as $- (\frac{2}{125})$ .

$| \frac{\frac{4}{5} - (\frac{2}{125}) \cdot {(\frac{15}{2})}^{2}}{5 \cdot 5 - 6} |$

Step 6.22

Apply the product rule to $\frac{15}{2}$ .

$| \frac{\frac{4}{5} - \frac{2}{125} \cdot \frac{15^{2}}{2^{2}}}{5 \cdot 5 - 6} |$

Step 6.23

Raise $15$ to the power of $2$ .

$| \frac{\frac{4}{5} - \frac{2}{125} \cdot \frac{225}{2^{2}}}{5 \cdot 5 - 6} |$

Step 6.24

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

$| \frac{\frac{4}{5} - \frac{2}{125} \cdot \frac{225}{4}}{5 \cdot 5 - 6} |$

Step 6.25

Cancel the common factor of $2$ .

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Step 6.25.1

Move the leading negative in $- \frac{2}{125}$ into the numerator.

$| \frac{\frac{4}{5} + \frac{- 2}{125} \cdot \frac{225}{4}}{5 \cdot 5 - 6} |$

Step 6.25.2

Factor $2$ out of $- 2$ .

$| \frac{\frac{4}{5} + \frac{2 (- 1)}{125} \cdot \frac{225}{4}}{5 \cdot 5 - 6} |$

Step 6.25.3

Factor $2$ out of $4$ .

$| \frac{\frac{4}{5} + \frac{2 \cdot - 1}{125} \cdot \frac{225}{2 \cdot 2}}{5 \cdot 5 - 6} |$

Step 6.25.4

Cancel the common factor.

$| \frac{\frac{4}{5} + \frac{2 \cdot - 1}{125} \cdot \frac{225}{2 \cdot 2}}{5 \cdot 5 - 6} |$

Step 6.25.5

Rewrite the expression.

$| \frac{\frac{4}{5} + \frac{- 1}{125} \cdot \frac{225}{2}}{5 \cdot 5 - 6} |$

Step 6.26

Cancel the common factor of $25$ .

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Step 6.26.1

Factor $25$ out of $125$ .

$| \frac{\frac{4}{5} + \frac{- 1}{25 (5)} \cdot \frac{225}{2}}{5 \cdot 5 - 6} |$

Step 6.26.2

Factor $25$ out of $225$ .

$| \frac{\frac{4}{5} + \frac{- 1}{25 \cdot 5} \cdot \frac{25 \cdot 9}{2}}{5 \cdot 5 - 6} |$

Step 6.26.3

Cancel the common factor.

$| \frac{\frac{4}{5} + \frac{- 1}{25 \cdot 5} \cdot \frac{25 \cdot 9}{2}}{5 \cdot 5 - 6} |$

Step 6.26.4

Rewrite the expression.

$| \frac{\frac{4}{5} + \frac{- 1}{5} \cdot \frac{9}{2}}{5 \cdot 5 - 6} |$

Step 6.27

Multiply $\frac{- 1}{5}$ by $\frac{9}{2}$ .

$| \frac{\frac{4}{5} + \frac{- 1 \cdot 9}{5 \cdot 2}}{5 \cdot 5 - 6} |$

Step 6.28

Multiply $- 1$ by $9$ .

$| \frac{\frac{4}{5} + \frac{- 9}{5 \cdot 2}}{5 \cdot 5 - 6} |$

Step 6.29

Multiply $5$ by $2$ .

$| \frac{\frac{4}{5} + \frac{- 9}{10}}{5 \cdot 5 - 6} |$

Step 6.30

Move the negative in front of the fraction.

$| \frac{\frac{4}{5} - \frac{9}{10}}{5 \cdot 5 - 6} |$

Step 6.31

To write $\frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$| \frac{\frac{4}{5} \cdot \frac{2}{2} - \frac{9}{10}}{5 \cdot 5 - 6} |$

Step 6.32

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.32.1

Multiply $\frac{4}{5}$ by $\frac{2}{2}$ .

$| \frac{\frac{4 \cdot 2}{5 \cdot 2} - \frac{9}{10}}{5 \cdot 5 - 6} |$

Step 6.32.2

Multiply $5$ by $2$ .

$| \frac{\frac{4 \cdot 2}{10} - \frac{9}{10}}{5 \cdot 5 - 6} |$

Step 6.33

Combine the numerators over the common denominator.

$| \frac{\frac{4 \cdot 2 - 9}{10}}{5 \cdot 5 - 6} |$

Step 6.34

Simplify the numerator.

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Step 6.34.1

Multiply $4$ by $2$ .

$| \frac{\frac{8 - 9}{10}}{5 \cdot 5 - 6} |$

Step 6.34.2

Subtract $9$ from $8$ .

$| \frac{\frac{- 1}{10}}{5 \cdot 5 - 6} |$

Step 6.35

Move the negative in front of the fraction.

$| \frac{- \frac{1}{10}}{5 \cdot 5 - 6} |$

Step 7

Simplify the denominator.

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Step 7.1

Multiply $5$ by $5$ .

$| \frac{- \frac{1}{10}}{25 - 6} |$

Step 7.2

Subtract $6$ from $25$ .

$| \frac{- \frac{1}{10}}{19} |$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$| - \frac{1}{10} \cdot \frac{1}{19} |$

Step 9

Multiply $- \frac{1}{10} \cdot \frac{1}{19}$ .

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Step 9.1

Multiply $\frac{1}{19}$ by $\frac{1}{10}$ .

$| - \frac{1}{19 \cdot 10} |$

Step 9.2

Multiply $19$ by $10$ .

$| - \frac{1}{190} |$

Step 10

$- \frac{1}{190}$ is approximately $- 0.00526315$ which is negative so negate $- \frac{1}{190}$ and remove the absolute value

$\frac{1}{190}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{190}$

Decimal Form:

$0.00526315 \dots$