Basic Math Examples

$- \frac{16}{31} \cdot {(\frac{3}{5} - \frac{1}{10})}^{2}$

Step 1

To write $\frac{3}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{16}{31} \cdot {(\frac{3}{5} \cdot \frac{2}{2} - \frac{1}{10})}^{2}$

Step 2

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

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Step 2.1

Multiply $\frac{3}{5}$ by $\frac{2}{2}$ .

$- \frac{16}{31} \cdot {(\frac{3 \cdot 2}{5 \cdot 2} - \frac{1}{10})}^{2}$

Step 2.2

Multiply $5$ by $2$ .

$- \frac{16}{31} \cdot {(\frac{3 \cdot 2}{10} - \frac{1}{10})}^{2}$

Step 3

Combine the numerators over the common denominator.

$- \frac{16}{31} \cdot {(\frac{3 \cdot 2 - 1}{10})}^{2}$

Step 4

Simplify the numerator.

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Step 4.1

Multiply $3$ by $2$ .

$- \frac{16}{31} \cdot {(\frac{6 - 1}{10})}^{2}$

Step 4.2

Subtract $1$ from $6$ .

$- \frac{16}{31} \cdot {(\frac{5}{10})}^{2}$

Step 5

Cancel the common factor of $5$ and $10$ .

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Step 5.1

Factor $5$ out of $5$ .

$- \frac{16}{31} \cdot {(\frac{5 (1)}{10})}^{2}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $10$ .

$- \frac{16}{31} \cdot {(\frac{5 \cdot 1}{5 \cdot 2})}^{2}$

Step 5.2.2

Cancel the common factor.

$- \frac{16}{31} \cdot {(\frac{5 \cdot 1}{5 \cdot 2})}^{2}$

Step 5.2.3

Rewrite the expression.

$- \frac{16}{31} \cdot {(\frac{1}{2})}^{2}$

Step 6

Simplify the expression.

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Step 6.1

Apply the product rule to $\frac{1}{2}$ .

$- \frac{16}{31} \cdot \frac{1^{2}}{2^{2}}$

Step 6.2

One to any power is one.

$- \frac{16}{31} \cdot \frac{1}{2^{2}}$

Step 6.3

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

$- \frac{16}{31} \cdot \frac{1}{4}$

Step 7

Cancel the common factor of $4$ .

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Step 7.1

Move the leading negative in $- \frac{16}{31}$ into the numerator.

$\frac{- 16}{31} \cdot \frac{1}{4}$

Step 7.2

Factor $4$ out of $- 16$ .

$\frac{4 (- 4)}{31} \cdot \frac{1}{4}$

Step 7.3

Cancel the common factor.

$\frac{4 \cdot - 4}{31} \cdot \frac{1}{4}$

Step 7.4

Rewrite the expression.

$\frac{- 4}{31}$

Step 8

Move the negative in front of the fraction.

$- \frac{4}{31}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{31}$

Decimal Form:

$- 0.12903225 \dots$