Evaluate -10/51*(3/5-1/10)^2

$- \frac{10}{51} \cdot {(\frac{3}{5} - \frac{1}{10})}^{2}$

Step 1

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

$- \frac{10}{51} \cdot {(\frac{3}{5} \cdot \frac{2}{2} - \frac{1}{10})}^{2}$

Step 2

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

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

$- \frac{10}{51} \cdot {(\frac{3 \cdot 2}{5 \cdot 2} - \frac{1}{10})}^{2}$

Multiply $5$ by $2$ .

$- \frac{10}{51} \cdot {(\frac{3 \cdot 2}{10} - \frac{1}{10})}^{2}$

Step 3

Combine the numerators over the common denominator.

$- \frac{10}{51} \cdot {(\frac{3 \cdot 2 - 1}{10})}^{2}$

Step 4

Simplify the numerator.

Multiply $3$ by $2$ .

$- \frac{10}{51} \cdot {(\frac{6 - 1}{10})}^{2}$

Subtract $1$ from $6$ .

$- \frac{10}{51} \cdot {(\frac{5}{10})}^{2}$

Step 5

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

Factor $5$ out of $5$ .

$- \frac{10}{51} \cdot {(\frac{5 (1)}{10})}^{2}$

Cancel the common factors.

Factor $5$ out of $10$ .

$- \frac{10}{51} \cdot {(\frac{5 \cdot 1}{5 \cdot 2})}^{2}$

Cancel the common factor.

$- \frac{10}{51} \cdot {(\frac{5 \cdot 1}{5 \cdot 2})}^{2}$

Rewrite the expression.

$- \frac{10}{51} \cdot {(\frac{1}{2})}^{2}$

Step 6

Simplify the expression.

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

$- \frac{10}{51} \cdot \frac{1^{2}}{2^{2}}$

One to any power is one.

$- \frac{10}{51} \cdot \frac{1}{2^{2}}$

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

$- \frac{10}{51} \cdot \frac{1}{4}$

Step 7

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{10}{51}$ into the numerator.

$\frac{- 10}{51} \cdot \frac{1}{4}$

Factor $2$ out of $- 10$ .

$\frac{2 (- 5)}{51} \cdot \frac{1}{4}$

Factor $2$ out of $4$ .

$\frac{2 \cdot - 5}{51} \cdot \frac{1}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 \cdot - 5}{51} \cdot \frac{1}{2 \cdot 2}$

Rewrite the expression.

$\frac{- 5}{51} \cdot \frac{1}{2}$

Step 8

Multiply $\frac{- 5}{51}$ by $\frac{1}{2}$ .

$\frac{- 5}{51 \cdot 2}$

Step 9

Simplify the expression.

Multiply $51$ by $2$ .

$\frac{- 5}{102}$

Move the negative in front of the fraction.

$- \frac{5}{102}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{102}$

Decimal Form:

$- 0.04901960 \dots$

Evaluate -10/51*(3/5-1/10)^2

Related Questions