Algebra Examples

$(4 ({(6 - 4)}^{2} - 3 (\frac{1}{3} - \frac{4}{5})) + 2) - \sqrt{49}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Subtract $4$ from $6$ .

$4 (2^{2} - 3 (\frac{1}{3} - \frac{4}{5})) + 2 - \sqrt{49}$

Step 1.1.2

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

$4 (4 - 3 (\frac{1}{3} - \frac{4}{5})) + 2 - \sqrt{49}$

Step 1.1.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$4 (4 - 3 (\frac{1}{3} \cdot \frac{5}{5} - \frac{4}{5})) + 2 - \sqrt{49}$

Step 1.1.4

To write $- \frac{4}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 (4 - 3 (\frac{1}{3} \cdot \frac{5}{5} - \frac{4}{5} \cdot \frac{3}{3})) + 2 - \sqrt{49}$

Step 1.1.5

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 1.1.5.1

Multiply $\frac{1}{3}$ by $\frac{5}{5}$ .

$4 (4 - 3 (\frac{5}{3 \cdot 5} - \frac{4}{5} \cdot \frac{3}{3})) + 2 - \sqrt{49}$

Step 1.1.5.2

Multiply $3$ by $5$ .

$4 (4 - 3 (\frac{5}{15} - \frac{4}{5} \cdot \frac{3}{3})) + 2 - \sqrt{49}$

Step 1.1.5.3

Multiply $\frac{4}{5}$ by $\frac{3}{3}$ .

$4 (4 - 3 (\frac{5}{15} - \frac{4 \cdot 3}{5 \cdot 3})) + 2 - \sqrt{49}$

Step 1.1.5.4

Multiply $5$ by $3$ .

$4 (4 - 3 (\frac{5}{15} - \frac{4 \cdot 3}{15})) + 2 - \sqrt{49}$

Step 1.1.6

Combine the numerators over the common denominator.

$4 (4 - 3 \frac{5 - 4 \cdot 3}{15}) + 2 - \sqrt{49}$

Step 1.1.7

Simplify the numerator.

Tap for more steps...

Step 1.1.7.1

Multiply $- 4$ by $3$ .

$4 (4 - 3 \frac{5 - 12}{15}) + 2 - \sqrt{49}$

Step 1.1.7.2

Subtract $12$ from $5$ .

$4 (4 - 3 (\frac{- 7}{15})) + 2 - \sqrt{49}$

Step 1.1.8

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.1.8.1

Factor $3$ out of $- 3$ .

$4 (4 + 3 (- 1) \frac{- 7}{15}) + 2 - \sqrt{49}$

Step 1.1.8.2

Factor $3$ out of $15$ .

$4 (4 + 3 \cdot - 1 \frac{- 7}{3 \cdot 5}) + 2 - \sqrt{49}$

Step 1.1.8.3

Cancel the common factor.

$4 (4 + 3 \cdot - 1 \frac{- 7}{3 \cdot 5}) + 2 - \sqrt{49}$

Step 1.1.8.4

Rewrite the expression.

$4 (4 - 1 (\frac{- 7}{5})) + 2 - \sqrt{49}$

Step 1.1.9

Move the negative in front of the fraction.

$4 (4 - 1 (- \frac{7}{5})) + 2 - \sqrt{49}$

Step 1.1.10

Multiply $- 1 (- \frac{7}{5})$ .

Tap for more steps...

Step 1.1.10.1

Multiply $- 1$ by $- 1$ .

$4 (4 + 1 (\frac{7}{5})) + 2 - \sqrt{49}$

Step 1.1.10.2

Multiply $\frac{7}{5}$ by $1$ .

$4 (4 + \frac{7}{5}) + 2 - \sqrt{49}$

Step 1.2

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

$4 (4 \cdot \frac{5}{5} + \frac{7}{5}) + 2 - \sqrt{49}$

Step 1.3

Combine $4$ and $\frac{5}{5}$ .

$4 (\frac{4 \cdot 5}{5} + \frac{7}{5}) + 2 - \sqrt{49}$

Step 1.4

Combine the numerators over the common denominator.

$4 \frac{4 \cdot 5 + 7}{5} + 2 - \sqrt{49}$

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $4$ by $5$ .

$4 \frac{20 + 7}{5} + 2 - \sqrt{49}$

Step 1.5.2

Add $20$ and $7$ .

$4 (\frac{27}{5}) + 2 - \sqrt{49}$

Step 1.6

Multiply $4 (\frac{27}{5})$ .

Tap for more steps...

Step 1.6.1

Combine $4$ and $\frac{27}{5}$ .

$\frac{4 \cdot 27}{5} + 2 - \sqrt{49}$

Step 1.6.2

Multiply $4$ by $27$ .

$\frac{108}{5} + 2 - \sqrt{49}$

Step 1.7

Rewrite $49$ as $7^{2}$ .

$\frac{108}{5} + 2 - \sqrt{7^{2}}$

Step 1.8

Pull terms out from under the radical, assuming positive real numbers.

$\frac{108}{5} + 2 - 1 \cdot 7$

Step 1.9

Multiply $- 1$ by $7$ .

$\frac{108}{5} + 2 - 7$

Step 2

Find the common denominator.

Tap for more steps...

Step 2.1

Write $2$ as a fraction with denominator $1$ .

$\frac{108}{5} + \frac{2}{1} - 7$

Step 2.2

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

$\frac{108}{5} + \frac{2}{1} \cdot \frac{5}{5} - 7$

Step 2.3

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

$\frac{108}{5} + \frac{2 \cdot 5}{5} - 7$

Step 2.4

Write $- 7$ as a fraction with denominator $1$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} + \frac{- 7}{1}$

Step 2.5

Multiply $\frac{- 7}{1}$ by $\frac{5}{5}$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} + \frac{- 7}{1} \cdot \frac{5}{5}$

Step 2.6

Multiply $\frac{- 7}{1}$ by $\frac{5}{5}$ .

$\frac{108}{5} + \frac{2 \cdot 5}{5} + \frac{- 7 \cdot 5}{5}$

Step 3

Combine the numerators over the common denominator.

$\frac{108 + 2 \cdot 5 - 7 \cdot 5}{5}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Multiply $2$ by $5$ .

$\frac{108 + 10 - 7 \cdot 5}{5}$

Step 4.2

Multiply $- 7$ by $5$ .

$\frac{108 + 10 - 35}{5}$

Step 5

Simplify by adding and subtracting.

Tap for more steps...

Step 5.1

Add $108$ and $10$ .

$\frac{118 - 35}{5}$

Step 5.2

Subtract $35$ from $118$ .

$\frac{83}{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{83}{5}$

Decimal Form:

$16.6$

Mixed Number Form:

$16 \frac{3}{5}$