Basic Math Examples

\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - \frac{3}{3}} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - \frac{3}{3}} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 1

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 1.1

Cancel the common factor.

\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - \frac{3}{3}} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - \frac{3}{3}} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 1.2

Rewrite the expression.

\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - 1 \cdot 1} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - 1 \cdot 1} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - 1 \cdot 1} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 (5 (\frac{2 + 2 \cdot 4}{6 - 1 \cdot 1} \cdot 4 + 2))}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Multiply

2

$2$ by

4

$4$ .

\frac{10^{2} - 3 \cdot 5 (\frac{2 + 8}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 \cdot 5 (\frac{2 + 8}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 2.2

Add

2

$2$ and

8

$8$ .

\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1 \cdot 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Multiply

- 1

$- 1$ by

1

$1$ .

\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{6 - 1} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 3.2

Subtract

1

$1$ from

6

$6$ .

\frac{10^{2} - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

\frac{10^{2} - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{10^{2} - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Raise

10

$10$ to the power of

2

$2$ .

\frac{100 - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 3 \cdot 5 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.2

Multiply

- 3

$- 3$ by

5

$5$ .

\frac{100 - 15 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 15 (\frac{10}{5} \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.3

Simplify each term.

Tap for more steps...

Step 4.3.1

Divide

10

$10$ by

5

$5$ .

\frac{100 - 15 (2 \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 15 (2 \cdot 4 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.3.2

Multiply

2

$2$ by

4

$4$ .

\frac{100 - 15 (8 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 15 (8 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

\frac{100 - 15 (8 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 15 (8 + 2)}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.4

Add

8

$8$ and

2

$2$ .

\frac{100 - 15 \cdot 10}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 15 \cdot 10}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.5

Multiply

- 15

$- 15$ by

10

$10$ .

\frac{100 - 150}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{100 - 150}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 4.6

Subtract

150

$150$ from

100

$100$ .

\frac{- 50}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

\frac{- 50}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{{(3 + 4 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

Add

3

$3$ and

4

$4$ .

\frac{- 50}{{(7 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{{(7 - 2)}^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.2

Subtract

2

$2$ from

7

$7$ .

\frac{- 50}{5^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{5^{2} - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.3

Raise

5

$5$ to the power of

2

$2$ .

\frac{- 50}{25 - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{25 - 2^{2} (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.4

Raise

2

$2$ to the power of

2

$2$ .

\frac{- 50}{25 - 1 \cdot 4 (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{25 - 1 \cdot 4 (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.5

Multiply

- 1

$- 1$ by

4

$4$ .

\frac{- 50}{25 - 4 (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{25 - 4 (12 \cdot 2 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.6

Simplify each term.

Tap for more steps...

Step 5.6.1

Multiply

12

$12$ by

2

$2$ .

\frac{- 50}{25 - 4 (24 - 4 \cdot 5) \cdot 1^{8}}

$\frac{- 50}{25 - 4 (24 - 4 \cdot 5) \cdot 1^{8}}$

Step 5.6.2

Multiply

- 4

$- 4$ by

5

$5$ .

\frac{- 50}{25 - 4 (24 - 20) \cdot 1^{8}}

$\frac{- 50}{25 - 4 (24 - 20) \cdot 1^{8}}$

\frac{- 50}{25 - 4 (24 - 20) \cdot 1^{8}}

$\frac{- 50}{25 - 4 (24 - 20) \cdot 1^{8}}$

Step 5.7

Subtract

20

$20$ from

24

$24$ .

\frac{- 50}{25 - 4 \cdot 4 \cdot 1^{8}}

$\frac{- 50}{25 - 4 \cdot 4 \cdot 1^{8}}$

Step 5.8

Multiply

- 4

$- 4$ by

4

$4$ .

\frac{- 50}{25 - 16 \cdot 1^{8}}

$\frac{- 50}{25 - 16 \cdot 1^{8}}$

Step 5.9

One to any power is one.

\frac{- 50}{25 - 16 \cdot 1}

$\frac{- 50}{25 - 16 \cdot 1}$

Step 5.10

Multiply

- 16

$- 16$ by

1

$1$ .

\frac{- 50}{25 - 16}

$\frac{- 50}{25 - 16}$

Step 5.11

Subtract

16

$16$ from

25

$25$ .

\frac{- 50}{9}

$\frac{- 50}{9}$

\frac{- 50}{9}

$\frac{- 50}{9}$

Step 6

Move the negative in front of the fraction.

- \frac{50}{9}

$- \frac{50}{9}$

Step 7

The result can be shown in multiple forms.

Exact Form:

- \frac{50}{9}

$- \frac{50}{9}$

Decimal Form:

- 5. ¯ 5

$- 5.\overline{5}$

Mixed Number Form:

- 5 \frac{5}{9}

$- 5 \frac{5}{9}$