Basic Math Examples

(1 - \frac{1}{5}) (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$(1 - \frac{1}{5}) (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1

Simplify.

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Step 1.1

Write

1

$1$ as a fraction with a common denominator.

(\frac{5}{5} - \frac{1}{5}) (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$(\frac{5}{5} - \frac{1}{5}) (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.2

Combine the numerators over the common denominator.

\frac{5 - 1}{5} (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{5 - 1}{5} (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.3

Subtract

1

$1$ from

5

$5$ .

\frac{4}{5} (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{4}{5} (1 - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.4

Write

1

$1$ as a fraction with a common denominator.

\frac{4}{5} (\frac{6}{6} - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{4}{5} (\frac{6}{6} - \frac{1}{6}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.5

Combine the numerators over the common denominator.

\frac{4}{5} \cdot \frac{6 - 1}{6} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{4}{5} \cdot \frac{6 - 1}{6} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.6

Subtract

1

$1$ from

6

$6$ .

\frac{4}{5} \cdot \frac{5}{6} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{4}{5} \cdot \frac{5}{6} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.7

Cancel the common factor of

2

$2$ .

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Step 1.7.1

Factor

2

$2$ out of

4

$4$ .

\frac{2 (2)}{5} \cdot \frac{5}{6} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2 (2)}{5} \cdot \frac{5}{6} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.7.2

Factor

2

$2$ out of

6

$6$ .

\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.7.3

Cancel the common factor.

\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2 \cdot 2}{5} \cdot \frac{5}{2 \cdot 3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.7.4

Rewrite the expression.

\frac{2}{5} \cdot \frac{5}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{5} \cdot \frac{5}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

\frac{2}{5} \cdot \frac{5}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{5} \cdot \frac{5}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.8

Cancel the common factor of

5

$5$ .

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Step 1.8.1

Cancel the common factor.

\frac{2}{5} \cdot \frac{5}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{5} \cdot \frac{5}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.8.2

Rewrite the expression.

2 (\frac{1}{3}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$2 (\frac{1}{3}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

2 (\frac{1}{3}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$2 (\frac{1}{3}) (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.9

Combine

2

$2$ and

\frac{1}{3}

$\frac{1}{3}$ .

\frac{2}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{3} (1 - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.10

Write

1

$1$ as a fraction with a common denominator.

\frac{2}{3} (\frac{7}{7} - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{3} (\frac{7}{7} - \frac{1}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.11

Combine the numerators over the common denominator.

\frac{2}{3} \cdot \frac{7 - 1}{7} (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{3} \cdot \frac{7 - 1}{7} (1 - \frac{1}{8}) y^{2} = 0$

Step 1.12

Subtract

1

$1$ from

7

$7$ .

\frac{2}{3} \cdot \frac{6}{7} (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{3} \cdot \frac{6}{7} (1 - \frac{1}{8}) y^{2} = 0$

Step 1.13

Cancel the common factor of

3

$3$ .

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Step 1.13.1

Factor

3

$3$ out of

6

$6$ .

\frac{2}{3} \cdot \frac{3 (2)}{7} (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{3} \cdot \frac{3 (2)}{7} (1 - \frac{1}{8}) y^{2} = 0$

Step 1.13.2

Cancel the common factor.

\frac{2}{3} \cdot \frac{3 \cdot 2}{7} (1 - \frac{1}{8}) y^{2} = 0

$\frac{2}{3} \cdot \frac{3 \cdot 2}{7} (1 - \frac{1}{8}) y^{2} = 0$

Step 1.13.3

Rewrite the expression.

2 (\frac{2}{7}) (1 - \frac{1}{8}) y^{2} = 0

$2 (\frac{2}{7}) (1 - \frac{1}{8}) y^{2} = 0$

2 (\frac{2}{7}) (1 - \frac{1}{8}) y^{2} = 0

$2 (\frac{2}{7}) (1 - \frac{1}{8}) y^{2} = 0$

Step 1.14

Combine

2

$2$ and

\frac{2}{7}

$\frac{2}{7}$ .

\frac{2 \cdot 2}{7} (1 - \frac{1}{8}) y^{2} = 0

$\frac{2 \cdot 2}{7} (1 - \frac{1}{8}) y^{2} = 0$

Step 1.15

Multiply

2

$2$ by

2

$2$ .

\frac{4}{7} (1 - \frac{1}{8}) y^{2} = 0

$\frac{4}{7} (1 - \frac{1}{8}) y^{2} = 0$

Step 1.16

Write

1

$1$ as a fraction with a common denominator.

\frac{4}{7} (\frac{8}{8} - \frac{1}{8}) y^{2} = 0

$\frac{4}{7} (\frac{8}{8} - \frac{1}{8}) y^{2} = 0$

Step 1.17

Combine the numerators over the common denominator.

\frac{4}{7} \cdot \frac{8 - 1}{8} y^{2} = 0

$\frac{4}{7} \cdot \frac{8 - 1}{8} y^{2} = 0$

Step 1.18

Subtract

1

$1$ from

8

$8$ .

\frac{4}{7} \cdot \frac{7}{8} y^{2} = 0

$\frac{4}{7} \cdot \frac{7}{8} y^{2} = 0$

Step 1.19

Cancel the common factor of

4

$4$ .

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Step 1.19.1

Factor

4

$4$ out of

8

$8$ .

\frac{4}{7} \cdot \frac{7}{4 (2)} y^{2} = 0

$\frac{4}{7} \cdot \frac{7}{4 (2)} y^{2} = 0$

Step 1.19.2

Cancel the common factor.

\frac{4}{7} \cdot \frac{7}{4 \cdot 2} y^{2} = 0

$\frac{4}{7} \cdot \frac{7}{4 \cdot 2} y^{2} = 0$

Step 1.19.3

Rewrite the expression.

\frac{1}{7} \cdot \frac{7}{2} y^{2} = 0

$\frac{1}{7} \cdot \frac{7}{2} y^{2} = 0$

\frac{1}{7} \cdot \frac{7}{2} y^{2} = 0

$\frac{1}{7} \cdot \frac{7}{2} y^{2} = 0$

Step 1.20

Cancel the common factor of

7

$7$ .

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Step 1.20.1

Cancel the common factor.

\frac{1}{7} \cdot \frac{7}{2} y^{2} = 0

$\frac{1}{7} \cdot \frac{7}{2} y^{2} = 0$

Step 1.20.2

Rewrite the expression.

\frac{1}{2} y^{2} = 0

$\frac{1}{2} y^{2} = 0$

\frac{1}{2} y^{2} = 0

$\frac{1}{2} y^{2} = 0$

\frac{1}{2} y^{2} = 0

$\frac{1}{2} y^{2} = 0$

Step 2

Multiply each term in

\frac{1}{2} y^{2} = 0

$\frac{1}{2} y^{2} = 0$ by

2

$2$ to eliminate the fractions.

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Step 2.1

Multiply each term in

\frac{1}{2} y^{2} = 0

$\frac{1}{2} y^{2} = 0$ by

2

$2$ .

\frac{1}{2} y^{2} \cdot 2 = 0 \cdot 2

$\frac{1}{2} y^{2} \cdot 2 = 0 \cdot 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

Combine

\frac{1}{2}

$\frac{1}{2}$ and

y^{2}

$y^{2}$ .

\frac{y^{2}}{2} \cdot 2 = 0 \cdot 2

$\frac{y^{2}}{2} \cdot 2 = 0 \cdot 2$

Step 2.2.2

Cancel the common factor of

2

$2$ .

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Step 2.2.2.1

Cancel the common factor.

\frac{y^{2}}{2} \cdot 2 = 0 \cdot 2

$\frac{y^{2}}{2} \cdot 2 = 0 \cdot 2$

Step 2.2.2.2

Rewrite the expression.

y^{2} = 0 \cdot 2

$y^{2} = 0 \cdot 2$

y^{2} = 0 \cdot 2

$y^{2} = 0 \cdot 2$

y^{2} = 0 \cdot 2

$y^{2} = 0 \cdot 2$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply

0

$0$ by

2

$2$ .

y^{2} = 0

$y^{2} = 0$

y^{2} = 0

$y^{2} = 0$

y^{2} = 0

$y^{2} = 0$

Step 3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

y = \pm \sqrt{0}

$y = \pm \sqrt{0}$

Step 4

Simplify

\pm \sqrt{0}

$\pm \sqrt{0}$ .

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Step 4.1

Rewrite

0

$0$ as

0^{2}

$0^{2}$ .

y = \pm \sqrt{0^{2}}

$y = \pm \sqrt{0^{2}}$

Step 4.2

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

y = \pm 0

$y = \pm 0$

Step 4.3

Plus or minus

0

$0$ is

0

$0$ .

y = 0

$y = 0$

y = 0

$y = 0$