What is 1-(1-5%)(1-6%) ?

The solution to 1-(1-5%)(1-6%) is 107/1000

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Popular >

simplify 1-(1-5%)(1-6%)

Solution

simplify

1 - (1 - 5%) (1 - 6%)

Solution

\frac{107}{1000}

Decimal Notation

0.107

Solution steps

1 - (1 - 5%) (1 - 6%)

(1 - 5%) (1 - 6%) = \frac{19}{20} \cdot \frac{47}{50}

(1 - 5%) (1 - 6%)

1 - 5% = \frac{19}{20}

1 - 5%

= 1 - 5% \cdot 1

5% \cdot 1 = \frac{1}{20}

5% \cdot 1

Convert

5%

into a fraction:

\frac{5}{100}

5%

Rewrite

5%

\frac{5}{100}

= \frac{5}{100}

= \frac{5}{100} \cdot 1

\frac{5}{100} \cdot 1 = \frac{1}{20}

\frac{5}{100} \cdot 1

Multiply the numbers:

\frac{5}{100} \cdot 1 = \frac{5}{100}

= \frac{5}{100}

Cancel the numbers:

\frac{5}{100} = \frac{1}{20}

= \frac{1}{20}

= \frac{1}{20}

= 1 - \frac{1}{20}

1 - \frac{1}{20} = \frac{19}{20}

1 - \frac{1}{20}

Convert

1

to fraction

: \frac{20}{20}

1

Apply the fraction rule:

a = \frac{ab}{b}

= \frac{1 \cdot 20}{20}

Multiply the numbers:

1 \cdot 20 = 20

= \frac{20}{20}

= \frac{20}{20} - \frac{1}{20}

\frac{20}{20} - \frac{1}{20} = \frac{19}{20}

\frac{20}{20} - \frac{1}{20}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{20 - 1}{20}

Subtract the numbers:

20 - 1 = 19

= \frac{19}{20}

= \frac{19}{20}

= \frac{19}{20}

= \frac{19}{20} (1 - 6%)

= \frac{19}{20} (1 - 6% \cdot 1)

6% \cdot 1 = \frac{3}{50}

6% \cdot 1

Convert

6%

into a fraction:

\frac{6}{100}

6%

Rewrite

6%

\frac{6}{100}

= \frac{6}{100}

= \frac{6}{100} \cdot 1

\frac{6}{100} \cdot 1 = \frac{3}{50}

\frac{6}{100} \cdot 1

Multiply the numbers:

\frac{6}{100} \cdot 1 = \frac{6}{100}

= \frac{6}{100}

Cancel

\frac{6}{100} : \frac{3}{50}

\frac{6}{100}

Factor the number:

6 = 2 \cdot 3

= \frac{2 \cdot 3}{100}

Factor the number:

100 = 2 \cdot 50

= \frac{2 \cdot 3}{2 \cdot 50}

Cancel the common factor:

2

= \frac{3}{50}

= \frac{3}{50}

= \frac{3}{50}

= \frac{19}{20} (1 - \frac{3}{50})

1 - \frac{3}{50} = \frac{47}{50}

1 - \frac{3}{50}

Convert

1

to fraction

: \frac{50}{50}

1

Apply the fraction rule:

a = \frac{ab}{b}

= \frac{1 \cdot 50}{50}

Multiply the numbers:

1 \cdot 50 = 50

= \frac{50}{50}

= \frac{50}{50} - \frac{3}{50}

\frac{50}{50} - \frac{3}{50} = \frac{47}{50}

\frac{50}{50} - \frac{3}{50}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{50 - 3}{50}

Subtract the numbers:

50 - 3 = 47

= \frac{47}{50}

= \frac{47}{50}

= \frac{19}{20} \cdot \frac{47}{50}

= 1 - \frac{19}{20} \cdot \frac{47}{50}

\frac{19}{20} \cdot \frac{47}{50} = \frac{893}{1000}

\frac{19}{20} \cdot \frac{47}{50}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{19 \cdot 47}{20 \cdot 50}

Multiply the numbers:

19 \cdot 47 = 893

= \frac{893}{20 \cdot 50}

Multiply the numbers:

20 \cdot 50 = 1000

= \frac{893}{1000}

= 1 - \frac{893}{1000}

1 - \frac{893}{1000} = \frac{107}{1000}

1 - \frac{893}{1000}

Convert

1

to fraction

: \frac{1000}{1000}

1

Apply the fraction rule:

a = \frac{ab}{b}

= \frac{1 \cdot 1000}{1000}

Multiply the numbers:

1 \cdot 1000 = 1000

= \frac{1000}{1000}

= \frac{1000}{1000} - \frac{893}{1000}

\frac{1000}{1000} - \frac{893}{1000} = \frac{107}{1000}

\frac{1000}{1000} - \frac{893}{1000}

Apply the fraction rule:

\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

= \frac{1000 - 893}{1000}

Subtract the numbers:

1000 - 893 = 107

= \frac{107}{1000}

= \frac{107}{1000}

= \frac{107}{1000}

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Frequently Asked Questions (FAQ)

What is 1-(1-5%)(1-6%) ?
The solution to 1-(1-5%)(1-6%) is 107/1000