What is 1× (1\div 2)-(1\div 2)\div 1000 ?

The solution to 1× (1\div 2)-(1\div 2)\div 1000 is 999/2000

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Pre Algebra >

1× (1\div 2)-(1\div 2)\div 1000

Solution

1 \times (1 \div 2) - (1 \div 2) \div 1000

Solution

\frac{999}{2000}

Decimal

0.4995

Solution steps

1 \times (1 \div 2) - (1 \div 2) \div 1000

Follow the PEMDAS order of operations

Calculate within parentheses

(1 \div 2) : \frac{1}{2}

1 \div 2

1 \div 2 = \frac{1}{2}

= \frac{1}{2}

= 1 \times \frac{1}{2} - (1 \div 2) \div 1000

Calculate within parentheses

(1 \div 2) : \frac{1}{2}

1 \div 2

1 \div 2 = \frac{1}{2}

= \frac{1}{2}

= 1 \times \frac{1}{2} - \frac{1}{2} \div 1000

Multiply and divide (left to right)

1 \times \frac{1}{2} : \frac{1}{2}

1 \times \frac{1}{2}

1 \times \frac{1}{2} = \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2} - \frac{1}{2} \div 1000

Multiply and divide (left to right)

\frac{1}{2} \div 1000 : \frac{1}{2000}

\frac{1}{2} \div 1000

Convert element to fraction:

1000 = \frac{1000}{1}

= \frac{1}{2} \div \frac{1000}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{1}{2} \cdot \frac{1}{1000}

Multiply fractions:

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

= \frac{1 \cdot 1}{2 \cdot 1000}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 1000}

Multiply the numbers:

2 \cdot 1000 = 2000

= \frac{1}{2000}

= \frac{1}{2} - \frac{1}{2000}

Add and subtract (left to right)

\frac{1}{2} - \frac{1}{2000} : \frac{999}{2000}

\frac{1}{2} - \frac{1}{2000}

\frac{1}{2} - \frac{1}{2000} = \frac{999}{2000}

\frac{1}{2} - \frac{1}{2000}

Least Common Multiplier of

2, 2000 : 2000

2, 2000

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

2000 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

2000

2000

divides by

22000 = 1000 \cdot 2

= 2 \cdot 1000

1000

divides by

21000 = 500 \cdot 2

= 2 \cdot 2 \cdot 500

500

divides by

2500 = 250 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 250

250

divides by

2250 = 125 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 125

125

divides by

5125 = 25 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 25

25

divides by

525 = 5 \cdot 5

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

Multiply each factor the greatest number of times it occurs in either

2

2000

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5 = 2000

= 2000

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

2000

For

\frac{1}{2} :

multiply the denominator and numerator by

1000

\frac{1}{2} = \frac{1 \cdot 1000}{2 \cdot 1000} = \frac{1000}{2000}

= \frac{1000}{2000} - \frac{1}{2000}

Since the denominators are equal, combine the fractions:

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

= \frac{1000 - 1}{2000}

Subtract the numbers:

1000 - 1 = 999

= \frac{999}{2000}

= \frac{999}{2000}

= \frac{999}{2000}

Popular Examples

Frequently Asked Questions (FAQ)

What is 1× (1\div 2)-(1\div 2)\div 1000 ?
The solution to 1× (1\div 2)-(1\div 2)\div 1000 is 999/2000

1× (1\div 2)-(1\div 2)\div 1000

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 1× (1\div 2)-(1\div 2)\div 1000 ?

Popular topics