What is (7\div 10-1\div 5)\div 10\div 7 ?

The solution to (7\div 10-1\div 5)\div 10\div 7 is 1/140

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Popular >

(7\div 10-1\div 5)\div 10\div 7

Solution

(7 \div 10 - 1 \div 5) \div 10 \div 7

Solution

\frac{1}{140}

Solution steps

(7 \div 10 - 1 \div 5) \div 10 \div 7

Follow the PEMDAS order of operations

Calculate within parentheses

(7 \div 10 - 1 \div 5) : \frac{1}{2}

7 \div 10 - 1 \div 5

Multiply and divide (left to right)

7 \div 10 : \frac{7}{10}

7 \div 10

7 \div 10 = \frac{7}{10}

= \frac{7}{10}

= \frac{7}{10} - 1 \div 5

Multiply and divide (left to right)

1 \div 5 : \frac{1}{5}

1 \div 5

1 \div 5 = \frac{1}{5}

= \frac{1}{5}

= \frac{7}{10} - \frac{1}{5}

Add and subtract (left to right)

\frac{7}{10} - \frac{1}{5} : \frac{1}{2}

\frac{7}{10} - \frac{1}{5}

\frac{7}{10} - \frac{1}{5} = \frac{1}{2}

\frac{7}{10} - \frac{1}{5}

Least Common Multiplier of

10, 5 : 10

10, 5

Least Common Multiplier (LCM)

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

10

5

= 2 \cdot 5

Multiply the numbers:

2 \cdot 5 = 10

= 10

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

10

For

\frac{1}{5} :

multiply the denominator and numerator by

2

\frac{1}{5} = \frac{1 \cdot 2}{5 \cdot 2} = \frac{2}{10}

= \frac{7}{10} - \frac{2}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{7 - 2}{10}

Subtract the numbers:

7 - 2 = 5

= \frac{5}{10}

Cancel the common factor:

5

= \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2} \div 10 \div 7

Multiply and divide (left to right)

\frac{1}{2} \div 10 \div 7 : \frac{1}{140}

\frac{1}{2} \div 10 \div 7

\frac{1}{2} \div 10 = \frac{1}{20}

\frac{1}{2} \div 10

Convert element to fraction:

10 = \frac{10}{1}

= \frac{1}{2} \div \frac{10}{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}{10}

Multiply fractions:

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

= \frac{1 \cdot 1}{2 \cdot 10}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 10}

Multiply the numbers:

2 \cdot 10 = 20

= \frac{1}{20}

= \frac{1}{20} \div 7

\frac{1}{20} \div 7 = \frac{1}{140}

\frac{1}{20} \div 7

Convert element to fraction:

7 = \frac{7}{1}

= \frac{1}{20} \div \frac{7}{1}

Apply the fraction rule:

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

= \frac{1}{20} \cdot \frac{1}{7}

Multiply fractions:

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

= \frac{1 \cdot 1}{20 \cdot 7}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{20 \cdot 7}

Multiply the numbers:

20 \cdot 7 = 140

= \frac{1}{140}

= \frac{1}{140}

= \frac{1}{140}

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Frequently Asked Questions (FAQ)

What is (7\div 10-1\div 5)\div 10\div 7 ?
The solution to (7\div 10-1\div 5)\div 10\div 7 is 1/140