What is 3\div (6/7-3/4) ?

The solution to 3\div (6/7-3/4) is 28

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Popular >

3\div (6/7-3/4)

Solution

3 \div (\frac{6}{7} - \frac{3}{4})

Solution

28

Solution steps

3 \div (\frac{6}{7} - \frac{3}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{6}{7} - \frac{3}{4}) : \frac{3}{28}

\frac{6}{7} - \frac{3}{4}

\frac{6}{7} - \frac{3}{4} = \frac{3}{28}

\frac{6}{7} - \frac{3}{4}

Least Common Multiplier of

7, 4 : 28

7, 4

Least Common Multiplier (LCM)

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

7

4

= 7 \cdot 2 \cdot 2

Multiply the numbers:

7 \cdot 2 \cdot 2 = 28

= 28

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

28

For

\frac{6}{7} :

multiply the denominator and numerator by

4

\frac{6}{7} = \frac{6 \cdot 4}{7 \cdot 4} = \frac{24}{28}

For

\frac{3}{4} :

multiply the denominator and numerator by

7

\frac{3}{4} = \frac{3 \cdot 7}{4 \cdot 7} = \frac{21}{28}

= \frac{24}{28} - \frac{21}{28}

Since the denominators are equal, combine the fractions:

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

= \frac{24 - 21}{28}

Subtract the numbers:

24 - 21 = 3

= \frac{3}{28}

= \frac{3}{28}

= 3 \div \frac{3}{28}

Multiply and divide (left to right)

3 \div \frac{3}{28} : 28

3 \div \frac{3}{28}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \div \frac{3}{28}

Apply the fraction rule:

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

= \frac{3}{1} \cdot \frac{28}{3}

Cross-cancel:

3

= \frac{28}{1}

Apply the fraction rule:

\frac{a}{1} = a

= 28

= 28

Popular Examples

-(3+1)^2

- (3 + 1)^{2}

32\div 8+13-2\times 9

32 \div 8 + 13 - 2 \times 9

12-[1-(-22+57)]

12 - [1 - (- 22 + 57)]

70-2+4

70 - 2 + 4

4\times 2(3+6)/3

4 \times 2 (3 + 6) /3

Frequently Asked Questions (FAQ)

What is 3\div (6/7-3/4) ?
The solution to 3\div (6/7-3/4) is 28