What is 1/2 \div (1/4+1/3) ?

The solution to 1/2 \div (1/4+1/3) is 6/7

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Popular >

1/2 \div (1/4+1/3)

Solution

\frac{1}{2} \div (\frac{1}{4} + \frac{1}{3})

Solution

\frac{6}{7}

Solution steps

\frac{1}{2} \div (\frac{1}{4} + \frac{1}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{4} + \frac{1}{3}) : \frac{7}{12}

\frac{1}{4} + \frac{1}{3}

\frac{1}{4} + \frac{1}{3} = \frac{7}{12}

\frac{1}{4} + \frac{1}{3}

Least Common Multiplier of

4, 3 : 12

4, 3

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

4

3

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

For

\frac{1}{4} :

multiply the denominator and numerator by

3

\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}

For

\frac{1}{3} :

multiply the denominator and numerator by

4

\frac{1}{3} = \frac{1 \cdot 4}{3 \cdot 4} = \frac{4}{12}

= \frac{3}{12} + \frac{4}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{3 + 4}{12}

Add the numbers:

3 + 4 = 7

= \frac{7}{12}

= \frac{7}{12}

= \frac{1}{2} \div \frac{7}{12}

Multiply and divide (left to right)

\frac{1}{2} \div \frac{7}{12} : \frac{6}{7}

\frac{1}{2} \div \frac{7}{12}

Apply the fraction rule:

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

= \frac{1}{2} \cdot \frac{12}{7}

Cross-cancel common factor:

2

= \frac{6}{7}

= \frac{6}{7}

Popular Examples

3+2\times 3

3 + 2 \times 3

(-1)^2+1

(- 1)^{2} + 1

4-4\times 4+8

4 - 4 \times 4 + 8

2^2+1^2

2^{2} + 1^{2}

2^{64}-1

2^{64} - 1

Frequently Asked Questions (FAQ)

What is 1/2 \div (1/4+1/3) ?
The solution to 1/2 \div (1/4+1/3) is 6/7