What is (7+3 1/8)\div (14+6 1/4) ?

The solution to (7+3 1/8)\div (14+6 1/4) is 1/2

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(7+3 1/8)\div (14+6 1/4)

(7 + 3 \frac{1}{8}) \div (14 + 6 \frac{1}{4})

\frac{1}{2}

Solution steps

(7 + 3 \frac{1}{8}) \div (14 + 6 \frac{1}{4})

Convert mixed numbers to improper fractions:

3 \frac{1}{8} = \frac{25}{8}

3 \frac{1}{8}

Convert mixed numbers to improper fraction:

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

3 \frac{1}{8} = \frac{3 \cdot 8 + 1}{8}

= \frac{25}{8}

= (7 + \frac{25}{8}) \div (14 + 6 \frac{1}{4})

Convert mixed numbers to improper fractions:

6 \frac{1}{4} = \frac{25}{4}

6 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

6 \frac{1}{4} = \frac{6 \cdot 4 + 1}{4}

= \frac{25}{4}

= (7 + \frac{25}{8}) \div (14 + \frac{25}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(7 + \frac{25}{8}) : \frac{81}{8}

7 + \frac{25}{8}

7 + \frac{25}{8} = \frac{81}{8}

7 + \frac{25}{8}

Convert element to fraction:

7 = \frac{7 \cdot 8}{8}

= \frac{7 \cdot 8}{8} + \frac{25}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{7 \cdot 8 + 25}{8}

7 \cdot 8 + 25 = 81

7 \cdot 8 + 25

Multiply the numbers:

7 \cdot 8 = 56

= 56 + 25

Add the numbers:

56 + 25 = 81

= 81

= \frac{81}{8}

= \frac{81}{8}

= \frac{81}{8} \div (14 + \frac{25}{4})

Calculate within parentheses

(14 + \frac{25}{4}) : \frac{81}{4}

14 + \frac{25}{4}

14 + \frac{25}{4} = \frac{81}{4}

14 + \frac{25}{4}

Convert element to fraction:

14 = \frac{14 \cdot 4}{4}

= \frac{14 \cdot 4}{4} + \frac{25}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{14 \cdot 4 + 25}{4}

14 \cdot 4 + 25 = 81

14 \cdot 4 + 25

Multiply the numbers:

14 \cdot 4 = 56

= 56 + 25

Add the numbers:

56 + 25 = 81

= 81

= \frac{81}{4}

= \frac{81}{4}

= \frac{81}{8} \div \frac{81}{4}

Multiply and divide (left to right)

\frac{81}{8} \div \frac{81}{4} : \frac{1}{2}

\frac{81}{8} \div \frac{81}{4}

Apply the fraction rule:

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

= \frac{81}{8} \cdot \frac{4}{81}

Multiply fractions:

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

= \frac{81 \cdot 4}{8 \cdot 81}

Cancel the common factor:

81

= \frac{4}{8}

Cancel the common factor:

4

= \frac{1}{2}

= \frac{1}{2}

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What is (7+3 1/8)\div (14+6 1/4) ?
The solution to (7+3 1/8)\div (14+6 1/4) is 1/2