What is (5/14)/(3/4) ?

The solution to (5/14)/(3/4) is 10/21

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Write the Fraction in Simplest Form (5/14)÷(3/4)

(5/14) / (3/4)

\frac{10}{21}

Solution steps

(5/14) / (3/4)

Follow the PEMDAS order of operations

Calculate within parentheses

(5/14) : \frac{5}{14}

5/14

5/14 = \frac{5}{14}

= \frac{5}{14}

= \frac{5}{14} / (3/4)

Calculate within parentheses

(3/4) : \frac{3}{4}

3/4

3/4 = \frac{3}{4}

= \frac{3}{4}

= \frac{5}{14} / \frac{3}{4}

Multiply and divide (left to right)

\frac{5}{14} / \frac{3}{4} : \frac{10}{21}

\frac{5}{14} / \frac{3}{4}

Apply the fraction rule:

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

= \frac{5}{14} \cdot \frac{4}{3}

Cross-cancel common factor:

2

4, 14

Greatest Common Divisor (GCD)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

14 : 2 \cdot 7

14

14

divides by

214 = 7 \cdot 2

= 2 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 7

The prime factors common to

4, 14

are

= 2

= \frac{5}{7} \cdot \frac{2}{3}

Multiply fractions:

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

= \frac{5 \cdot 2}{7 \cdot 3}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{10}{7 \cdot 3}

Multiply the numbers:

7 \cdot 3 = 21

= \frac{10}{21}

= \frac{10}{21}

180 - 117

\frac{15}{11}

t o a p erce n t a g e 0.196

0.86

\frac{69}{7}