What is 5/7 \div (5-1 1/4) ?

The solution to 5/7 \div (5-1 1/4) is 4/21

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Popular >

5/7 \div (5-1 1/4)

Solution

\frac{5}{7} \div (5 - 1 \frac{1}{4})

Solution

\frac{4}{21}

Solution steps

\frac{5}{7} \div (5 - 1 \frac{1}{4})

Convert mixed numbers to improper fractions:

1 \frac{1}{4} = \frac{5}{4}

1 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

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

= \frac{5}{4}

= \frac{5}{7} \div (5 - \frac{5}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(5 - \frac{5}{4}) : \frac{15}{4}

5 - \frac{5}{4}

5 - \frac{5}{4} = \frac{15}{4}

5 - \frac{5}{4}

Convert element to fraction:

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

= \frac{5 \cdot 4}{4} - \frac{5}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 4 - 5}{4}

5 \cdot 4 - 5 = 15

5 \cdot 4 - 5

Multiply the numbers:

5 \cdot 4 = 20

= 20 - 5

Subtract the numbers:

20 - 5 = 15

= 15

= \frac{15}{4}

= \frac{15}{4}

= \frac{5}{7} \div \frac{15}{4}

Multiply and divide (left to right)

\frac{5}{7} \div \frac{15}{4} : \frac{4}{21}

\frac{5}{7} \div \frac{15}{4}

Apply the fraction rule:

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

= \frac{5}{7} \cdot \frac{4}{15}

Cross-cancel common factor:

5

5, 15

Greatest Common Divisor (GCD)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

15 : 3 \cdot 5

15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5

The prime factors common to

5, 15

are

= 5

= \frac{1}{7} \cdot \frac{4}{3}

Multiply fractions:

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

= \frac{1 \cdot 4}{7 \cdot 3}

Multiply the numbers:

1 \cdot 4 = 4

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

Multiply the numbers:

7 \cdot 3 = 21

= \frac{4}{21}

= \frac{4}{21}

Popular Examples

5-(8+3)-6

5 - (8 + 3) - 6

18+3(10/15)

18 + 3 (\frac{10}{15})

1^3-1^2+1-1

1^{3} - 1^{2} + 1 - 1

3-2+(1-7-(5-(2-2)-1)+1)

3 - 2 + (1 - 7 - (5 - (2 - 2) - 1) + 1)

(3+5)^2+(12\div 4)

(3 + 5)^{2} + (12 \div 4)

Frequently Asked Questions (FAQ)

What is 5/7 \div (5-1 1/4) ?
The solution to 5/7 \div (5-1 1/4) is 4/21