What is 2-5 1/2 \div 2 14/15 ?

The solution to 2-5 1/2 \div 2 14/15 is 1/8

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Popular >

2-5 1/2 \div 2 14/15

Solution

2 - 5 \frac{1}{2} \div 2 \frac{14}{15}

Solution

\frac{1}{8}

Solution steps

2 - 5 \frac{1}{2} \div 2 \frac{14}{15}

Convert mixed numbers to improper fractions:

5 \frac{1}{2} = \frac{11}{2}

5 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

5 \frac{1}{2} = \frac{5 \cdot 2 + 1}{2}

= \frac{11}{2}

= 2 - \frac{11}{2} \div 2 \frac{14}{15}

Convert mixed numbers to improper fractions:

2 \frac{14}{15} = \frac{44}{15}

2 \frac{14}{15}

Convert mixed numbers to improper fraction:

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

2 \frac{14}{15} = \frac{2 \cdot 15 + 14}{15}

= \frac{44}{15}

= 2 - \frac{11}{2} \div \frac{44}{15}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{11}{2} \div \frac{44}{15} : \frac{15}{8}

\frac{11}{2} \div \frac{44}{15}

Apply the fraction rule:

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

= \frac{11}{2} \cdot \frac{15}{44}

Cross-cancel common factor:

11

11, 44

Greatest Common Divisor (GCD)

Prime factorization of

11 : 11

11

11

is a prime number, therefore no factorization is possible

= 11

Prime factorization of

44 : 2 \cdot 2 \cdot 11

44

44

divides by

244 = 22 \cdot 2

= 2 \cdot 22

22

divides by

222 = 11 \cdot 2

= 2 \cdot 2 \cdot 11

2, 11

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 11

The prime factors common to

11, 44

are

= 11

= \frac{1}{2} \cdot \frac{15}{4}

Multiply fractions:

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

= \frac{1 \cdot 15}{2 \cdot 4}

Multiply the numbers:

1 \cdot 15 = 15

= \frac{15}{2 \cdot 4}

Multiply the numbers:

2 \cdot 4 = 8

= \frac{15}{8}

= 2 - \frac{15}{8}

Add and subtract (left to right)

2 - \frac{15}{8} : \frac{1}{8}

2 - \frac{15}{8}

2 - \frac{15}{8} = \frac{1}{8}

2 - \frac{15}{8}

Convert element to fraction:

2 = \frac{2 \cdot 8}{8}

= \frac{2 \cdot 8}{8} - \frac{15}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 8 - 15}{8}

2 \cdot 8 - 15 = 1

2 \cdot 8 - 15

Multiply the numbers:

2 \cdot 8 = 16

= 16 - 15

Subtract the numbers:

16 - 15 = 1

= 1

= \frac{1}{8}

= \frac{1}{8}

= \frac{1}{8}

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Frequently Asked Questions (FAQ)

What is 2-5 1/2 \div 2 14/15 ?
The solution to 2-5 1/2 \div 2 14/15 is 1/8