What is 3 1/15 \div 4-7/2 ?

The solution to 3 1/15 \div 4-7/2 is -41/15

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Popular >

3 1/15 \div 4-7/2

Solution

3 \frac{1}{15} \div 4 - \frac{7}{2}

Solution

- \frac{41}{15}

Solution steps

3 \frac{1}{15} \div 4 - \frac{7}{2}

Convert mixed numbers to improper fractions:

3 \frac{1}{15} = \frac{46}{15}

3 \frac{1}{15}

Convert mixed numbers to improper fraction:

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

3 \frac{1}{15} = \frac{3 \cdot 15 + 1}{15}

= \frac{46}{15}

= \frac{46}{15} \div 4 - \frac{7}{2}

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{46}{15} \div 4 : \frac{23}{30}

\frac{46}{15} \div 4

Convert element to fraction:

4 = \frac{4}{1}

= \frac{46}{15} \div \frac{4}{1}

Apply the fraction rule:

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

= \frac{46}{15} \cdot \frac{1}{4}

Cross-cancel common factor:

2

46, 4

Greatest Common Divisor (GCD)

Prime factorization of

46 : 2 \cdot 23

46

46

divides by

246 = 23 \cdot 2

= 2 \cdot 23

2, 23

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 23

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

46, 4

are

= 2

= \frac{23}{15} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{23 \cdot 1}{15 \cdot 2}

Multiply the numbers:

23 \cdot 1 = 23

= \frac{23}{15 \cdot 2}

Multiply the numbers:

15 \cdot 2 = 30

= \frac{23}{30}

= \frac{23}{30} - \frac{7}{2}

Add and subtract (left to right)

\frac{23}{30} - \frac{7}{2} : - \frac{41}{15}

\frac{23}{30} - \frac{7}{2}

\frac{23}{30} - \frac{7}{2} = - \frac{41}{15}

\frac{23}{30} - \frac{7}{2}

Least Common Multiplier of

30, 2 : 30

30, 2

Least Common Multiplier (LCM)

Prime factorization of

30 : 2 \cdot 3 \cdot 5

30

30

divides by

230 = 15 \cdot 2

= 2 \cdot 15

15

divides by

315 = 5 \cdot 3

= 2 \cdot 3 \cdot 5

2, 3, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 5

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

30

2

= 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

For

\frac{7}{2} :

multiply the denominator and numerator by

15

\frac{7}{2} = \frac{7 \cdot 15}{2 \cdot 15} = \frac{105}{30}

= \frac{23}{30} - \frac{105}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{23 - 105}{30}

Subtract the numbers:

23 - 105 = - 82

= \frac{- 82}{30}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{82}{30}

Cancel the common factor:

2

= - \frac{41}{15}

= - \frac{41}{15}

= - \frac{41}{15}

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Frequently Asked Questions (FAQ)

What is 3 1/15 \div 4-7/2 ?
The solution to 3 1/15 \div 4-7/2 is -41/15