What is 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 ?

The solution to 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 is -495/196

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3\div 7+5\div 14-3\div 49+1\div 4-7\div 2

Solution

3 \div 7 + 5 \div 14 - 3 \div 49 + 1 \div 4 - 7 \div 2

Solution

- \frac{495}{196}

Solution steps

3 \div 7 + 5 \div 14 - 3 \div 49 + 1 \div 4 - 7 \div 2

Follow the PEMDAS order of operations

Multiply and divide (left to right)

3 \div 7 : \frac{3}{7}

3 \div 7

3 \div 7 = \frac{3}{7}

= \frac{3}{7}

= \frac{3}{7} + 5 \div 14 - 3 \div 49 + 1 \div 4 - 7 \div 2

Multiply and divide (left to right)

5 \div 14 : \frac{5}{14}

5 \div 14

5 \div 14 = \frac{5}{14}

= \frac{5}{14}

= \frac{3}{7} + \frac{5}{14} - 3 \div 49 + 1 \div 4 - 7 \div 2

Multiply and divide (left to right)

3 \div 49 : \frac{3}{49}

3 \div 49

3 \div 49 = \frac{3}{49}

= \frac{3}{49}

= \frac{3}{7} + \frac{5}{14} - \frac{3}{49} + 1 \div 4 - 7 \div 2

Multiply and divide (left to right)

1 \div 4 : \frac{1}{4}

1 \div 4

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

= \frac{1}{4}

= \frac{3}{7} + \frac{5}{14} - \frac{3}{49} + \frac{1}{4} - 7 \div 2

Multiply and divide (left to right)

7 \div 2 : \frac{7}{2}

7 \div 2

7 \div 2 = \frac{7}{2}

= \frac{7}{2}

= \frac{3}{7} + \frac{5}{14} - \frac{3}{49} + \frac{1}{4} - \frac{7}{2}

Add and subtract (left to right)

\frac{3}{7} + \frac{5}{14} - \frac{3}{49} + \frac{1}{4} - \frac{7}{2} : - \frac{495}{196}

\frac{3}{7} + \frac{5}{14} - \frac{3}{49} + \frac{1}{4} - \frac{7}{2}

\frac{3}{7} + \frac{5}{14} = \frac{11}{14}

\frac{3}{7} + \frac{5}{14}

Least Common Multiplier of

7, 14 : 14

7, 14

Least Common Multiplier (LCM)

Prime factorization of

7 : 7

7

7

is a prime number, therefore no factorization is possible

= 7

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

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

7

14

= 7 \cdot 2

Multiply the numbers:

7 \cdot 2 = 14

= 14

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

14

For

\frac{3}{7} :

multiply the denominator and numerator by

2

\frac{3}{7} = \frac{3 \cdot 2}{7 \cdot 2} = \frac{6}{14}

= \frac{6}{14} + \frac{5}{14}

Since the denominators are equal, combine the fractions:

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

= \frac{6 + 5}{14}

Add the numbers:

6 + 5 = 11

= \frac{11}{14}

= \frac{11}{14} - \frac{3}{49} + \frac{1}{4} - \frac{7}{2}

\frac{11}{14} - \frac{3}{49} = \frac{71}{98}

\frac{11}{14} - \frac{3}{49}

Least Common Multiplier of

14, 49 : 98

14, 49

Least Common Multiplier (LCM)

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

Prime factorization of

49 : 7 \cdot 7

49

49

divides by

749 = 7 \cdot 7

= 7 \cdot 7

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

14

49

= 2 \cdot 7 \cdot 7

Multiply the numbers:

2 \cdot 7 \cdot 7 = 98

= 98

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

98

For

\frac{11}{14} :

multiply the denominator and numerator by

7

\frac{11}{14} = \frac{11 \cdot 7}{14 \cdot 7} = \frac{77}{98}

For

\frac{3}{49} :

multiply the denominator and numerator by

2

\frac{3}{49} = \frac{3 \cdot 2}{49 \cdot 2} = \frac{6}{98}

= \frac{77}{98} - \frac{6}{98}

Since the denominators are equal, combine the fractions:

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

= \frac{77 - 6}{98}

Subtract the numbers:

77 - 6 = 71

= \frac{71}{98}

= \frac{71}{98} + \frac{1}{4} - \frac{7}{2}

\frac{71}{98} + \frac{1}{4} = \frac{191}{196}

\frac{71}{98} + \frac{1}{4}

Least Common Multiplier of

98, 4 : 196

98, 4

Least Common Multiplier (LCM)

Prime factorization of

98 : 2 \cdot 7 \cdot 7

98

98

divides by

298 = 49 \cdot 2

= 2 \cdot 49

49

divides by

749 = 7 \cdot 7

= 2 \cdot 7 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 7 \cdot 7

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

98

4

= 2 \cdot 2 \cdot 7 \cdot 7

Multiply the numbers:

2 \cdot 2 \cdot 7 \cdot 7 = 196

= 196

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

196

For

\frac{71}{98} :

multiply the denominator and numerator by

2

\frac{71}{98} = \frac{71 \cdot 2}{98 \cdot 2} = \frac{142}{196}

For

\frac{1}{4} :

multiply the denominator and numerator by

49

\frac{1}{4} = \frac{1 \cdot 49}{4 \cdot 49} = \frac{49}{196}

= \frac{142}{196} + \frac{49}{196}

Since the denominators are equal, combine the fractions:

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

= \frac{142 + 49}{196}

Add the numbers:

142 + 49 = 191

= \frac{191}{196}

= \frac{191}{196} - \frac{7}{2}

\frac{191}{196} - \frac{7}{2} = - \frac{495}{196}

\frac{191}{196} - \frac{7}{2}

Least Common Multiplier of

196, 2 : 196

196, 2

Least Common Multiplier (LCM)

Prime factorization of

196 : 2 \cdot 2 \cdot 7 \cdot 7

196

196

divides by

2196 = 98 \cdot 2

= 2 \cdot 98

98

divides by

298 = 49 \cdot 2

= 2 \cdot 2 \cdot 49

49

divides by

749 = 7 \cdot 7

= 2 \cdot 2 \cdot 7 \cdot 7

2, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 7 \cdot 7

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

196

2

= 2 \cdot 2 \cdot 7 \cdot 7

Multiply the numbers:

2 \cdot 2 \cdot 7 \cdot 7 = 196

= 196

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

196

For

\frac{7}{2} :

multiply the denominator and numerator by

98

\frac{7}{2} = \frac{7 \cdot 98}{2 \cdot 98} = \frac{686}{196}

= \frac{191}{196} - \frac{686}{196}

Since the denominators are equal, combine the fractions:

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

= \frac{191 - 686}{196}

Subtract the numbers:

191 - 686 = - 495

= \frac{- 495}{196}

Apply the fraction rule:

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

= - \frac{495}{196}

= - \frac{495}{196}

= - \frac{495}{196}

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Frequently Asked Questions (FAQ)

What is 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 ?
The solution to 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 is -495/196

3\div 7+5\div 14-3\div 49+1\div 4-7\div 2

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 3\div 7+5\div 14-3\div 49+1\div 4-7\div 2 ?

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