What is 2+3/9-1 8/4+3/5 ?

The solution to 2+3/9-1 8/4+3/5 is -1/15

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Popular >

2+3/9-1 8/4+3/5

Solution

2 + \frac{3}{9} - 1 \frac{8}{4} + \frac{3}{5}

Solution

- \frac{1}{15}

Solution steps

2 + \frac{3}{9} - 1 \frac{8}{4} + \frac{3}{5}

Convert mixed numbers to improper fractions:

1 \frac{8}{4} = \frac{12}{4}

1 \frac{8}{4}

Convert mixed numbers to improper fraction:

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

1 \frac{8}{4} = \frac{1 \cdot 4 + 8}{4}

= \frac{12}{4}

= 2 + \frac{3}{9} - \frac{12}{4} + \frac{3}{5}

\frac{3}{9} = \frac{1}{3}

Cancel the common factor:

3

\frac{1}{3}

= 2 + \frac{1}{3} - \frac{12}{4} + \frac{3}{5}

\frac{12}{4} = 3

Divide the numbers:

\frac{12}{4} = 3

3

= 2 + \frac{1}{3} - 3 + \frac{3}{5}

Follow the PEMDAS order of operations

Add and subtract (left to right)

2 + \frac{1}{3} - 3 + \frac{3}{5} : - \frac{1}{15}

2 + \frac{1}{3} - 3 + \frac{3}{5}

2 + \frac{1}{3} = \frac{7}{3}

2 + \frac{1}{3}

Convert element to fraction:

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

= \frac{2 \cdot 3}{3} + \frac{1}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{2 \cdot 3 + 1}{3}

2 \cdot 3 + 1 = 7

2 \cdot 3 + 1

Multiply the numbers:

2 \cdot 3 = 6

= 6 + 1

Add the numbers:

6 + 1 = 7

= 7

= \frac{7}{3}

= \frac{7}{3} - 3 + \frac{3}{5}

\frac{7}{3} - 3 = - \frac{2}{3}

\frac{7}{3} - 3

Convert element to fraction:

3 = \frac{3 \cdot 3}{3}

= - \frac{3 \cdot 3}{3} + \frac{7}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 3 \cdot 3 + 7}{3}

- 3 \cdot 3 + 7 = - 2

- 3 \cdot 3 + 7

Multiply the numbers:

3 \cdot 3 = 9

= - 9 + 7

Add/Subtract the numbers:

- 9 + 7 = - 2

= - 2

= \frac{- 2}{3}

Apply the fraction rule:

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

= - \frac{2}{3}

= - \frac{2}{3} + \frac{3}{5}

- \frac{2}{3} + \frac{3}{5} = - \frac{1}{15}

- \frac{2}{3} + \frac{3}{5}

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

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

15

For

\frac{2}{3} :

multiply the denominator and numerator by

5

\frac{2}{3} = \frac{2 \cdot 5}{3 \cdot 5} = \frac{10}{15}

For

\frac{3}{5} :

multiply the denominator and numerator by

3

\frac{3}{5} = \frac{3 \cdot 3}{5 \cdot 3} = \frac{9}{15}

= - \frac{10}{15} + \frac{9}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{- 10 + 9}{15}

Add/Subtract the numbers:

- 10 + 9 = - 1

= \frac{- 1}{15}

Apply the fraction rule:

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

= - \frac{1}{15}

= - \frac{1}{15}

= - \frac{1}{15}

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2^{10}-2^{512}

2^{10} - 2^{512}

2(7)+2(2)

2 (7) + 2 (2)

Frequently Asked Questions (FAQ)

What is 2+3/9-1 8/4+3/5 ?
The solution to 2+3/9-1 8/4+3/5 is -1/15