What is 5/6-1/2+2-1/3 ?

The solution to 5/6-1/2+2-1/3 is 2

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5/6-1/2+2-1/3

Solution

\frac{5}{6} - \frac{1}{2} + 2 - \frac{1}{3}

Solution

2

Solution steps

\frac{5}{6} - \frac{1}{2} + 2 - \frac{1}{3}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{5}{6} - \frac{1}{2} = \frac{1}{3}

\frac{5}{6} - \frac{1}{2}

Least Common Multiplier of

6, 2 : 6

6, 2

Least Common Multiplier (LCM)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

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

6

2

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

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

6

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= \frac{5}{6} - \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{5 - 3}{6}

Subtract the numbers:

5 - 3 = 2

= \frac{2}{6}

Cancel the common factor:

2

= \frac{1}{3}

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

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

\frac{1}{3} + 2

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} - \frac{1}{3}

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

\frac{7}{3} - \frac{1}{3}

Apply rule

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

= \frac{7 - 1}{3}

Subtract the numbers:

7 - 1 = 6

= \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2

= 2

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3(-4)^2

3 (- 4)^{2}

2-2× 3+3

2 - 2 \times 3 + 3

Frequently Asked Questions (FAQ)

What is 5/6-1/2+2-1/3 ?
The solution to 5/6-1/2+2-1/3 is 2

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