What is -3+4/3-(-3/2) ?

The solution to -3+4/3-(-3/2) is -1/6

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-3+4/3-(-3/2)

- 3 + \frac{4}{3} - (- \frac{3}{2})

- \frac{1}{6}

Solution steps

- 3 + \frac{4}{3} - (- \frac{3}{2})

Follow the PEMDAS order of operations

Add and subtract (left to right)

- 3 + \frac{4}{3} = - \frac{5}{3}

= - \frac{5}{3} - (- \frac{3}{2})

Apply rule

- (- a) = + a

- (- \frac{3}{2}) = + \frac{3}{2}

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

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

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

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 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

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 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{5}{3} :

multiply the denominator and numerator by

2

\frac{5}{3} = \frac{5 \cdot 2}{3 \cdot 2} = \frac{10}{6}

For

\frac{3}{2} :

multiply the denominator and numerator by

3

\frac{3}{2} = \frac{3 \cdot 3}{2 \cdot 3} = \frac{9}{6}

= - \frac{10}{6} + \frac{9}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 10 + 9}{6}

Add/Subtract the numbers:

- 10 + 9 = - 1

= \frac{- 1}{6}

Apply the fraction rule:

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

= - \frac{1}{6}

= - \frac{1}{6}

2 (5)^{2} - 3 (5) + 5

(0)^{2} + 4 (0) + 3

2 \times 3 + 5^{2} - 2^{3}

4 \div 2 (3 + 1)

\frac{2 ( - 2 ) ^{2} - 1}{( - 2 ) ^{2}}