What is 3/2 (6)-3+5/3 (3) ?

The solution to 3/2 (6)-3+5/3 (3) is 11

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3/2 (6)-3+5/3 (3)

\frac{3}{2} (6) - 3 + \frac{5}{3} (3)

11

Solution steps

\frac{3}{2} (6) - 3 + \frac{5}{3} (3)

Follow the PEMDAS order of operations

Multiply and divide (left to right)

\frac{3}{2} (6) : 9

\frac{3}{2} (6)

Apply rule:

(a) = a

(6) = 6

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

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

\frac{3}{2} \cdot 6

Convert element to fraction:

6 = \frac{6}{1}

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

Apply the fraction rule:

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

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

Cancel

\frac{3 \cdot 6}{2 \cdot 1} : 9

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

Multiply the numbers:

2 \cdot 1 = 2

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

Divide the numbers:

\frac{6}{2} = 3

= 3 \cdot 3

Multiply the numbers:

3 \cdot 3 = 9

= 9

= 9

= 9

= 9 - 3 + \frac{5}{3} (3)

Multiply and divide (left to right)

\frac{5}{3} (3) : 5

\frac{5}{3} (3)

Apply rule:

(a) = a

(3) = 3

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

Convert element to fraction:

3 = \frac{3}{1}

= \frac{5}{3} \cdot \frac{3}{1}

Cross-cancel common factor:

3

= \frac{5}{1}

Divide the numbers:

\frac{5}{1} = 5

= 5

= 9 - 3 + 5

Add and subtract (left to right)

9 - 3 + 5 : 11

9 - 3 + 5

9 - 3 = 6

= 6 + 5

6 + 5 = 11

= 11

= 11

\frac{4 ^{2} - 16}{4 - 4}

\frac{1}{2} (4 \cdot 5) - 2^{3}

2^{0} + 3

\frac{1}{4} (6 + 3 + 1)^{2}

5 (3) + (- 7) (- 2)^{2}