What is (6-5/2)(3+8/3) ?

The solution to (6-5/2)(3+8/3) is 19 5/6

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Popular >

(6-5/2)(3+8/3)

Solution

(6 - \frac{5}{2}) (3 + \frac{8}{3})

Solution

19 \frac{5}{6}

Solution steps

(6 - \frac{5}{2}) (3 + \frac{8}{3})

Follow the PEMDAS order of operations

Calculate within parentheses

(6 - \frac{5}{2}) : \frac{7}{2}

6 - \frac{5}{2}

6 - \frac{5}{2} = \frac{7}{2}

6 - \frac{5}{2}

Convert element to fraction:

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

= \frac{6 \cdot 2}{2} - \frac{5}{2}

Since the denominators are equal, combine the fractions:

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

= \frac{6 \cdot 2 - 5}{2}

6 \cdot 2 - 5 = 7

6 \cdot 2 - 5

Multiply the numbers:

6 \cdot 2 = 12

= 12 - 5

Subtract the numbers:

12 - 5 = 7

= 7

= \frac{7}{2}

= \frac{7}{2}

= \frac{7}{2} (3 + \frac{8}{3})

Calculate within parentheses

(3 + \frac{8}{3}) : \frac{17}{3}

3 + \frac{8}{3}

3 + \frac{8}{3} = \frac{17}{3}

3 + \frac{8}{3}

Convert element to fraction:

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

= \frac{3 \cdot 3}{3} + \frac{8}{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 + 8}{3}

3 \cdot 3 + 8 = 17

3 \cdot 3 + 8

Multiply the numbers:

3 \cdot 3 = 9

= 9 + 8

Add the numbers:

9 + 8 = 17

= 17

= \frac{17}{3}

= \frac{17}{3}

= \frac{7}{2} \cdot \frac{17}{3}

Multiply and divide (left to right)

\frac{7}{2} \cdot \frac{17}{3} : \frac{119}{6}

\frac{7}{2} \cdot \frac{17}{3}

Apply the fraction rule:

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

= \frac{7 \cdot 17}{2 \cdot 3}

Multiply the numbers:

7 \cdot 17 = 119

= \frac{119}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{119}{6}

= \frac{119}{6}

Convert improper fractions to mixed numbers:

\frac{119}{6} = 19 \frac{5}{6}

\frac{119}{6} = 19

Remainder

5

\frac{119}{6}

Write the problem in long division format

6 \overline{∣ 119}

Divide

11

6

to get

1

Divide

11

6

to get

1

1 6 \overline{∣ 119}

Multiply the quotient digit

(1)

by the divisor

6

1 6 \overline{∣ 119} \underline{6}

Subtract

6

from

11

1 6 \overline{∣ 119} \underline{6} 5

Bring down the next number of the dividend

1 6 \overline{∣ 119} \underline{6} 59

1 6 \overline{∣ 119} \underline{6} 59

Divide

59

6

to get

9

Divide

59

6

to get

9

19 6 \overline{∣ 119} \underline{6} 59

Multiply the quotient digit

(9)

by the divisor

6

19 6 \overline{∣ 119} \underline{6} 59 \underline{54}

Subtract

54

from

59

19 6 \overline{∣ 119} \underline{6} 59 \underline{54} 5

19 6 \overline{∣ 119} \underline{6} 59 \underline{54} 5

The solution for Long Division of

\frac{119}{6}

19

with remainder of

5

19 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{119}{6} = 19 \frac{5}{6}

= 19 \frac{5}{6}

= 19 \frac{5}{6}

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Frequently Asked Questions (FAQ)

What is (6-5/2)(3+8/3) ?
The solution to (6-5/2)(3+8/3) is 19 5/6