What is 20/3 \div 2-(2+1/4*2) ?

The solution to 20/3 \div 2-(2+1/4*2) is 5/6

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20/3 \div 2-(2+1/4*2)

Solution

\frac{20}{3} \div 2 - (2 + \frac{1}{4} \cdot 2)

Solution

\frac{5}{6}

Solution steps

\frac{20}{3} \div 2 - (2 + \frac{1}{4} \cdot 2)

Follow the PEMDAS order of operations

Calculate within parentheses

(2 + \frac{1}{4} \cdot 2) : \frac{5}{2}

2 + \frac{1}{4} \cdot 2

Multiply and divide (left to right)

\frac{1}{4} \cdot 2 : \frac{1}{2}

\frac{1}{4} \cdot 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{1}{4} \cdot \frac{2}{1}

Apply the fraction rule:

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

= \frac{1 \cdot 2}{4 \cdot 1}

\frac{1 \cdot 2}{4 \cdot 1} = \frac{1}{2}

\frac{1 \cdot 2}{4 \cdot 1}

\frac{1 \cdot 2}{4 \cdot 1} = \frac{2}{4}

\frac{1 \cdot 2}{4 \cdot 1}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{4 \cdot 1}

Multiply the numbers:

4 \cdot 1 = 4

= \frac{2}{4}

= \frac{2}{4}

Cancel the numbers:

\frac{2}{4} = \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

= 2 + \frac{1}{2}

Add and subtract (left to right)

2 + \frac{1}{2} : \frac{5}{2}

2 + \frac{1}{2}

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

2 + \frac{1}{2}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 2 + 1 = 5

2 \cdot 2 + 1

Multiply the numbers:

2 \cdot 2 = 4

= 4 + 1

Add the numbers:

4 + 1 = 5

= 5

= \frac{5}{2}

= \frac{5}{2}

= \frac{5}{2}

= \frac{20}{3} \div 2 - \frac{5}{2}

Multiply and divide (left to right)

\frac{20}{3} \div 2 : \frac{10}{3}

\frac{20}{3} \div 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{20}{3} \div \frac{2}{1}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{20}{3} \cdot \frac{1}{2}

Cross-cancel common factor:

2

= \frac{10}{3}

= \frac{10}{3} - \frac{5}{2}

Add and subtract (left to right)

\frac{10}{3} - \frac{5}{2} : \frac{5}{6}

\frac{10}{3} - \frac{5}{2}

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

\frac{10}{3} - \frac{5}{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{10}{3} :

multiply the denominator and numerator by

2

\frac{10}{3} = \frac{10 \cdot 2}{3 \cdot 2} = \frac{20}{6}

For

\frac{5}{2} :

multiply the denominator and numerator by

3

\frac{5}{2} = \frac{5 \cdot 3}{2 \cdot 3} = \frac{15}{6}

= \frac{20}{6} - \frac{15}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{20 - 15}{6}

Subtract the numbers:

20 - 15 = 5

= \frac{5}{6}

= \frac{5}{6}

= \frac{5}{6}

Popular Examples

+(-4-7)+(-3-4-5-8)

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(-36\div (-9))+3(-9+3(14-19))

(- 36 \div (- 9)) + 3 (- 9 + 3 (14 - 19))

4(0)+3

4 (0) + 3

2*(15-2)-[11-(7-3)]

2 \cdot (15 - 2) - [11 - (7 - 3)]

(-36)\div (-3)\times 5-(90\div 3+30)

(- 36) \div (- 3) \times 5 - (90 \div 3 + 30)

Frequently Asked Questions (FAQ)

What is 20/3 \div 2-(2+1/4*2) ?
The solution to 20/3 \div 2-(2+1/4*2) is 5/6