What is (5+3\div 2\div 6-4)*(4\div 2-3+6)\div (7-8\div 2-2)^2 ?

The solution to (5+3\div 2\div 6-4)*(4\div 2-3+6)\div (7-8\div 2-2)^2 is 6 1/4

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(5+3\div 2\div 6-4)*(4\div 2-3+6)\div (7-8\div 2-2)^2

Solution

(5 + 3 \div 2 \div 6 - 4) \cdot (4 \div 2 - 3 + 6) \div (7 - 8 \div 2 - 2)^{2}

Solution

6 \frac{1}{4}

Solution steps

(5 + 3 \div 2 \div 6 - 4) (4 \div 2 - 3 + 6) \div (7 - 8 \div 2 - 2)^{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(5 + 3 \div 2 \div 6 - 4) : \frac{5}{4}

5 + 3 \div 2 \div 6 - 4

Multiply and divide (left to right)

3 \div 2 \div 6 : \frac{1}{4}

3 \div 2 \div 6

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

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

\frac{3}{2} \div 6 = \frac{1}{4}

\frac{3}{2} \div 6

Convert element to fraction:

6 = \frac{6}{1}

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

Apply the fraction rule:

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

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

Cross-cancel common factor:

3

3, 6

Greatest Common Divisor (GCD)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

The prime factors common to

3, 6

are

= 3

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 = 1

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= \frac{1}{4}

= 5 + \frac{1}{4} - 4

Add and subtract (left to right)

5 + \frac{1}{4} - 4 : \frac{5}{4}

5 + \frac{1}{4} - 4

5 + \frac{1}{4} = \frac{21}{4}

5 + \frac{1}{4}

Convert element to fraction:

5 = \frac{5 \cdot 4}{4}

= \frac{5 \cdot 4}{4} + \frac{1}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 4 + 1}{4}

5 \cdot 4 + 1 = 21

5 \cdot 4 + 1

Multiply the numbers:

5 \cdot 4 = 20

= 20 + 1

Add the numbers:

20 + 1 = 21

= 21

= \frac{21}{4}

= \frac{21}{4} - 4

\frac{21}{4} - 4 = \frac{5}{4}

\frac{21}{4} - 4

Convert element to fraction:

4 = \frac{4 \cdot 4}{4}

= - \frac{4 \cdot 4}{4} + \frac{21}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{- 4 \cdot 4 + 21}{4}

- 4 \cdot 4 + 21 = 5

- 4 \cdot 4 + 21

Multiply the numbers:

4 \cdot 4 = 16

= - 16 + 21

Add/Subtract the numbers:

- 16 + 21 = 5

= 5

= \frac{5}{4}

= \frac{5}{4}

= \frac{5}{4}

= \frac{5}{4} (4 \div 2 - 3 + 6) \div (7 - 8 \div 2 - 2)^{2}

Calculate within parentheses

(4 \div 2 - 3 + 6) : 5

4 \div 2 - 3 + 6

Multiply and divide (left to right)

4 \div 2 : 2

4 \div 2

4 \div 2 = 2

= 2

= 2 - 3 + 6

Add and subtract (left to right)

2 - 3 + 6 : 5

2 - 3 + 6

2 - 3 = - 1

= - 1 + 6

- 1 + 6 = 5

= 5

= 5

= \frac{5}{4} \cdot 5 \div (7 - 8 \div 2 - 2)^{2}

Calculate within parentheses

(7 - 8 \div 2 - 2) : 1

7 - 8 \div 2 - 2

Multiply and divide (left to right)

8 \div 2 : 4

8 \div 2

8 \div 2 = 4

= 4

= 7 - 4 - 2

Add and subtract (left to right)

7 - 4 - 2 : 1

7 - 4 - 2

7 - 4 = 3

= 3 - 2

3 - 2 = 1

= 1

= 1

= \frac{5}{4} \cdot 5 \div 1^{2}

Calculate exponents

1^{2} : 1

1^{2}

1^{2} = 1

= 1

= \frac{5}{4} \cdot 5 \div 1

Multiply and divide (left to right)

\frac{5}{4} \cdot 5 \div 1 : \frac{25}{4}

\frac{5}{4} \cdot 5 \div 1

\frac{5}{4} \cdot 5 = \frac{25}{4}

\frac{5}{4} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

= \frac{5}{4} \cdot \frac{5}{1}

Apply the fraction rule:

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

= \frac{5 \cdot 5}{4 \cdot 1}

Multiply the numbers:

5 \cdot 5 = 25

= \frac{25}{4 \cdot 1}

Multiply the numbers:

4 \cdot 1 = 4

= \frac{25}{4}

= \frac{25}{4} \div 1

\frac{25}{4} \div 1 = \frac{25}{4}

\frac{25}{4} \div 1

Convert element to fraction:

1 = \frac{1}{1}

= \frac{25}{4} \div \frac{1}{1}

Apply the fraction rule:

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

= \frac{25}{4} \cdot \frac{1}{1}

Apply rule

\frac{a}{a} = 1

\frac{1}{1} = 1

= 1 \cdot \frac{25}{4}

Multiply:

\frac{25}{4} \cdot 1 = \frac{25}{4}

= \frac{25}{4}

= \frac{25}{4}

= \frac{25}{4}

Convert improper fractions to mixed numbers:

\frac{25}{4} = 6 \frac{1}{4}

\frac{25}{4} = 6

Remainder

1

\frac{25}{4}

Write the problem in long division format

4 \overline{∣ 25}

Divide

25

4

to get

6

Divide

25

4

to get

6

6 4 \overline{∣ 25}

Multiply the quotient digit

(6)

by the divisor

4

6 4 \overline{∣ 25} \underline{24}

Subtract

24

from

25

6 4 \overline{∣ 25} \underline{24} 1

6 4 \overline{∣ 25} \underline{24} 1

The solution for Long Division of

\frac{25}{4}

6

with remainder of

1

6 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{25}{4} = 6 \frac{1}{4}

= 6 \frac{1}{4}

= 6 \frac{1}{4}

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Frequently Asked Questions (FAQ)

What is (5+3\div 2\div 6-4)*(4\div 2-3+6)\div (7-8\div 2-2)^2 ?
The solution to (5+3\div 2\div 6-4)*(4\div 2-3+6)\div (7-8\div 2-2)^2 is 6 1/4