What is 8^2\div (42)-3+5(1/5) ?

The solution to 8^2\div (42)-3+5(1/5) is -10/21

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8^2\div (42)-3+5(1/5)

8^{2} \div (42) - 3 + 5 (\frac{1}{5})

- \frac{10}{21}

Solution steps

8^{2} \div (42) - 3 + 5 (\frac{1}{5})

Follow the PEMDAS order of operations

Calculate exponents

8^{2} : 64

8^{2}

8^{2} = 64

= 64

= 64 \div (42) - 3 + 5 (\frac{1}{5})

Multiply and divide (left to right)

64 \div (42) : \frac{64}{( 42 )}

64 \div (42)

64 \div (42) = \frac{64}{( 42 )}

= \frac{64}{( 42 )}

= \frac{64}{( 42 )} - 3 + 5 (\frac{1}{5})

Multiply and divide (left to right)

5 (\frac{1}{5}) : 1

5 (\frac{1}{5})

Apply rule:

(a) = a

(\frac{1}{5}) = \frac{1}{5}

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

Convert element to fraction:

5 = \frac{5}{1}

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

Cross-cancel common factor:

5

= 1

= \frac{64}{( 42 )} - 3 + 1

Add and subtract (left to right)

\frac{64}{( 42 )} - 3 + 1 : - \frac{10}{21}

\frac{64}{( 42 )} - 3 + 1

\frac{64}{( 42 )} - 3 = - \frac{31}{21}

\frac{64}{42} - 3

Cancel

\frac{64}{42} : \frac{32}{21}

\frac{64}{42}

Cancel the common factor:

2

= \frac{32}{21}

= \frac{32}{21} - 3

Convert element to fraction:

3 = \frac{3 \cdot 21}{21}

= - \frac{3 \cdot 21}{21} + \frac{32}{21}

Since the denominators are equal, combine the fractions:

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

= \frac{- 3 \cdot 21 + 32}{21}

- 3 \cdot 21 + 32 = - 31

- 3 \cdot 21 + 32

Multiply the numbers:

3 \cdot 21 = 63

= - 63 + 32

Add/Subtract the numbers:

- 63 + 32 = - 31

= - 31

= \frac{- 31}{21}

Apply the fraction rule:

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

= - \frac{31}{21}

= - \frac{31}{21} + 1

- \frac{31}{21} + 1 = - \frac{10}{21}

- \frac{31}{21} + 1

Convert element to fraction:

1 = \frac{1 \cdot 21}{21}

= \frac{1 \cdot 21}{21} - \frac{31}{21}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 21 - 31}{21}

1 \cdot 21 - 31 = - 10

1 \cdot 21 - 31

Multiply the numbers:

1 \cdot 21 = 21

= 21 - 31

Subtract the numbers:

21 - 31 = - 10

= - 10

= \frac{- 10}{21}

Apply the fraction rule:

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

= - \frac{10}{21}

= - \frac{10}{21}

= - \frac{10}{21}

9 \times 8 + 6 \times 8

1 + 8 (33 - 1)

6^{3} - 10 \div 5

7 [5 + 9 (3 \times 6)]

4 (4) + 6