What is 500-(2^5-20+15\div 4)\div 2 ?

The solution to 500-(2^5-20+15\div 4)\div 2 is 492 1/8

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Popular >

500-(2^5-20+15\div 4)\div 2

Solution

500 - (2^{5} - 20 + 15 \div 4) \div 2

Solution

492 \frac{1}{8}

Solution steps

500 - (2^{5} - 20 + 15 \div 4) \div 2

Follow the PEMDAS order of operations

Calculate within parentheses

(2^{5} - 20 + 15 \div 4) : \frac{63}{4}

2^{5} - 20 + 15 \div 4

Calculate exponents

2^{5} : 32

2^{5}

2^{5} = 32

= 32

= 32 - 20 + 15 \div 4

Multiply and divide (left to right)

15 \div 4 : \frac{15}{4}

15 \div 4

15 \div 4 = \frac{15}{4}

= \frac{15}{4}

= 32 - 20 + \frac{15}{4}

Add and subtract (left to right)

32 - 20 + \frac{15}{4} : \frac{63}{4}

32 - 20 + \frac{15}{4}

32 - 20 = 12

= 12 + \frac{15}{4}

12 + \frac{15}{4} = \frac{63}{4}

12 + \frac{15}{4}

Convert element to fraction:

12 = \frac{12 \cdot 4}{4}

= \frac{12 \cdot 4}{4} + \frac{15}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{12 \cdot 4 + 15}{4}

12 \cdot 4 + 15 = 63

12 \cdot 4 + 15

Multiply the numbers:

12 \cdot 4 = 48

= 48 + 15

Add the numbers:

48 + 15 = 63

= 63

= \frac{63}{4}

= \frac{63}{4}

= \frac{63}{4}

= 500 - \frac{63}{4} \div 2

Multiply and divide (left to right)

\frac{63}{4} \div 2 : \frac{63}{8}

\frac{63}{4} \div 2

Convert element to fraction:

2 = \frac{2}{1}

= \frac{63}{4} \div \frac{2}{1}

Apply the fraction rule:

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

= \frac{63}{4} \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{63 \cdot 1}{4 \cdot 2}

Multiply the numbers:

63 \cdot 1 = 63

= \frac{63}{4 \cdot 2}

Multiply the numbers:

4 \cdot 2 = 8

= \frac{63}{8}

= 500 - \frac{63}{8}

Add and subtract (left to right)

500 - \frac{63}{8} : \frac{3937}{8}

500 - \frac{63}{8}

500 - \frac{63}{8} = \frac{3937}{8}

500 - \frac{63}{8}

Convert element to fraction:

500 = \frac{500 \cdot 8}{8}

= \frac{500 \cdot 8}{8} - \frac{63}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{500 \cdot 8 - 63}{8}

500 \cdot 8 - 63 = 3937

500 \cdot 8 - 63

Multiply the numbers:

500 \cdot 8 = 4000

= 4000 - 63

Subtract the numbers:

4000 - 63 = 3937

= 3937

= \frac{3937}{8}

= \frac{3937}{8}

= \frac{3937}{8}

Convert improper fractions to mixed numbers:

\frac{3937}{8} = 492 \frac{1}{8}

\frac{3937}{8} = 492

Remainder

1

\frac{3937}{8}

Write the problem in long division format

8 \overline{∣ 3937}

Divide

39

8

to get

4

Divide

39

8

to get

4

4 8 \overline{∣ 3937}

Multiply the quotient digit

(4)

by the divisor

8

4 8 \overline{∣ 3937} \underline{32}

Subtract

32

from

39

4 8 \overline{∣ 3937} \underline{32} 7

Bring down the next number of the dividend

4 8 \overline{∣ 3937} \underline{32} 73

4 8 \overline{∣ 3937} \underline{32} 73

Divide

73

8

to get

9

Divide

73

8

to get

9

49 8 \overline{∣ 3937} \underline{32} 73

Multiply the quotient digit

(9)

by the divisor

8

49 8 \overline{∣ 3937} \underline{32} 73 \underline{72}

Subtract

72

from

73

49 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 1

Bring down the next number of the dividend

49 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 17

49 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 17

Divide

17

8

to get

2

Divide

17

8

to get

2

492 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 17

Multiply the quotient digit

(2)

by the divisor

8

492 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 17 \underline{16}

Subtract

16

from

17

492 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 17 \underline{16} 1

492 8 \overline{∣ 3937} \underline{32} 73 \underline{72} 17 \underline{16} 1

The solution for Long Division of

\frac{3937}{8}

492

with remainder of

1

492 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{3937}{8} = 492 \frac{1}{8}

= 492 \frac{1}{8}

= 492 \frac{1}{8}

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Frequently Asked Questions (FAQ)

What is 500-(2^5-20+15\div 4)\div 2 ?
The solution to 500-(2^5-20+15\div 4)\div 2 is 492 1/8