What is (1/8+51/4-1/20)× 91/16 ?

The solution to (1/8+51/4-1/20)× 91/16 is 72 603/640

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Popular Pre Algebra >

(1/8+51/4-1/20)× 91/16

Solution

(1/8 + 51/4 - 1/20) \times 91/16

Solution

72 \frac{603}{640}

Decimal

72.9421875

Solution steps

(1/8 + 51/4 - 1/20) \times 91/16

Follow the PEMDAS order of operations

Calculate within parentheses

(1/8 + 51/4 - 1/20) : \frac{513}{40}

1/8 + 51/4 - 1/20

Multiply and divide (left to right)

1/8 : \frac{1}{8}

1/8

1/8 = \frac{1}{8}

= \frac{1}{8}

= \frac{1}{8} + 51/4 - 1/20

Multiply and divide (left to right)

51/4 : \frac{51}{4}

51/4

51/4 = \frac{51}{4}

= \frac{51}{4}

= \frac{1}{8} + \frac{51}{4} - 1/20

Multiply and divide (left to right)

1/20 : \frac{1}{20}

1/20

1/20 = \frac{1}{20}

= \frac{1}{20}

= \frac{1}{8} + \frac{51}{4} - \frac{1}{20}

Add and subtract (left to right)

\frac{1}{8} + \frac{51}{4} - \frac{1}{20} : \frac{513}{40}

\frac{1}{8} + \frac{51}{4} - \frac{1}{20}

\frac{1}{8} + \frac{51}{4} = \frac{103}{8}

\frac{1}{8} + \frac{51}{4}

Least Common Multiplier of

8, 4 : 8

8, 4

Least Common Multiplier (LCM)

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Multiply each factor the greatest number of times it occurs in either

8

4

= 2 \cdot 2 \cdot 2

Multiply the numbers:

2 \cdot 2 \cdot 2 = 8

= 8

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

8

For

\frac{51}{4} :

multiply the denominator and numerator by

2

\frac{51}{4} = \frac{51 \cdot 2}{4 \cdot 2} = \frac{102}{8}

= \frac{1}{8} + \frac{102}{8}

Since the denominators are equal, combine the fractions:

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

= \frac{1 + 102}{8}

Add the numbers:

1 + 102 = 103

= \frac{103}{8}

= \frac{103}{8} - \frac{1}{20}

\frac{103}{8} - \frac{1}{20} = \frac{513}{40}

\frac{103}{8} - \frac{1}{20}

Least Common Multiplier of

8, 20 : 40

8, 20

Least Common Multiplier (LCM)

Prime factorization of

8 : 2 \cdot 2 \cdot 2

8

8

divides by

28 = 4 \cdot 2

= 2 \cdot 4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

Prime factorization of

20 : 2 \cdot 2 \cdot 5

20

20

divides by

220 = 10 \cdot 2

= 2 \cdot 10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 5

Multiply each factor the greatest number of times it occurs in either

8

20

= 2 \cdot 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 2 \cdot 5 = 40

= 40

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

40

For

\frac{103}{8} :

multiply the denominator and numerator by

5

\frac{103}{8} = \frac{103 \cdot 5}{8 \cdot 5} = \frac{515}{40}

For

\frac{1}{20} :

multiply the denominator and numerator by

2

\frac{1}{20} = \frac{1 \cdot 2}{20 \cdot 2} = \frac{2}{40}

= \frac{515}{40} - \frac{2}{40}

Since the denominators are equal, combine the fractions:

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

= \frac{515 - 2}{40}

Subtract the numbers:

515 - 2 = 513

= \frac{513}{40}

= \frac{513}{40}

= \frac{513}{40}

= \frac{513}{40} \times 91/16

Multiply and divide (left to right)

\frac{513}{40} \times 91/16 : \frac{46683}{640}

\frac{513}{40} \times 91/16

\frac{513}{40} \times 91 = \frac{46683}{40}

\frac{513}{40} \cdot 91

Convert element to fraction:

91 = \frac{91}{1}

= \frac{513}{40} \cdot \frac{91}{1}

Apply the fraction rule:

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

= \frac{513 \cdot 91}{40 \cdot 1}

Multiply the numbers:

513 \cdot 91 = 46683

= \frac{46683}{40 \cdot 1}

Multiply the numbers:

40 \cdot 1 = 40

= \frac{46683}{40}

= \frac{46683}{40} /16

\frac{46683}{40} /16 = \frac{46683}{640}

\frac{46683}{40} /16

Convert element to fraction:

16 = \frac{16}{1}

= \frac{46683}{40} \div \frac{16}{1}

Apply the fraction rule:

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

= \frac{46683}{40} \cdot \frac{1}{16}

Multiply fractions:

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

= \frac{46683 \cdot 1}{40 \cdot 16}

Multiply the numbers:

46683 \cdot 1 = 46683

= \frac{46683}{40 \cdot 16}

Multiply the numbers:

40 \cdot 16 = 640

= \frac{46683}{640}

= \frac{46683}{640}

= \frac{46683}{640}

Convert improper fractions to mixed numbers:

\frac{46683}{640} = 72 \frac{603}{640}

\frac{46683}{640} = 72

Remainder

603

\frac{46683}{640}

Write the problem in long division format

640 \overline{∣ 46683}

Divide

4668

640

to get

7

Divide

4668

640

to get

7

7 640 \overline{∣ 46683}

Multiply the quotient digit

(7)

by the divisor

640

7 640 \overline{∣ 46683} \underline{4480}

Subtract

4480

from

4668

7 640 \overline{∣ 46683} \underline{4480} 188

Bring down the next number of the dividend

7 640 \overline{∣ 46683} \underline{4480} 1883

7 640 \overline{∣ 46683} \underline{4480} 1883

Divide

1883

640

to get

2

Divide

1883

640

to get

2

72 640 \overline{∣ 46683} \underline{4480} 1883

Multiply the quotient digit

(2)

by the divisor

640

72 640 \overline{∣ 46683} \underline{4480} 1883 \underline{1280}

Subtract

1280

from

1883

72 640 \overline{∣ 46683} \underline{4480} 1883 \underline{1280} 603

72 640 \overline{∣ 46683} \underline{4480} 1883 \underline{1280} 603

The solution for Long Division of

\frac{46683}{640}

72

with remainder of

603

72 Remainder 603

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{46683}{640} = 72 \frac{603}{640}

= 72 \frac{603}{640}

= 72 \frac{603}{640}

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Frequently Asked Questions (FAQ)

What is (1/8+51/4-1/20)× 91/16 ?
The solution to (1/8+51/4-1/20)× 91/16 is 72 603/640

(1/8+51/4-1/20)× 91/16

Solution

Solution

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Frequently Asked Questions (FAQ)

What is (1/8+51/4-1/20)× 91/16 ?

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