What is 52/31\times 11/157\times 62/77\times 21\times 11/6 ?

The solution to 52/31\times 11/157\times 62/77\times 21\times 11/6 is 3 101/157

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Popular >

52/31\times 11/157\times 62/77\times 21\times 11/6

Solution

52/31 \times 11/157 \times 62/77 \times 21 \times 11/6

Solution

3 \frac{101}{157}

Solution steps

52/31 \times 11/157 \times 62/77 \times 21 \times 11/6

Follow the PEMDAS order of operations

Multiply and divide (left to right)

52/31 = \frac{52}{31}

= \frac{52}{31} \times 11/157 \times 62/77 \times 21 \times 11/6

\frac{52}{31} \times 11 = \frac{572}{31}

\frac{52}{31} \cdot 11

Convert element to fraction:

11 = \frac{11}{1}

= \frac{52}{31} \cdot \frac{11}{1}

Apply the fraction rule:

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

= \frac{52 \cdot 11}{31 \cdot 1}

Multiply the numbers:

52 \cdot 11 = 572

= \frac{572}{31 \cdot 1}

Multiply the numbers:

31 \cdot 1 = 31

= \frac{572}{31}

= \frac{572}{31} /157 \times 62/77 \times 21 \times 11/6

\frac{572}{31} /157 = \frac{572}{4867}

\frac{572}{31} /157

Convert element to fraction:

157 = \frac{157}{1}

= \frac{572}{31} \div \frac{157}{1}

Apply the fraction rule:

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

= \frac{572}{31} \cdot \frac{1}{157}

Multiply fractions:

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

= \frac{572 \cdot 1}{31 \cdot 157}

Multiply the numbers:

572 \cdot 1 = 572

= \frac{572}{31 \cdot 157}

Multiply the numbers:

31 \cdot 157 = 4867

= \frac{572}{4867}

= \frac{572}{4867} \times 62/77 \times 21 \times 11/6

\frac{572}{4867} \times 62 = \frac{1144}{157}

\frac{572}{4867} \cdot 62

Convert element to fraction:

62 = \frac{62}{1}

= \frac{572}{4867} \cdot \frac{62}{1}

Apply the fraction rule:

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

= \frac{572 \cdot 62}{4867 \cdot 1}

Cancel

\frac{572 \cdot 62}{4867 \cdot 1} : \frac{1144}{157}

\frac{572 \cdot 62}{4867 \cdot 1}

Multiply the numbers:

4867 \cdot 1 = 4867

= \frac{572 \cdot 62}{4867}

Factor the number:

62 = 31 \cdot 2

= \frac{572 \cdot 31 \cdot 2}{4867}

Factor the number:

4867 = 31 \cdot 157

= \frac{572 \cdot 31 \cdot 2}{31 \cdot 157}

Cancel the common factor:

31

= \frac{572 \cdot 2}{157}

Multiply the numbers:

572 \cdot 2 = 1144

= \frac{1144}{157}

= \frac{1144}{157}

= \frac{1144}{157} /77 \times 21 \times 11/6

\frac{1144}{157} /77 = \frac{104}{1099}

\frac{1144}{157} /77

Convert element to fraction:

77 = \frac{77}{1}

= \frac{1144}{157} \div \frac{77}{1}

Apply the fraction rule:

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

= \frac{1144}{157} \cdot \frac{1}{77}

Cross-cancel common factor:

11

1144, 77

Greatest Common Divisor (GCD)

Prime factorization of

1144 : 2 \cdot 2 \cdot 2 \cdot 11 \cdot 13

1144

1144

divides by

21144 = 572 \cdot 2

= 2 \cdot 572

572

divides by

2572 = 286 \cdot 2

= 2 \cdot 2 \cdot 286

286

divides by

2286 = 143 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 143

143

divides by

11143 = 13 \cdot 11

= 2 \cdot 2 \cdot 2 \cdot 11 \cdot 13

2, 11, 13

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 11 \cdot 13

Prime factorization of

77 : 7 \cdot 11

77

77

divides by

777 = 11 \cdot 7

= 7 \cdot 11

7, 11

are all prime numbers, therefore no further factorization is possible

= 7 \cdot 11

The prime factors common to

1144, 77

are

= 11

= \frac{104}{157} \cdot \frac{1}{7}

Multiply fractions:

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

= \frac{104 \cdot 1}{157 \cdot 7}

Multiply the numbers:

104 \cdot 1 = 104

= \frac{104}{157 \cdot 7}

Multiply the numbers:

157 \cdot 7 = 1099

= \frac{104}{1099}

= \frac{104}{1099} \times 21 \times 11/6

\frac{104}{1099} \times 21 = \frac{312}{157}

\frac{104}{1099} \cdot 21

Convert element to fraction:

21 = \frac{21}{1}

= \frac{104}{1099} \cdot \frac{21}{1}

Apply the fraction rule:

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

= \frac{104 \cdot 21}{1099 \cdot 1}

Cancel

\frac{104 \cdot 21}{1099 \cdot 1} : \frac{312}{157}

\frac{104 \cdot 21}{1099 \cdot 1}

Multiply the numbers:

1099 \cdot 1 = 1099

= \frac{104 \cdot 21}{1099}

Factor the number:

21 = 7 \cdot 3

= \frac{104 \cdot 7 \cdot 3}{1099}

Factor the number:

1099 = 7 \cdot 157

= \frac{104 \cdot 7 \cdot 3}{7 \cdot 157}

Cancel the common factor:

7

= \frac{104 \cdot 3}{157}

Multiply the numbers:

104 \cdot 3 = 312

= \frac{312}{157}

= \frac{312}{157}

= \frac{312}{157} \times 11/6

\frac{312}{157} \times 11 = \frac{3432}{157}

\frac{312}{157} \cdot 11

Convert element to fraction:

11 = \frac{11}{1}

= \frac{312}{157} \cdot \frac{11}{1}

Apply the fraction rule:

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

= \frac{312 \cdot 11}{157 \cdot 1}

Multiply the numbers:

312 \cdot 11 = 3432

= \frac{3432}{157 \cdot 1}

Multiply the numbers:

157 \cdot 1 = 157

= \frac{3432}{157}

= \frac{3432}{157} /6

\frac{3432}{157} /6 = \frac{572}{157}

\frac{3432}{157} /6

Convert element to fraction:

6 = \frac{6}{1}

= \frac{3432}{157} \div \frac{6}{1}

Apply the fraction rule:

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

= \frac{3432}{157} \cdot \frac{1}{6}

Cross-cancel common factor:

6

= \frac{572}{157}

= \frac{572}{157}

Convert improper fractions to mixed numbers:

\frac{572}{157} = 3 \frac{101}{157}

\frac{572}{157} = 3

Remainder

101

\frac{572}{157}

Write the problem in long division format

157 \overline{∣ 572}

Divide

572

157

to get

3

Divide

572

157

to get

3

3 157 \overline{∣ 572}

Multiply the quotient digit

(3)

by the divisor

157

3 157 \overline{∣ 572} \underline{471}

Subtract

471

from

572

3 157 \overline{∣ 572} \underline{471} 101

3 157 \overline{∣ 572} \underline{471} 101

The solution for Long Division of

\frac{572}{157}

3

with remainder of

101

3 Remainder 101

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{572}{157} = 3 \frac{101}{157}

= 3 \frac{101}{157}

= 3 \frac{101}{157}

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Frequently Asked Questions (FAQ)

What is 52/31\times 11/157\times 62/77\times 21\times 11/6 ?
The solution to 52/31\times 11/157\times 62/77\times 21\times 11/6 is 3 101/157