The solution to 5-5/6-6/60 is 4 1/15

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Popular Pre Algebra >

5-5/6-6/60

Solution

5 - \frac{5}{6} - \frac{6}{60}

Solution

4 \frac{1}{15}

Decimal

4.06666 \dots

Solution steps

5 - \frac{5}{6} - \frac{6}{60}

\frac{6}{60} = \frac{1}{10}

Cancel the common factor:

6

\frac{1}{10}

= 5 - \frac{5}{6} - \frac{1}{10}

Follow the PEMDAS order of operations

Add and subtract (left to right)

5 - \frac{5}{6} - \frac{1}{10} : \frac{61}{15}

5 - \frac{5}{6} - \frac{1}{10}

5 - \frac{5}{6} = \frac{25}{6}

5 - \frac{5}{6}

Convert element to fraction:

5 = \frac{5 \cdot 6}{6}

= \frac{5 \cdot 6}{6} - \frac{5}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{5 \cdot 6 - 5}{6}

5 \cdot 6 - 5 = 25

5 \cdot 6 - 5

Multiply the numbers:

5 \cdot 6 = 30

= 30 - 5

Subtract the numbers:

30 - 5 = 25

= 25

= \frac{25}{6}

= \frac{25}{6} - \frac{1}{10}

\frac{25}{6} - \frac{1}{10} = \frac{61}{15}

\frac{25}{6} - \frac{1}{10}

Least Common Multiplier of

6, 10 : 30

6, 10

Least Common Multiplier (LCM)

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

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 5

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

6

10

= 2 \cdot 3 \cdot 5

Multiply the numbers:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

For

\frac{25}{6} :

multiply the denominator and numerator by

5

\frac{25}{6} = \frac{25 \cdot 5}{6 \cdot 5} = \frac{125}{30}

For

\frac{1}{10} :

multiply the denominator and numerator by

3

\frac{1}{10} = \frac{1 \cdot 3}{10 \cdot 3} = \frac{3}{30}

= \frac{125}{30} - \frac{3}{30}

Since the denominators are equal, combine the fractions:

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

= \frac{125 - 3}{30}

Subtract the numbers:

125 - 3 = 122

= \frac{122}{30}

Cancel the common factor:

2

= \frac{61}{15}

= \frac{61}{15}

= \frac{61}{15}

Convert improper fractions to mixed numbers:

\frac{61}{15} = 4 \frac{1}{15}

\frac{61}{15} = 4

Remainder

1

\frac{61}{15}

Write the problem in long division format

15 \overline{∣ 61}

Divide

61

15

to get

4

Divide

61

15

to get

4

4 15 \overline{∣ 61}

Multiply the quotient digit

(4)

by the divisor

15

4 15 \overline{∣ 61} \underline{60}

Subtract

60

from

61

4 15 \overline{∣ 61} \underline{60} 1

4 15 \overline{∣ 61} \underline{60} 1

The solution for Long Division of

\frac{61}{15}

4

with remainder of

1

4 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{61}{15} = 4 \frac{1}{15}

= 4 \frac{1}{15}

= 4 \frac{1}{15}

Popular Examples

2× ((-12+36)\div 6+(8-5)\div (-3))-6

18\div [12\div (-2)]

(-56+30)+(60-(-30))

(548521-35567)+(548+25600)-(82145-58)

-(-36+12-4)-[+4-(12-15)]

Frequently Asked Questions (FAQ)

What is 5-5/6-6/60 ?
The solution to 5-5/6-6/60 is 4 1/15

5-5/6-6/60

Solution

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Frequently Asked Questions (FAQ)

What is 5-5/6-6/60 ?

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