What is 14+146/9-1/12 ?

The solution to 14+146/9-1/12 is 30 5/36

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Popular >

14+146/9-1/12

Solution

14 + \frac{146}{9} - \frac{1}{12}

Solution

30 \frac{5}{36}

Solution steps

14 + \frac{146}{9} - \frac{1}{12}

Follow the PEMDAS order of operations

Add and subtract (left to right)

14 + \frac{146}{9} = \frac{272}{9}

14 + \frac{146}{9}

Convert element to fraction:

14 = \frac{14 \cdot 9}{9}

= \frac{14 \cdot 9}{9} + \frac{146}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{14 \cdot 9 + 146}{9}

14 \cdot 9 + 146 = 272

14 \cdot 9 + 146

Multiply the numbers:

14 \cdot 9 = 126

= 126 + 146

Add the numbers:

126 + 146 = 272

= 272

= \frac{272}{9}

= \frac{272}{9} - \frac{1}{12}

\frac{272}{9} - \frac{1}{12} = \frac{1085}{36}

\frac{272}{9} - \frac{1}{12}

Least Common Multiplier of

9, 12 : 36

9, 12

Least Common Multiplier (LCM)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Prime factorization of

12 : 2 \cdot 2 \cdot 3

12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 3

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

9

12

= 3 \cdot 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 \cdot 2 = 36

= 36

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

36

For

\frac{272}{9} :

multiply the denominator and numerator by

4

\frac{272}{9} = \frac{272 \cdot 4}{9 \cdot 4} = \frac{1088}{36}

For

\frac{1}{12} :

multiply the denominator and numerator by

3

\frac{1}{12} = \frac{1 \cdot 3}{12 \cdot 3} = \frac{3}{36}

= \frac{1088}{36} - \frac{3}{36}

Since the denominators are equal, combine the fractions:

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

= \frac{1088 - 3}{36}

Subtract the numbers:

1088 - 3 = 1085

= \frac{1085}{36}

= \frac{1085}{36}

Convert improper fractions to mixed numbers:

\frac{1085}{36} = 30 \frac{5}{36}

\frac{1085}{36} = 30

Remainder

5

\frac{1085}{36}

Write the problem in long division format

36 \overline{∣ 1085}

Divide

108

36

to get

3

Divide

108

36

to get

3

3 36 \overline{∣ 1085}

Multiply the quotient digit

(3)

by the divisor

36

3 36 \overline{∣ 1085} \underline{108}

Subtract

108

from

108

3 36 \overline{∣ 1085} \underline{108} 0

Bring down the next number of the dividend

3 36 \overline{∣ 1085} \underline{108} 05

3 36 \overline{∣ 1085} \underline{108} 05

Divide

5

36

to get

0

Divide

5

36

to get

0

30 36 \overline{∣ 1085} \underline{108} 05

Multiply the quotient digit

(0)

by the divisor

36

30 36 \overline{∣ 1085} \underline{108} 05 \underline{0}

Subtract

0

from

5

30 36 \overline{∣ 1085} \underline{108} 05 \underline{0} 5

30 36 \overline{∣ 1085} \underline{108} 05 \underline{0} 5

The solution for Long Division of

\frac{1085}{36}

30

with remainder of

5

30 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{1085}{36} = 30 \frac{5}{36}

= 30 \frac{5}{36}

= 30 \frac{5}{36}

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5\times (3+2\times (2+5-3))-10\times 2\div 4

5 \times (3 + 2 \times (2 + 5 - 3)) - 10 \times 2 \div 4

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- 2 + 6 - 10 - 4

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2^{3} - 2^{2} \times 8 \div 2^{3}

33-45-76-2+43+35

33 - 45 - 76 - 2 + 43 + 35

Frequently Asked Questions (FAQ)

What is 14+146/9-1/12 ?
The solution to 14+146/9-1/12 is 30 5/36