What is 16-1/4-4/6-1/2 ?

The solution to 16-1/4-4/6-1/2 is 14 7/12

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Popular Pre Algebra >

16-1/4-4/6-1/2

Solution

16 - \frac{1}{4} - \frac{4}{6} - \frac{1}{2}

Solution

14 \frac{7}{12}

Decimal

14.58333 \dots

Solution steps

16 - \frac{1}{4} - \frac{4}{6} - \frac{1}{2}

\frac{4}{6} = \frac{2}{3}

Cancel the common factor:

2

\frac{2}{3}

= 16 - \frac{1}{4} - \frac{2}{3} - \frac{1}{2}

Follow the PEMDAS order of operations

Add and subtract (left to right)

16 - \frac{1}{4} - \frac{2}{3} - \frac{1}{2} : \frac{175}{12}

16 - \frac{1}{4} - \frac{2}{3} - \frac{1}{2}

16 - \frac{1}{4} = \frac{63}{4}

16 - \frac{1}{4}

Convert element to fraction:

16 = \frac{16 \cdot 4}{4}

= \frac{16 \cdot 4}{4} - \frac{1}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{16 \cdot 4 - 1}{4}

16 \cdot 4 - 1 = 63

16 \cdot 4 - 1

Multiply the numbers:

16 \cdot 4 = 64

= 64 - 1

Subtract the numbers:

64 - 1 = 63

= 63

= \frac{63}{4}

= \frac{63}{4} - \frac{2}{3} - \frac{1}{2}

\frac{63}{4} - \frac{2}{3} = \frac{181}{12}

\frac{63}{4} - \frac{2}{3}

Least Common Multiplier of

4, 3 : 12

4, 3

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

4

3

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

For

\frac{63}{4} :

multiply the denominator and numerator by

3

\frac{63}{4} = \frac{63 \cdot 3}{4 \cdot 3} = \frac{189}{12}

For

\frac{2}{3} :

multiply the denominator and numerator by

4

\frac{2}{3} = \frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{12}

= \frac{189}{12} - \frac{8}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{189 - 8}{12}

Subtract the numbers:

189 - 8 = 181

= \frac{181}{12}

= \frac{181}{12} - \frac{1}{2}

\frac{181}{12} - \frac{1}{2} = \frac{175}{12}

\frac{181}{12} - \frac{1}{2}

Least Common Multiplier of

12, 2 : 12

12, 2

Least Common Multiplier (LCM)

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

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

12

2

= 2 \cdot 2 \cdot 3

Multiply the numbers:

2 \cdot 2 \cdot 3 = 12

= 12

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

12

For

\frac{1}{2} :

multiply the denominator and numerator by

6

\frac{1}{2} = \frac{1 \cdot 6}{2 \cdot 6} = \frac{6}{12}

= \frac{181}{12} - \frac{6}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{181 - 6}{12}

Subtract the numbers:

181 - 6 = 175

= \frac{175}{12}

= \frac{175}{12}

= \frac{175}{12}

Convert improper fractions to mixed numbers:

\frac{175}{12} = 14 \frac{7}{12}

\frac{175}{12} = 14

Remainder

7

\frac{175}{12}

Write the problem in long division format

12 \overline{∣ 175}

Divide

17

12

to get

1

Divide

17

12

to get

1

1 12 \overline{∣ 175}

Multiply the quotient digit

(1)

by the divisor

12

1 12 \overline{∣ 175} \underline{12}

Subtract

12

from

17

1 12 \overline{∣ 175} \underline{12} 5

Bring down the next number of the dividend

1 12 \overline{∣ 175} \underline{12} 55

1 12 \overline{∣ 175} \underline{12} 55

Divide

55

12

to get

4

Divide

55

12

to get

4

14 12 \overline{∣ 175} \underline{12} 55

Multiply the quotient digit

(4)

by the divisor

12

14 12 \overline{∣ 175} \underline{12} 55 \underline{48}

Subtract

48

from

55

14 12 \overline{∣ 175} \underline{12} 55 \underline{48} 7

14 12 \overline{∣ 175} \underline{12} 55 \underline{48} 7

The solution for Long Division of

\frac{175}{12}

14

with remainder of

7

14 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{175}{12} = 14 \frac{7}{12}

= 14 \frac{7}{12}

= 14 \frac{7}{12}

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Frequently Asked Questions (FAQ)

What is 16-1/4-4/6-1/2 ?
The solution to 16-1/4-4/6-1/2 is 14 7/12

16-1/4-4/6-1/2

Solution

Solution

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Frequently Asked Questions (FAQ)

What is 16-1/4-4/6-1/2 ?

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