The solution to 17-1/3-1/2 is 16 1/6

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Popular Pre Algebra >

17-1/3-1/2

Solution

17 - \frac{1}{3} - \frac{1}{2}

Solution

16 \frac{1}{6}

Decimal

16.16666 \dots

Solution steps

17 - \frac{1}{3} - \frac{1}{2}

Follow the PEMDAS order of operations

Add and subtract (left to right)

17 - \frac{1}{3} = \frac{50}{3}

17 - \frac{1}{3}

Convert element to fraction:

17 = \frac{17 \cdot 3}{3}

= \frac{17 \cdot 3}{3} - \frac{1}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{17 \cdot 3 - 1}{3}

17 \cdot 3 - 1 = 50

17 \cdot 3 - 1

Multiply the numbers:

17 \cdot 3 = 51

= 51 - 1

Subtract the numbers:

51 - 1 = 50

= 50

= \frac{50}{3}

= \frac{50}{3} - \frac{1}{2}

\frac{50}{3} - \frac{1}{2} = \frac{97}{6}

\frac{50}{3} - \frac{1}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 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

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

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

6

For

\frac{50}{3} :

multiply the denominator and numerator by

2

\frac{50}{3} = \frac{50 \cdot 2}{3 \cdot 2} = \frac{100}{6}

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= \frac{100}{6} - \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{100 - 3}{6}

Subtract the numbers:

100 - 3 = 97

= \frac{97}{6}

= \frac{97}{6}

Convert improper fractions to mixed numbers:

\frac{97}{6} = 16 \frac{1}{6}

\frac{97}{6} = 16

Remainder

1

\frac{97}{6}

Write the problem in long division format

6 \overline{∣ 97}

Divide

9

6

to get

1

Divide

9

6

to get

1

1 6 \overline{∣ 97}

Multiply the quotient digit

(1)

by the divisor

6

1 6 \overline{∣ 97} \underline{6}

Subtract

6

from

9

1 6 \overline{∣ 97} \underline{6} 3

Bring down the next number of the dividend

1 6 \overline{∣ 97} \underline{6} 37

1 6 \overline{∣ 97} \underline{6} 37

Divide

37

6

to get

6

Divide

37

6

to get

6

16 6 \overline{∣ 97} \underline{6} 37

Multiply the quotient digit

(6)

by the divisor

6

16 6 \overline{∣ 97} \underline{6} 37 \underline{36}

Subtract

36

from

37

16 6 \overline{∣ 97} \underline{6} 37 \underline{36} 1

16 6 \overline{∣ 97} \underline{6} 37 \underline{36} 1

The solution for Long Division of

\frac{97}{6}

16

with remainder of

1

16 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{97}{6} = 16 \frac{1}{6}

= 16 \frac{1}{6}

= 16 \frac{1}{6}

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What is 17-1/3-1/2 ?
The solution to 17-1/3-1/2 is 16 1/6

17-1/3-1/2

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