The solution to 1/2+3-1/6 is 3 1/3

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Popular Pre Algebra >

1/2+3-1/6

Solution

\frac{1}{2} + 3 - \frac{1}{6}

Solution

3 \frac{1}{3}

Decimal

3.33333 \dots

Solution steps

\frac{1}{2} + 3 - \frac{1}{6}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{1}{2} + 3 = \frac{7}{2}

\frac{1}{2} + 3

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

3 \cdot 2 + 1 = 7

3 \cdot 2 + 1

Multiply the numbers:

3 \cdot 2 = 6

= 6 + 1

Add the numbers:

6 + 1 = 7

= 7

= \frac{7}{2}

= \frac{7}{2} - \frac{1}{6}

\frac{7}{2} - \frac{1}{6} = \frac{10}{3}

\frac{7}{2} - \frac{1}{6}

Least Common Multiplier of

2, 6 : 6

2, 6

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

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

2

6

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 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{7}{2} :

multiply the denominator and numerator by

3

\frac{7}{2} = \frac{7 \cdot 3}{2 \cdot 3} = \frac{21}{6}

= \frac{21}{6} - \frac{1}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{21 - 1}{6}

Subtract the numbers:

21 - 1 = 20

= \frac{20}{6}

Cancel the common factor:

2

= \frac{10}{3}

= \frac{10}{3}

Convert improper fractions to mixed numbers:

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

\frac{10}{3} = 3

Remainder

1

\frac{10}{3}

Write the problem in long division format

3 \overline{∣ 10}

Divide

10

3

to get

3

Divide

10

3

to get

3

3 3 \overline{∣ 10}

Multiply the quotient digit

(3)

by the divisor

3

3 3 \overline{∣ 10} \underline{9}

Subtract

9

from

10

3 3 \overline{∣ 10} \underline{9} 1

3 3 \overline{∣ 10} \underline{9} 1

The solution for Long Division of

\frac{10}{3}

3

with remainder of

1

3 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

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

= 3 \frac{1}{3}

= 3 \frac{1}{3}

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3^2-3(12*3)+2^3(7-3*2)

40-5^2

Frequently Asked Questions (FAQ)

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

1/2+3-1/6

Solution

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Frequently Asked Questions (FAQ)

What is 1/2+3-1/6 ?

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