The solution to 3-7/3+29/6 is 5 1/2

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3-7/3+29/6

Solution

3 - \frac{7}{3} + \frac{29}{6}

Solution

5 \frac{1}{2}

Solution steps

3 - \frac{7}{3} + \frac{29}{6}

Follow the PEMDAS order of operations

Add and subtract (left to right)

3 - \frac{7}{3} = \frac{2}{3}

3 - \frac{7}{3}

Convert element to fraction:

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

= \frac{3 \cdot 3}{3} - \frac{7}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{3 \cdot 3 - 7}{3}

3 \cdot 3 - 7 = 2

3 \cdot 3 - 7

Multiply the numbers:

3 \cdot 3 = 9

= 9 - 7

Subtract the numbers:

9 - 7 = 2

= 2

= \frac{2}{3}

= \frac{2}{3} + \frac{29}{6}

\frac{2}{3} + \frac{29}{6} = \frac{11}{2}

\frac{2}{3} + \frac{29}{6}

Least Common Multiplier of

3, 6 : 6

3, 6

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

3

6

= 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{2}{3} :

multiply the denominator and numerator by

2

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

= \frac{4}{6} + \frac{29}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{4 + 29}{6}

Add the numbers:

4 + 29 = 33

= \frac{33}{6}

Cancel the common factor:

3

= \frac{11}{2}

= \frac{11}{2}

Convert improper fractions to mixed numbers:

\frac{11}{2} = 5 \frac{1}{2}

\frac{11}{2} = 5

Remainder

1

\frac{11}{2}

Write the problem in long division format

2 \overline{∣ 11}

Divide

11

2

to get

5

Divide

11

2

to get

5

5 2 \overline{∣ 11}

Multiply the quotient digit

(5)

by the divisor

2

5 2 \overline{∣ 11} \underline{10}

Subtract

10

from

11

5 2 \overline{∣ 11} \underline{10} 1

5 2 \overline{∣ 11} \underline{10} 1

The solution for Long Division of

\frac{11}{2}

5

with remainder of

1

5 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{11}{2} = 5 \frac{1}{2}

= 5 \frac{1}{2}

= 5 \frac{1}{2}

Popular Examples

simplify 2/3+1/2 simplify

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15 - \frac{1}{2} (2)

2^3-3^3

2^{3} - 3^{3}

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\frac{2}{5} \cdot (\frac{3}{4} \cdot 2)

5^2-5

5^{2} - 5

Frequently Asked Questions (FAQ)

What is 3-7/3+29/6 ?
The solution to 3-7/3+29/6 is 5 1/2

3-7/3+29/6

Solution

Solution

Popular Examples

Frequently Asked Questions (FAQ)

What is 3-7/3+29/6 ?