What is (4 2/3+1 1/6)-1 5/6 ?

The solution to (4 2/3+1 1/6)-1 5/6 is 4

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Popular >

(4 2/3+1 1/6)-1 5/6

Solution

(4 \frac{2}{3} + 1 \frac{1}{6}) - 1 \frac{5}{6}

Solution

4

Solution steps

(4 \frac{2}{3} + 1 \frac{1}{6}) - 1 \frac{5}{6}

Convert mixed numbers to improper fractions:

1 \frac{5}{6} = \frac{11}{6}

1 \frac{5}{6}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

1 \frac{5}{6} = \frac{1 \cdot 6 + 5}{6}

= \frac{11}{6}

= (4 \frac{2}{3} + 1 \frac{1}{6}) - \frac{11}{6}

Convert mixed numbers to improper fractions:

4 \frac{2}{3} = \frac{14}{3}

4 \frac{2}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

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

= \frac{14}{3}

= (\frac{14}{3} + 1 \frac{1}{6}) - \frac{11}{6}

Convert mixed numbers to improper fractions:

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

1 \frac{1}{6}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

1 \frac{1}{6} = \frac{1 \cdot 6 + 1}{6}

= \frac{7}{6}

= (\frac{14}{3} + \frac{7}{6}) - \frac{11}{6}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{14}{3} + \frac{7}{6}) : \frac{35}{6}

\frac{14}{3} + \frac{7}{6}

\frac{14}{3} + \frac{7}{6} = \frac{35}{6}

\frac{14}{3} + \frac{7}{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{14}{3} :

multiply the denominator and numerator by

2

\frac{14}{3} = \frac{14 \cdot 2}{3 \cdot 2} = \frac{28}{6}

= \frac{28}{6} + \frac{7}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{28 + 7}{6}

Add the numbers:

28 + 7 = 35

= \frac{35}{6}

= \frac{35}{6}

= \frac{35}{6} - \frac{11}{6}

Add and subtract (left to right)

\frac{35}{6} - \frac{11}{6} : 4

\frac{35}{6} - \frac{11}{6}

\frac{35}{6} - \frac{11}{6} = 4

\frac{35}{6} - \frac{11}{6}

Apply rule

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

= \frac{35 - 11}{6}

Subtract the numbers:

35 - 11 = 24

= \frac{24}{6}

Divide the numbers:

\frac{24}{6} = 4

= 4

= 4

= 4

Popular Examples

3(1)^2+3(1)+1

3 (1)^{2} + 3 (1) + 1

7^2-10

7^{2} - 10

3(2^2-3)+15

3 (2^{2} - 3) + 15

(5-2)*180

(5 - 2) \cdot 180

simplify-((14)/(-2))simplify

- (\frac{14}{- 2})

Frequently Asked Questions (FAQ)

What is (4 2/3+1 1/6)-1 5/6 ?
The solution to (4 2/3+1 1/6)-1 5/6 is 4