What is (5/3+2/8)+1/4 ?

The solution to (5/3+2/8)+1/4 is 2 1/6

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Popular >

(5/3+2/8)+1/4

Solution

(\frac{5}{3} + \frac{2}{8}) + \frac{1}{4}

Solution

2 \frac{1}{6}

Solution steps

(\frac{5}{3} + \frac{2}{8}) + \frac{1}{4}

\frac{2}{8} = \frac{1}{4}

Cancel the common factor:

2

\frac{1}{4}

= \frac{5}{3} + \frac{1}{4} + \frac{1}{4}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{5}{3} + \frac{1}{4} + \frac{1}{4} : \frac{13}{6}

\frac{5}{3} + \frac{1}{4} + \frac{1}{4}

\frac{5}{3} + \frac{1}{4} = \frac{23}{12}

\frac{5}{3} + \frac{1}{4}

Least Common Multiplier of

3, 4 : 12

3, 4

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

3

4

= 3 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 2 \cdot 2 = 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{5}{3} :

multiply the denominator and numerator by

4

\frac{5}{3} = \frac{5 \cdot 4}{3 \cdot 4} = \frac{20}{12}

For

\frac{1}{4} :

multiply the denominator and numerator by

3

\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}

= \frac{20}{12} + \frac{3}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{20 + 3}{12}

Add the numbers:

20 + 3 = 23

= \frac{23}{12}

= \frac{23}{12} + \frac{1}{4}

\frac{23}{12} + \frac{1}{4} = \frac{13}{6}

\frac{23}{12} + \frac{1}{4}

Least Common Multiplier of

12, 4 : 12

12, 4

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

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

12

4

= 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}{4} :

multiply the denominator and numerator by

3

\frac{1}{4} = \frac{1 \cdot 3}{4 \cdot 3} = \frac{3}{12}

= \frac{23}{12} + \frac{3}{12}

Since the denominators are equal, combine the fractions:

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

= \frac{23 + 3}{12}

Add the numbers:

23 + 3 = 26

= \frac{26}{12}

Cancel the common factor:

2

= \frac{13}{6}

= \frac{13}{6}

= \frac{13}{6}

Convert improper fractions to mixed numbers:

\frac{13}{6} = 2 \frac{1}{6}

\frac{13}{6} = 2

Remainder

1

\frac{13}{6}

Write the problem in long division format

6 \overline{∣ 13}

Divide

13

6

to get

2

Divide

13

6

to get

2

2 6 \overline{∣ 13}

Multiply the quotient digit

(2)

by the divisor

6

2 6 \overline{∣ 13} \underline{12}

Subtract

12

from

13

2 6 \overline{∣ 13} \underline{12} 1

2 6 \overline{∣ 13} \underline{12} 1

The solution for Long Division of

\frac{13}{6}

2

with remainder of

1

2 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{13}{6} = 2 \frac{1}{6}

= 2 \frac{1}{6}

= 2 \frac{1}{6}

Popular Examples

1733+(5/32)*3

1733 + (\frac{5}{32}) \cdot 3

6\times 8^2

6 \times 8^{2}

180-47-90

180 - 47 - 90

424\times 9+22

424 \times 9 + 22

5-2(2^2-6+2-8/4+6)^2

5 - 2 (2^{2} - 6 + 2 - \frac{8}{4} + 6)^{2}

Frequently Asked Questions (FAQ)

What is (5/3+2/8)+1/4 ?
The solution to (5/3+2/8)+1/4 is 2 1/6