What is 4 5/3-2+2 4/5 ?

The solution to 4 5/3-2+2 4/5 is 6 7/15

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4 5/3-2+2 4/5

Solution

4 \frac{5}{3} - 2 + 2 \frac{4}{5}

Solution

6 \frac{7}{15}

Solution steps

4 \frac{5}{3} - 2 + 2 \frac{4}{5}

Convert mixed numbers to improper fractions:

4 \frac{5}{3} = \frac{17}{3}

4 \frac{5}{3}

Convert mixed numbers to improper fraction:

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

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

= \frac{17}{3}

= \frac{17}{3} - 2 + 2 \frac{4}{5}

Convert mixed numbers to improper fractions:

2 \frac{4}{5} = \frac{14}{5}

2 \frac{4}{5}

Convert mixed numbers to improper fraction:

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

2 \frac{4}{5} = \frac{2 \cdot 5 + 4}{5}

= \frac{14}{5}

= \frac{17}{3} - 2 + \frac{14}{5}

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{17}{3} - 2 + \frac{14}{5} : \frac{97}{15}

\frac{17}{3} - 2 + \frac{14}{5}

\frac{17}{3} - 2 = \frac{11}{3}

\frac{17}{3} - 2

Convert element to fraction:

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

= - \frac{2 \cdot 3}{3} + \frac{17}{3}

Since the denominators are equal, combine the fractions:

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

= \frac{- 2 \cdot 3 + 17}{3}

- 2 \cdot 3 + 17 = 11

- 2 \cdot 3 + 17

Multiply the numbers:

2 \cdot 3 = 6

= - 6 + 17

Add/Subtract the numbers:

- 6 + 17 = 11

= 11

= \frac{11}{3}

= \frac{11}{3} + \frac{14}{5}

\frac{11}{3} + \frac{14}{5} = \frac{97}{15}

\frac{11}{3} + \frac{14}{5}

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

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

15

For

\frac{11}{3} :

multiply the denominator and numerator by

5

\frac{11}{3} = \frac{11 \cdot 5}{3 \cdot 5} = \frac{55}{15}

For

\frac{14}{5} :

multiply the denominator and numerator by

3

\frac{14}{5} = \frac{14 \cdot 3}{5 \cdot 3} = \frac{42}{15}

= \frac{55}{15} + \frac{42}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{55 + 42}{15}

Add the numbers:

55 + 42 = 97

= \frac{97}{15}

= \frac{97}{15}

= \frac{97}{15}

Convert improper fractions to mixed numbers:

\frac{97}{15} = 6 \frac{7}{15}

\frac{97}{15} = 6

Remainder

7

\frac{97}{15}

Write the problem in long division format

15 \overline{∣ 97}

Divide

97

15

to get

6

Divide

97

15

to get

6

6 15 \overline{∣ 97}

Multiply the quotient digit

(6)

by the divisor

15

6 15 \overline{∣ 97} \underline{90}

Subtract

90

from

97

6 15 \overline{∣ 97} \underline{90} 7

6 15 \overline{∣ 97} \underline{90} 7

The solution for Long Division of

\frac{97}{15}

6

with remainder of

7

6 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{97}{15} = 6 \frac{7}{15}

= 6 \frac{7}{15}

= 6 \frac{7}{15}

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\frac{1}{2} \cdot (- 2) + 2

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6(5)(3^2)(2)-10

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((-1)^5(3)+5)/(-2)

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

(34-12)\div 2+7

(34 - 12) \div 2 + 7

Frequently Asked Questions (FAQ)

What is 4 5/3-2+2 4/5 ?
The solution to 4 5/3-2+2 4/5 is 6 7/15