What is (5 2/3-2/9)× 3 ?

The solution to (5 2/3-2/9)× 3 is 16 1/3

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Popular Pre Algebra >

(5 2/3-2/9)× 3

Solution

(5 \frac{2}{3} - \frac{2}{9}) \times 3

Solution

16 \frac{1}{3}

Decimal

16.33333 \dots

Solution steps

(5 \frac{2}{3} - \frac{2}{9}) \cdot 3

Convert mixed numbers to improper fractions:

5 \frac{2}{3} = \frac{17}{3}

5 \frac{2}{3}

Convert mixed numbers to improper fraction:

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

5 \frac{2}{3} = \frac{5 \cdot 3 + 2}{3}

= \frac{17}{3}

= (\frac{17}{3} - \frac{2}{9}) \cdot 3

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{17}{3} - \frac{2}{9}) : \frac{49}{9}

\frac{17}{3} - \frac{2}{9}

\frac{17}{3} - \frac{2}{9} = \frac{49}{9}

\frac{17}{3} - \frac{2}{9}

Least Common Multiplier of

3, 9 : 9

3, 9

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

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

3

9

= 3 \cdot 3

Multiply the numbers:

3 \cdot 3 = 9

= 9

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

9

For

\frac{17}{3} :

multiply the denominator and numerator by

3

\frac{17}{3} = \frac{17 \cdot 3}{3 \cdot 3} = \frac{51}{9}

= \frac{51}{9} - \frac{2}{9}

Since the denominators are equal, combine the fractions:

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

= \frac{51 - 2}{9}

Subtract the numbers:

51 - 2 = 49

= \frac{49}{9}

= \frac{49}{9}

= \frac{49}{9} \cdot 3

Multiply and divide (left to right)

\frac{49}{9} \cdot 3 : \frac{49}{3}

\frac{49}{9} \cdot 3

Convert element to fraction:

3 = \frac{3}{1}

= \frac{49}{9} \cdot \frac{3}{1}

Apply the fraction rule:

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

= \frac{49 \cdot 3}{9 \cdot 1}

\frac{49 \cdot 3}{9 \cdot 1} = \frac{49}{3}

\frac{49 \cdot 3}{9 \cdot 1}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{49 \cdot 3}{9}

Factor the number:

9 = 3 \cdot 3

= \frac{49 \cdot 3}{3 \cdot 3}

Cancel the common factor:

3

= \frac{49}{3}

= \frac{49}{3}

= \frac{49}{3}

Convert improper fractions to mixed numbers:

\frac{49}{3} = 16 \frac{1}{3}

\frac{49}{3} = 16

Remainder

1

\frac{49}{3}

Write the problem in long division format

3 \overline{∣ 49}

Divide

4

3

to get

1

Divide

4

3

to get

1

1 3 \overline{∣ 49}

Multiply the quotient digit

(1)

by the divisor

3

1 3 \overline{∣ 49} \underline{3}

Subtract

3

from

4

1 3 \overline{∣ 49} \underline{3} 1

Bring down the next number of the dividend

1 3 \overline{∣ 49} \underline{3} 19

1 3 \overline{∣ 49} \underline{3} 19

Divide

19

3

to get

6

Divide

19

3

to get

6

16 3 \overline{∣ 49} \underline{3} 19

Multiply the quotient digit

(6)

by the divisor

3

16 3 \overline{∣ 49} \underline{3} 19 \underline{18}

Subtract

18

from

19

16 3 \overline{∣ 49} \underline{3} 19 \underline{18} 1

16 3 \overline{∣ 49} \underline{3} 19 \underline{18} 1

The solution for Long Division of

\frac{49}{3}

16

with remainder of

1

16 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{49}{3} = 16 \frac{1}{3}

= 16 \frac{1}{3}

= 16 \frac{1}{3}

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What is (5 2/3-2/9)× 3 ?
The solution to (5 2/3-2/9)× 3 is 16 1/3

(5 2/3-2/9)× 3

Solution

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Frequently Asked Questions (FAQ)

What is (5 2/3-2/9)× 3 ?

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